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Geometry Q&A Archive of September 24, 2021

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September 24 of 2021

Consider the parallelogram below: Explain how we know that a + b = 180. Explain how we know that b = d. Explain how we know that a + b + c + d = 360. An object is described as weighing 7.5 grams.

A forest has perimeter of 400 km. If the boundaries of the forest are rectangular, what is the largest area the forest can have? Ifthe boundary could have any shape, what is the largest area that the forest could have?

Line is parallel to line p. Use this fact to answer the following questions. âˆ 5 = âˆ 3 . . n How do we know that a = b? A A+unat interior angles are equal to 180 degrees. Because parallel lines or intersected by a transversal, alternate interior angles are equal. Answer: Set up an equation…

Smallville is 5 miles north of Gotham: You are miles from Smallville and 6 miles from Gotham. Using your ruler and compass, draw map, with scale: Use your map to identify and position, positions, you might occupy_

Let Pl1 and Plz be the planes Pli I +y +2 = 4 Plz 31 + 2 = 0 (a) Are Pl, and Plz parallel, perpendicular o neither? (b) Find parametric equations for the line of intersection of Pl1 and Plz.

Pointwise Characterization of Perpendicular Bisector Proof The perpendicular bisector of a segment AB is a line such that intersects AB at its midpoint and / is perpendicular to AB. Prove the following theorem: Pointwise Characterization of Perpendicular Bisector: A point lies on the…

Drawing of the floor plan for 20 cm. At right is scale 3:46. The actual dimensions of Nzinga's dollhouse times the measurements dollhouse are 12 cm provided - in the floor plan at right. Use the measurements provided in the diagram to find the area and perimeter of her floor plan. Draw a…

Definite angle and use the related terms: vertex, sides exterior and interior. Use appropriate symbols to designate angles and whole parts (line, ray, and degree in your answers). The vertex angle the interior angle 45 the exterior angle in degrees 315 340 45 Objective…

An angle that's a supplementary angle. a) angle b) angle c) angle d) angle What is the complement and supplement of a 60 degree angle? â‚¬: Objective 12: Classify an angle as acute, right, obtuse, straight, or reflex. What type of angle has the given measure 26Â°? Obtuse Acute Right Straight…

Degree angle Given two planes that touch and create with each other; the two planes intersecting the same plane perpendicular intersecting non-parallel create a 90-degree angle. Given two planes that touch and do not intersect with each other; the two planes intersecting the same plane…

The closed curve below is an ellipse with foci A and B. The point C is the reflection of the point A over the major axis. The points D and E are on the ellipse and the tangent line at point D intersects the tangent line at point E. The equation of the ellipse suggests that âˆ SAE = âˆ ZTBE.…

Homeowners often face significant fluctuations in their property taxes, which are based on the valuation determined by the municipality. The measurement of living space can greatly impact your property taxes. Suppose the floor plan for a home is shown in the figure below. How many square feet…

My lawn has the shape shown in the figure below, where the dimensions are in feet.

The size of a computer monitor (also called display) is usually measured in terms of the diagonal of the rectangle. The monitor measures 10.3 inches by 18.3 inches. What is the length of the diagonal? (Round to the nearest whole number.) 188.49

The soup can has a diameter of 4.1 inches and a height of 9.032 inches. How many square inches of metal are required to make the soup can? (Round your answer to one decimal place)

An isosceles triangle has two equal sides. Consider the line segment starting from the vertex that touches both of the equal sides and meets the opposite side at a right angle. It is a fact that this segment cuts the opposite side (the base) in half. Use this fact to find the area and perimeter…

Using circle A pictured to the right, give an example of the following: Minor Arc: Major Arc: Inscribed Angle: Central Angle: Solve for the value of x in each of the following:

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Suppose you are in a lighthouse on top of a 100m vertical cliff, you spot a large rock is at an angle of depression of 62 degrees. Then a ship comes into view heading towards the rock at an angle of depression of 12 degrees. You use your radio to call the captain of the ship that they are…

Suppose that a 10-meter ladder is leaning against a building such that the angle of elevation from the ground to the building is 62 degrees. Find the distance of the foot of the ladder from the wall. Also, find the distance from the ground to the top of the ladder.

Chapter 6: Polygons Polygon: Concave: Classify Polygons: - 4 sides - 5 sides - 6 sides - 7 sides - 8 sides - 9 sides - 10 sides - 41 sides - 12 sides Regular Polygon: FORMULAS: - Sum of the interior angles - Interior angle - Exterior angle - Sum of Exterior angles - Each exterior angle -…

6 2) 4k 1) 6 2 Solve H 9 2.3 each proportion Round 8 answers the to nearest hundredth

Define the barycentric coordinates of a point X in a plane with respect to a triangle AABC b) A triangle has vertices A = (1,3),B = (6,0) and € = (8,4). Find the coordinates of the barycenter G the orthocenter H.

a) Write the transformation matrices for the following transformations: Translation, Rotation about origin. b) Describe the steps to obtain the rotation of an object about a point P(h,k). c) A line segment AB has endpoints (1,1) and (1,4). Find the endpoints of the rotated segment through 90Â°…

Given a circle with center 0 and a point A inside the circle. construct the inverse point of A. b) Show that your construction point A' is indeed the inverse of A_ In the Poincare disc model of hyperbolic geometry, construct the h-line from two omega points P and Q-

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To estimate the area of a circle, Irene divided the circle into 30 congruent sectors. Then she combined pairs of sectors into shapes as shown below. As the shapes resemble rectangles, she treats the shapes as rectangles with the height (radius) and the base equal to the length of the curved…

Find an angle between 0 and 2π that is coterminal with - 5 /6 π. Express your answer in radians in terms of π.

An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4 ft long with a diameter of 2.4 ft. Suppose oil is drained at a rate of 1.7 ft^3 per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for…

Prove that the connected sum of torus and RP2 is topologically the same as the connected sum of Klein bottle and RP2 (in the same way that we proved that the connected sum of RP2 with RP? is the same topologically as the Klein bottle).

10. For each of the following graphs, give the vertex set, the edge set, and the degree of each vertex. 11. Explain why the two graphs below represent the same graph. Then, draw a third figure that represents the same graph.

Below is the flight schedule for Delta airlines flights (edges) between six cities (vertices): New Orleans Los Angeles_ New York City, Chicago, Atlanta, and Las Vegas. Draw a graph representing this data_ Monday: New Orleans to LA, NYC to Las Vegas Tuesday: Chicago to Atlanta, NYC to LA…

1% Regular Septagon 20 What is the angle marked "a" in this figure? 145Â° 300Â° 500Â°

Math 210B Homework: Chapter 12 online Score: 0.33 of pt 12.1.9 Use a ruler, protractor; and compass to construct; when possible triang properties. Complete parts (a) through (c) (a) A triangle with sides of length 6cm, 3 cm, and 13 cm How many noncongruent triangles of this form can be…

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Stloment EG = Hf Rotations Given Given Not In The Real Complex Property: SS Steps 1, % Length = (Mfg {G = fG AeGf AHig

Text: https://www.mathxcon.com/StudentPlayer/Homework.aspx?homeworkid=32o Math 210B Homework: Chapter 10 Score: 0 of 1 pt 10.3-8 26 9A 4627 9 B. 1480 pc_ 1872 D; 4725 Click to select your answer and then click Check Answer All parts showing Type here to search

Compute the volume of a shape bounded by a parametric equation

mass of the upper half of the ball (Ifyou take the hemisphere to have its origin at (0,0,0) and its base in the XY-plane the z-coordinate ofthe center of mass is the "average value ofz" over the hemisphere, or the total moment divided by the volume:) Parametrize the upper hemisphere using…

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Length 1 Width 1 Rectangle is the length of the 1-dimensional rectangle.

Find the area of the sector shown at the right: The radius of the circle is units and the minor arc is 3.93 units. Express your answer to the nearest tenth of a square unit. Lines AE and BD are tangent to circles Q and O at A, E, B, and D as shown in the diagram below. If AC:CE = 5:3, and BD =…

Let circle with center O, and B be points with not AB. Let X be a point on the same side of OB as A and on the opposite side of O from B. Prove the following equality about degree measure âˆ D (AXB) = âˆ D (AOB).

Exercise 3. Evolutes and involutes (10 + 5 + 5 + 5 + 5 points) (a) The locus of the centres of curvature of a parametrized curve a(s) = (x(s), Y(s)) is called its evolute. Express the evolute of a as a parametrized curve Y(s) = (e(s), n(s)) solely in terms of x, Y, and their derivatives. (b)…

Find the farmer's distance between the newly divided north border L and the south interstate. The two plots of land are 15 meters apart.

The sides of a right-angled triangle have lengths of 12, 16, and 21. Find the bisector that intersects the hypotenuse; also find the segment that the bisector divides the hypotenuse into. The drawing shown in the accompanying diagram represents a right-angled roof truss, represented by…

In hyperbolic geometry, what is the possible range for the degree measure of the base angles of an isosceles triangle with a right angle? Sketch three different such triangles in the Poincare disk model, suggesting that the angle measure of the base angle indeed can attain any value in that…

10. The small square is inscribed inside the circle and the larger circle circumscribes the same circle. If A1 is the area of the large square and A2 is the area of the small square, what is the ration A1 / A2?

Refer to the Write Up directions found on the website and the date found on our calendar. You may use other paper and/or type your answer. Name: Section 11.2 Given the series, apply the Ratio Test to determine the Radius and interval of Convergence. Be sure to apply appropriate tests to…

17. A small heater has a rectangular filter that is 16 in. by 20 in. Another larger heater requires a similar filter that has a width of 48 in. What is the length of this larger filter?

Refer to the following figure for Exercises 15-18. Segment AC is a diameter; BC = 115°, ∠DOC = 25°, and OA = 8 cm. 15. Find the lengths (in cm) of AC and DC. Round to the nearest hundredth. 16. Find the lengths (in cm) of BC and AD. Round to the nearest hundredth. Answers: [Also, label the…

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Following the rules for working with measures, find the required values: 120 in 12.2 in 10.3 in 9.1 in The lateral surface area of the prism in the illustration above is in^2. If h = 11.2 in, what is the total surface area of the prism in in^2? Also, what is the volume of the prism in in^3?

Problem 1.4: In ABC, let F, E, and D be the feet of the perpendiculars drawn from the vertices A, B, and C. Let the corresponding altitudes and the sides extended to meet each other at the points M, N, and L. Prove that M, N, and L are collinear. INSTRUCTOR: M. BRAKALOVA YOUR NAME

Which of the plans for IProot Koulocorkio Dooe AABC = ADEF using the previous question? Based on the methods chosen. Use the distance formula to find AB and DE. Then, use similar triangles to find angle ZAWD and angle ZB = angle ZE. Use the distance formula to find BC and EF. Then, use the…

Lonsicer AABC with vertices at A(-3,3), B(-3, T), and C(3,3); and ADEF with vertices at D(2, 2), and E(2,2). Which method(s) work for proving the triangles are congruent? SSS or SAS only ASA only ASA only SSS, SAS, ASA SSS only ASA or SAS only SAS only

(a) What is the order of S4? (b) Obtain & nontrivial 4 X 4 matrix representation for this group: (c) Identify the classes of this group and show that the character of each of the matrices in part (b) is the same for each class_ (d) Identify the subgroup of S4 that corresponds to only the…

PARALLEL LINES CUT BY A TRANSVERSAL {Coloring Activity} 1 Find the value of x. 2 Find the value of x. 3 Find the value of x. 4 Find the value of y. 5 Find the value of y. 6 Find the value of y. 7 Find the value of y. 8 Find the value of y. 9 Find the value of y. 10 Find the value of x. 11 Find…

Free figures below. Now, how many have more than one line of reflection symmetry? 12 of them 8 of them of them

Additional problem 2* (Steiner chain) Let % and %' be two circles tangent to each other at some point A. Show that you can fill the region between % and %' with circles %n; for n â‚¬ Z, tangent to both % and %' and such that %n is tangent to %n+1 and %n-1. Hint: Invert in A. Suppose that % is a…

Additional problem 1* Let A; B; and 0 be three distinct points in R?, and let & be a circle with centre 0. Show that there exists unique generalised circle (i.e , & circle or line) through and B and orthogonal to % . Hint: Invert in A_ Show that such generalised circle intersects as well

6: Geulletr $ ABC with a hypotenuse. Calculate the sin A, cos A, and tan A for the right side equals 14, the shorter side equals 7, and the longer side equals 16, the hypotenuse. Angle A is the angle created by the shorter side and the hypotenuse, and Angle â‚¬ is the right angle. Draw the…

Arc length A circle has a radius of 5. An arc in this circle has a central angle of 162°. What is the length of the arc? Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.

Text: The text must be constructed on one figure; Hence the question. Using straightedge and compass only, construct the âˆš3 + 2 length segment (the length is given below). Write out all steps of how to construct the length. Here, that is the square root of square root of…

4. (6 pts) In the drawing below, DE is parallel to BC, and BD = 2AD. a) Is triangle ADE similar to triangle ABC? Explain. b) If the two triangles are similar, what is the scale factor? c) What is the ratio between the areas of triangle ADE and triangle ABC?

A certain circle can be represented by the following equation: x^2 + y^2 - 2y - 99 = 0 What is the center of this circle? What is the radius of this circle? units

The pie chart below shows how the annual budget for Equipment Producers Incorporated is divided by department. Use this chart to answer the questions below: (a) Which department accounts for approximately one-eighth of the annual budget? Select One (b) Approximately what percentage of the…

A certain circle can be represented by the following equation: 22 +y? + 182 + 14y + 105 = 0 What is the center of this circle What is the radius of this circle units Do 4 problems Check

10 The small square is inscribed inside the circle and the larger circle circumscribes the same circle: If Al is the area of the large square and A2 is the area of the small square, what is the ration Al A22

1.) Use Brahmagupta'$ Formula to find the area of a square with sides of length 6 inches 2.) Use Brahmagupta' $ Formula to find the area of a rectangle with a length of 8 cm and a width of 6 cm: 3.) Find the length of the diameter of the circle in which quadrilateral ABCD is inscribed

28. Find the measure of 17 in Illustration_

(1,8) (5,-2) Which of the following is the distance of the line segment? 2+/34 6,7 2 /6 VTo

Exercises The following exercises illustrate the result above about invariant funetions of quadruples: They show that the invariants obtained by permuting the variables in the cross-ratio y = [p gr;s] are simple functions of y, such as 4/yandy -1. 5.8.1 If [p.4rs] =% show that [p,4:s,r] = Iy.…

Tonc ( FW = 0 (6)In the figure below, suppose two chords intersect at point V inside the circle. VM = 26, VK = 39, and VN = 19.5. Find JK. JK = 0 search Type here 3n 8 Hcld

Find each length below. (a) In the figure below, two chords intersect inside the circle at point E. Suppose that EM = 14, EK = 10.5, and EN = 21. Find JK. JK = (b) In the figure below, a tangent and a secant are drawn to a circle from exterior point U. Suppose that UC = 5.5 and UG = 11. Find…

Mon 22 of 30 (I point) Title: Tirie Rem F 19 Write an equation of the circle with center (7, 8) and radius r = 6.

Given quadrilateral ABCD with diagonal AC. If BC = 1 AB and AC = LDC, find DA if AB = 4, BC = 3, and DC = âˆš2.

A quarter circle with radius BC = 4 is given below. Semicircles are constructed with diameters AB and BC. Find the area of the region enclosed by the bold curves. [Hint: Write an area formula like we did in class for area example 2. At some point, you will also need to construct a few simple…

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Triangle ABC is & right triangle with the right angle at vertex B Find k; the y-value of point C_ Graph ABC. An algebraic solution must be given: (5 points) A(3,4), B(S,-3), C(-2,k)

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Find the lateral area of each cone to the nearest whole number.

On 7th April and B respectively. In the following figure, let BGA and PB LBDA be tangents to the circle O at points BCAD is shown that cyclic te 2 a=Y-

Find the area of a rhombus in terms of the lengths of its diagonals d, and d Will the same formula you derived in part (a) work for kites? Why or why not?

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16.5 Surface integrals of vector fields: Problem 2 Previous Problem Problem List Next Problem Compute the surface integral over the given oriented surface: F = (0, 4, 1) where the sphere x^2 + y^2 + z^2 = 220 outward-pointing normal is correct Submit Answer

21. Suppose m 8x 67 3x 14 Find the 1 of x

Look at quadrilaterals A' B' B A, B' C" C B, and their angle sum.

The formula for the area S of a circle of radius a in double elliptic geometry is S = 2Ï€a^2 cos. Show that S approaches the area of the double elliptic plane when a approaches Ï€k.

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Q2 - Find the parametric equation of a circle of radius R, centered at (x = a, y = 6), using the arc length as a parameter. Q3 - Find the unit tangent vector to the curve r(t) = [t, +2, +3] at the points where it cuts the plane 2x = 2 - 1.

10 ft 8 ft Hint: Circumference of a circle: C = ?d Find the perimeter of this figure to the nearest hundredth. Use 3.14 to approximate ?. P = [?] ft Notice that only half of the circle is included in the figure!

My Homework Name Independent Practice Find the total surface area of each pyramid: Round to the nearest tenth: (Examples 1-3) 15 mm 7cm 17 mm 17 mm 5 cm 5 cm 17 mm A ~ 125 mm2 6 m 8.3 m 15.9 cm 5.2 m 8.2 cm 8.2 cm 5, A triangular pyramid has a slant height of 0.75 meter: The equilateral…

Expected Value You earn 1 point for each correct response on a multiple choice test and lose 0.5 point for each incorrect response. Each question has 4 answer choices. If a student just guesses, what is the expected value of the guess?

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Parabola is a curve that represents any portion of the directrix (focus) F(x, 6) and the point (x, y) on the parabola. The following steps work to find the equation of the parabola: Step 1: FP = DP Step 2: Vk = âˆš((x - (-8))^2 + (y - 6)^2) Step 3: 12t + 36 = x^2 + 6x + 64 Step 4: y = 2y +…

Parabola is a locus of F(2,9) and directrix of y = Dx, where D represents any point on the directrix. P(x, y) represents any point on the parabola. While the following steps provide a solution: Step 1: FP = DP Step 2: V(x-2) = (VG-2) - (VG-m) Step 3: 1 + 4 - 4 + 7 (8y + 81) = y (22v +…

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QUESTION 4 For AABC, RS BC . If AR = 5, RB = 2.5,and RS = 4, find BC a,6 bb.3 c 2 d,7.5

Given that ZM = ZQ, MP = 6, PR = 4, and NQ = 15, find P

Find the surface area and the volume of the cement block in the figure shown. What is the surface area of the cement block? 956 in.² What is the volume of the cement block?

Using a compass and straightedge only, construct the last vertex, write out all steps, and prove your result. Below, we are given vertex A and B and the incenter of triangle ABC. Using a compass and a straightedge, construct the last vertex C.

13 Congruence: What other information do you need in order to prove that two triangles are congruent?

Instructions (10 points): Draw any triangle AABC on your own paper: Use what you have learned in this unit to construct the Euler Line by finding the centroid, circumcenter and orthocenter of a triangle: Carefully label the intersection points and record your work as you finish each…

Show that the triangle whose vertices are P(- 4,4), Q(- 11, - 12), and R(3,4) is isosceles. Find the lengths of all three sides. PQ = (Round to three decimal places as needed.) QR = (Round to three decimal places as needed.) PR = (Round to three decimal places as needed.) Is the triangle an…

Mass of the upper half of the ball (If you take the hemisphere to have its origin at (0,0,0) and its base in the XY-plane, the z-coordinate of the center of mass is the "average value of z" over the hemisphere, or the total moment divided by the volume). Parametrize the upper hemisphere using…

Proof: 1. RS = UZ (Given) 2. RT = US (Given) 3. ST = TS (Reflexive Property of Equality) 4. RS = UI (Transitive Property of Equality) 5. RT = US (Given) 6. ST = TS (Reflexive Property of Equality) 7. A RST = AUT (SSS Congruence) 8. A RST e AUTS (Definition of Subset)

Based on the drawing, where can the sink be located along the countertop that is 50 units away from the stove and 15 units away from the small island? The location should minimize the perimeter, which should be below 26 units.

The sides of a right triangle are 6, 8, and 10. Find the altitude drawn to the hypotenuse. (A) 2.4 (B) 4.8 (C) 3.4 (D) 3.5 (E) 4.2

Euclidean geometry, find the value of x in the given diagram: 10 S(a(Ï€ { ^ ~'70440 | 35) 147 <

2.2.6 Show that if two triangles have two pairs of corresponding sides in proportion and the angles included by the proportional sides are congruent; then the triangles are similar: (SAS similarity) Hint: Use the converse of the Thales Theorem for triangles.

Sin A= Sin B= Cos A = 13 12

Creen Chloe bought a swimming pool for her backyard that measured 8 feet across and 3 feet deep. She fills the pool half way to the top. Assuming that one cubic foot of water is 7.5 gallons of water, about how many gallons of water will Chloe put in the pool?

Chloe bought a swimming pool for her backyard that measured 8 feet across and 3 feet deep. She fills the pool half way to the top. Assuming that one cubic foot of water is 7.5 gallons of water, about how many gallons of water will Chloe put in the pool?

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Consider the tabletop template of the regular hexagon shown below: a. Draw all radii from the center of the circumscribed circle to each vertex of the hexagon. b. What is the measure of each of the central angles formed by the radii? Explain how you arrived at your answer. c. Classify the…

K / (5,, (3 Nor Aba *lRahm Nole: Figure not drawn to scale. The figure above shows right triangle ABC. Line contains points A and B and the point (3, 1). If the coordinates of point B are (5, ?) and if the measure of âˆ BAC is 60Â°, what is the value of y?

The floor of the bathroom area measures 2 square feet; the living room, kitchen, and bedroom are in the house. The north and south walls of the living room are parallel.

Find the measures of the interior angles of the following triangle. The interior angles measure 26Â° and...

Find the missing angle or angles. 56 62 0A 72 0 B. 34 OC. 54 0 D. 62 "

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Give the definition of the apothem. If a regular hexagon is inscribed in a circle of radius R, the sides of the regular hexagon have length R. What is the length of the apothem in such a regular hexagon? What is the area of such a regular hexagon? If a regular hexagon is circumscribed about a…

The circle graph shows how a family budgets its annual income. If the total annual income is $150,000, what amount is budgeted for Food? Housing 24% Savings 7% Leisure 13% Insurance 10% Food 17% Auto 13% Clothing 16%

Many people think that if you want to find the area of an irregularly shaped object (like a footprint) you could measure the perimeter by putting string around it, then reshape the piece of string into a regularly shaped object (like a rectangle) and then find the area based on the measure of…

y(n) = u(n) * sum(alpha^k from k=0 to n) = (1-alpha^(n+1))/(1-alpha) * u(n) When n -> infinity, y(n) = 1/(1-alpha) y(n) = x(n) * h(n) = sum(x(k)h(n-k) from k=-infinity to infinity) = sum(alpha^k u(n-k)u(k) from k=-infinity to infinity) = sum(alpha^k from k=0 to n) = (1-alpha^(n+1))/(1-alpha) *…

That AB = AC, AABC has been inscribed. It is known in circle M, DC || AB, and mâˆ DCB. Find: - The measure of âˆ ZBDC - The measure of âˆ DAC 46 514 REASONING In circle E shown, chords AB and CD are parallel: (a) What does this information tell you about âˆ I and âˆ 2? Why? Given your answer…

Assignment DJaic Period: Using degrees, find the amplitude and period of each function. Then graph: 1) Period: 180 degrees, Amplitude: 1, y = sin(20) 2) Period: 360 degrees, Amplitude: 2, y = sin(40) 3) Period: 360 degrees, Amplitude: 1, y = cos(40) 4) Period: 360 degrees, Amplitude: 2, y =…

2-icch bele i: drilled through Eleck (cube) of wocd thet picaalg 'ES Le3 @L 'sueli dde. How much wood is leftin the block after the bole i: deu can of tuna with height of - and diameter of 12 cm cost 950. Another can has : height of cm and diameter of 14 cm If the second cost $1.69,which is the…

7 in 4/10/2019 MAFS.912.6-C0.1.3 Trapezoid RSTU is shown. Write the trapezoid onto itself for the line that would map the MAFS.912.G-Co.1.3 Figure rhombus and Figure 2 is rectangle Neither unique square. Which transformation can be used to map Figure onto itself? Rotation of 90 degrees…

Taxicab Triangles Draw three right triangles on the graph. Measure their sides using taxicab distances. Hypotenuse (long side) Leg (short side) Leg (short side) Triangle Triangle Triangle Then mark dots on the graph. The Pythagorean Theorem does not apply to taxicab geometry. Why not come…

UIC SaTfle Distance Toi Given that there are the same two points X and Y, describe a rule for finding all the points' distance from X. 5. Find all points that are the same distance from G as from H.

Hexagon is graphed on the coordinate plane. Part A: Find the area of the hexagon. Part B: Find the perimeter of the hexagon. 5433402 Given triangle ABC with vertices (-8, 2), (-2, 2), and (-2, 8), determine which sequence of rigid transformations would map…

Triangles DEF and GHI are shown in the coordinate plane. Part A: Triangle DEF is the image of ABC after transformation or a sequence of transformations. Which could be the transformation or sequence of transformations? Select all that apply. - Translation 1 unit right and 3 units down,…

Consider the points in the following diagram. Ac5i7) 5451+/5-7/42 141/+ 6-1-3 ~I+h-41= 7 751+H- Il24 J54Iet S 5 - 3 ` I 2 ] 4 5 6E7 0 4 7 (zzV) Find all points that are the same distance from B. Find all points that are the same distance from C as from D. Find all points that are the same…

Find the volume of the region between the cylinder z = 5y^2 and the xy-plane that is bounded by the planes x = 0, x = 3, y = 0, and y = 3. The volume is (Type simplified fraction).

14. Which is NOT a true statement about a rhombus? RO = 28 cm, then RB = 14 cm. mZRHB = mZHRB RH = OH mZRMO = mZRHO 15. Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each other: Parallelogram, Rectangle, Rhombus,…

25. To the nearest meter; find the volume of the prism below: . 1235 m? 1140 m? 1080 m 190 m? 13m 19m " 1 10m 26_ A barn silo consists of & cylinder with _ hemisphere 'Yz sphere) on top_ What is the volume of the silo? 1390 m} 1524 m- 1657 m 2059 m" 25 m 8 m-

19. Find the closest value for x 12.6 16.1 20.4 25.6 20. The sketch of a stained glass window is shown in the shape of a semi-circle. Ignoring the seams, how much glass would be needed for the window? 61 f12 181 ft? 361 ft? 721 ft?

7 _ Find the number of diagonals in a hexagon b. d. 12 91 ' 8 The measure of a vertex angle in an isosceles triangle is 468_ What is the measure of one base angle in the triangle? : . - "3 " , "uc , <<: ` 230 460 3 670 920 "'

Welcome to the world of geometry! In this text, we will explore the concept of supplementary angles and polygons. Let's dive in! Given the following information: - Wlcn proves allb and Il m 23sini - Zazlo, 27e212 ZSe21O, L14 and Z1S are supplementary - Z6 = L9, L2 and Z14 are…

In the figure below, line a is parallel to line b. Find the measure of angle S if: the measure of angle 6 is 3x + 22 and the measure of angle 8 is x + 58. b. 76Â° d 104Â° 18 978

Find sides x and y in the triangle below. a. x=15, y=7.5 b. x=20, y=10 c. x=15√2, y=15 d. x=(30√3)⁄3, y=(15√3)⁄3 Find the measure of the missing angle "?". a. 24° b. 20° c. 35° d. 31° In the figure below a || b. Find m∠5 if:

Question 5: Use Voronoi construction on a representative part of the structure to estimate the average number of nearest neighbors about a disc.

Let AABC be a triangle, let Î± be the bisector of the angle ZCAB. Let P be the intersection of Î± and BC. Let R be the point on the line AB such that AR = AC, and let X = AP âˆ© RC. Let Q denote the intersection point between the line through B and X and AC. a) Show that the triangle AARC is…

A box is formed by cutting squares from the four corners of a 5"-wide by 7"-long sheet of paper and folding up the sides. Let x represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches). a. Write a formula that expresses V in…

Ifthe triangle is equiangular in the hyperbolic plane _ will that force it to be equilateral? If not, give constructed example: If ves, justify why

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9) 364 + 28y + y + x^2 = -26x 10) x^2 + y^2 + 24x + 10y + 160 = 0 11) ~6x = ~x? + 32y - 264 - y^2 12) -6x + x^2 = 97 + 10y - y^2

The quadrilateral LMNO in the following figure is a parallelogram. M (a,b) N C' h M 0 (c, 0) L (0,0) Find the coordinates of vertex N based on the coordinates of the other vertices already listed in the figure. Using the given information and the results of part b, show that the diagonals of a…

Solve the triangle using the conventional system for labeling a right triangle, C is the right angle. a = 21.0 and c = 30.0 Remember to round your answers to the appropriate number of significant digits_ A = B = b =

Whether it is possible to tessellate? Determine the combination of regular S-gons that will tessellate the plane using only squares and regular T-gons. We know that a combination of squares and regular polygons will tessellate the plane. Explain why these 64-gons work, but regular octagons…

Prove that e is irrational: Steps to prove that if an n-gon is constructible, then a Zn-gon is constructible. And if GCD(a,b) = 1 and an a-gon is constructible, then a b-gon is constructible. Hint: Use the half-angle identity to prove that is constructible. Use the equation ax + by implies x…

Consider the cone $z^2 = x^2 + y^2$ between $z = 0$ and $z = 1$. (a) Find the surface area of this cone. (b) Find the volume of the region above this cone and inside the sphere of radius $\sqrt{2}$ centered at the origin that encloses the cone.

Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r?

In the simple highway network shown in the following figure, the cost function (C) depends on the link traffic flow (f). (a) Write down the mathematical models for UE and SO (denote the flow from 0 to D as fop). (b) If f3 = 6 and f5 = 2, find the value of C4 (Wardrop's first principle…

Gt > G, Over 0 < q < r < $ < t, for geometric Brownian motion (Gt) â‰ 0, show that ratios and Gq are G, independent random variables.

Find the area and perimeter of the Norman window shown below: 10 10 & 8 f

(6) Sketch the ellipse 2 =1. Then fnd an cquation of its tangent line at the point (_4,0). Sketch the ellipee Then find equation of its tangent line the point Sketch the ellipse 634 @=1 = 1 Then find an equation of its tangent line at the point (2,3).

Given: mZT = 30, mZvUS = 1358 Prove mZS = 1058

Show that if M € Rk is an m-manifold and N € Rl is an n-manifold, then the product M x N = {(~,y) : x € M,y e N} € Rk+l is an (n + m)-manifold.

point) Find the minimum distance from the point (1,1,15) to the paraboloid given by the equation 2 = 22 + y?_ Minimum distance 5.94540564902 Note: If you need to find roots of a polynomial of degree > 3, you may want to use a calculator of computer to do so numerically. Also be sure that you…

Bicycle gearing allows the rider to control the speed and effort required to pedal. By adjusting the gear ratio, which is the number of teeth on the front and rear gears, the rider can make each pedal revolution turn the rear wheel a certain number of times. Suppose we have a bicycle with a…

Bicycle gearing allows the rider to control the speed and effort required to pedal. The gears on a bicycle are made up of teeth on the front and rear wheels. When the pedal is turned, it rotates the front wheel, which in turn rotates the rear wheel. The number of teeth on each wheel determines…

The supplement of an angle is 608 less than twice the supplement of the complement of the angle. Find the measure of the complement.

Arnex has a 309, 60", a 1508 , a 458, and a 1358 angle in his pocket. He takes out two of the five angles. Find the probability that The two angles are supplementary The two angles are complementary

The measure of the supplement of an angle is 308 less than five times the measure of the complement: Find two-fifths the mea- sure of the complement:

For 7.20, the crucial observation is that the circumcenter and orthocenter are the same point if and only if the angle bisectors are altitudes. You should justify this observation as part of your proof. The justification shouldn't take more than line two.

Five times the complement of an angle less twice the angle'$ supplement is 40:. Find the measure of the supplement.

Write a two-column proof; Given: [ 1L,2I=2 Prove: Ilt Complete the proof by filling in the blanks (1, 2, and 3). Proof: Statements Reasons 1. Given 1L,2I=2 2. L is congruent to itself Reflexive Property 3. m I! 3. Definition of congruent angles

10. Find mZRST. Give a reason for each step (informal proof). (3x)^9 (4x - 24)^9

Given: mLI = (3x+30), mLZ = (Sx-10), and x = 20 Prove: mLI || mLZ Statements: 1. mLI = 3x + 30 2. mLZ = Sx - 10 3. x = 20 4. mLI = 3(20) + 30 5. mLI = 90 6. mLZ = 5(20) - 10 7. mLZ = 90 8. mLI = mLZ 9. Therefore, mLI || mLZ Reasoning: Given…

The supplement of an angle is four times the complement of the angle. Find the measure of the complement:

Given: XY = 1, YW = AB = 1, BC = (2x)^(50) Find: mLDBC

The larger of two supplementary angles exceeds 7 times the smaller by 4 Find the measure of the larger angle.

Text: Given: ! || m Prove: mâˆ I + mâˆ 2 = 180Â° Proof: Statements Reasons 1. Given Given 2. âˆ I || âˆ 2 Definition of parallel lines 3. âˆ I + âˆ 2 = 180Â° Angle sum of a straight line

13. Given: mZI = (3x+30), mZ2 = (5x-10), and x = 20. Prove: mLI = mZ2. Statements: 1. mZI = 3x + 30 2. mZ2 = 5x - 10 3. x = 20 4. mZI = 3(20) + 30 5. mZI = 90 6. mZ2 = 5(20) - 10 7. mZ2 = 90 8. mZI = mZ2 Reasoning: Given

The measure of angle A is 415Â°. One of two complementary angles added to one-half the other yields 729. Find half the measure of the larger angle.

12_ Find the value of x $0 that m Iln. Give reason for each step (informal proof): (Gx + 522 (Sx - 12)8

11. Given: ? | m Prove: ZI = Z2 Statements Reasons

One of two complementary angles added to one-half the other yields 729_ Find half the measure of the larger.

10. Find mZRST. Give a reason for each step (informal proof). S/31)9 (4x 24)9_

Proof Statements Reasons [ 2 LLm _ 3. m || ! 1. Given 2. [2] 3. [3]

Find the missing length for each triangle a_ b_ 18

SLT24-29 Determine which practice problems make sure method! Mark any can prove the triangles congruent. Use congruence statements and tick marks for special cases. If congruent, write congruence statement. Are the triangles congruent? If yes, by which method? If yes, congruence statement: UILa…

Find the measure of the acute or right angle formed by intersecting lines s0 that C can bel mapped to C" using two reflections. The rotation (T,y) (-I, y) maps C to C"' The measure of the angle is

Let us recall the midline theorem of a triangle: the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to half of it. A quadrilateral which has two opposite sides parallel and the other two opposite sides not parallel is called a…

Prove that the midpoints of the sides of any quadrilateral are vertices of a parallelogram. Hint: the midline theorem.

The scale of two similar quadrilaterals. The perimeter of the small quadrilateral is 50 centimeters. What is the perimeter of the larger quadrilateral? If the dimensions of a rectangle with a perimeter of 24 inches are tripled, what will be the perimeter in inches of the new rectangle? If the…

Make sure to do the entire problem. Problem 7.6 is an "if and only if" statement. Hints and reminders: you have to write proofs in both directions. But Problem 7.4 also requires two directions. For example, so you will need to write proofs in both directions.

For example, you have to write proofs in both directions. But Problem 7 also requires two directions. Once you've figured out your answer, you need to explain why that kind of triangle has its orthocenter at vertex B. Then you need to explain what other kind of triangle does. Put differently,…

Perform the following series of rigid transformations on ∆ABC. Translate ∆ABC by moving it 5 units to the right and 2 units up. Draw the line y = -x and reflect ∆A'B'C' across the line. Rotate ∆A"B"C" counterclockwise about the origin by 270°.

7 V 8 1| with radius units and center at the origin:

Near this sketch asserts that non-Euclidean geometry, the ratio of the circumference of a circle to its diameter, remains constant, unlike in Euclidean geometry. The following questions illustrate this fact: In Riemannian geometry, assume the Earth is a sphere with a radius of 1. Call some…

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Consider the parallelogram below: Explain how we know that a + b = 180. Explain how we know that b = d. Explain how we know that a + b + c + d = 360. An object is described as weighing 7.5 grams.

A forest has perimeter of 400 km. If the boundaries of the forest are rectangular, what is the largest area the forest can have? Ifthe boundary could have any shape, what is the largest area that the forest could have?

Line is parallel to line p. Use this fact to answer the following questions. âˆ 5 = âˆ 3 . . n How do we know that a = b? A A+unat interior angles are equal to 180 degrees. Because parallel lines or intersected by a transversal, alternate interior angles are equal. Answer: Set up an equation…

Smallville is 5 miles north of Gotham: You are miles from Smallville and 6 miles from Gotham. Using your ruler and compass, draw map, with scale: Use your map to identify and position, positions, you might occupy_

Let Pl1 and Plz be the planes Pli I +y +2 = 4 Plz 31 + 2 = 0 (a) Are Pl, and Plz parallel, perpendicular o neither? (b) Find parametric equations for the line of intersection of Pl1 and Plz.

Pointwise Characterization of Perpendicular Bisector Proof The perpendicular bisector of a segment AB is a line such that intersects AB at its midpoint and / is perpendicular to AB. Prove the following theorem: Pointwise Characterization of Perpendicular Bisector: A point lies on the…

Definite angle and use the related terms: vertex, sides exterior and interior. Use appropriate symbols to designate angles and whole parts (line, ray, and degree in your answers). The vertex angle the interior angle 45 the exterior angle in degrees 315 340 45 Objective…

An angle that's a supplementary angle. a) angle b) angle c) angle d) angle What is the complement and supplement of a 60 degree angle? â‚¬: Objective 12: Classify an angle as acute, right, obtuse, straight, or reflex. What type of angle has the given measure 26Â°? Obtuse Acute Right Straight…

Degree angle Given two planes that touch and create with each other; the two planes intersecting the same plane perpendicular intersecting non-parallel create a 90-degree angle. Given two planes that touch and do not intersect with each other; the two planes intersecting the same plane…

The closed curve below is an ellipse with foci A and B. The point C is the reflection of the point A over the major axis. The points D and E are on the ellipse and the tangent line at point D intersects the tangent line at point E. The equation of the ellipse suggests that âˆ SAE = âˆ ZTBE.…

Homeowners often face significant fluctuations in their property taxes, which are based on the valuation determined by the municipality. The measurement of living space can greatly impact your property taxes. Suppose the floor plan for a home is shown in the figure below. How many square feet…

My lawn has the shape shown in the figure below, where the dimensions are in feet.

The size of a computer monitor (also called display) is usually measured in terms of the diagonal of the rectangle. The monitor measures 10.3 inches by 18.3 inches. What is the length of the diagonal? (Round to the nearest whole number.) 188.49

The soup can has a diameter of 4.1 inches and a height of 9.032 inches. How many square inches of metal are required to make the soup can? (Round your answer to one decimal place)

An isosceles triangle has two equal sides. Consider the line segment starting from the vertex that touches both of the equal sides and meets the opposite side at a right angle. It is a fact that this segment cuts the opposite side (the base) in half. Use this fact to find the area and perimeter…

Using circle A pictured to the right, give an example of the following: Minor Arc: Major Arc: Inscribed Angle: Central Angle: Solve for the value of x in each of the following:

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Suppose you are in a lighthouse on top of a 100m vertical cliff, you spot a large rock is at an angle of depression of 62 degrees. Then a ship comes into view heading towards the rock at an angle of depression of 12 degrees. You use your radio to call the captain of the ship that they are…

Suppose that a 10-meter ladder is leaning against a building such that the angle of elevation from the ground to the building is 62 degrees. Find the distance of the foot of the ladder from the wall. Also, find the distance from the ground to the top of the ladder.

Chapter 6: Polygons Polygon: Concave: Classify Polygons: - 4 sides - 5 sides - 6 sides - 7 sides - 8 sides - 9 sides - 10 sides - 41 sides - 12 sides Regular Polygon: FORMULAS: - Sum of the interior angles - Interior angle - Exterior angle - Sum of Exterior angles - Each exterior angle -…

6 2) 4k 1) 6 2 Solve H 9 2.3 each proportion Round 8 answers the to nearest hundredth

a) Write the transformation matrices for the following transformations: Translation, Rotation about origin. b) Describe the steps to obtain the rotation of an object about a point P(h,k). c) A line segment AB has endpoints (1,1) and (1,4). Find the endpoints of the rotated segment through 90Â°…

Given a circle with center 0 and a point A inside the circle. construct the inverse point of A. b) Show that your construction point A' is indeed the inverse of A_ In the Poincare disc model of hyperbolic geometry, construct the h-line from two omega points P and Q-

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To estimate the area of a circle, Irene divided the circle into 30 congruent sectors. Then she combined pairs of sectors into shapes as shown below. As the shapes resemble rectangles, she treats the shapes as rectangles with the height (radius) and the base equal to the length of the curved…

Find an angle between 0 and 2π that is coterminal with - 5 /6 π. Express your answer in radians in terms of π.

An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4 ft long with a diameter of 2.4 ft. Suppose oil is drained at a rate of 1.7 ft^3 per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for…

Prove that the connected sum of torus and RP2 is topologically the same as the connected sum of Klein bottle and RP2 (in the same way that we proved that the connected sum of RP2 with RP? is the same topologically as the Klein bottle).

10. For each of the following graphs, give the vertex set, the edge set, and the degree of each vertex. 11. Explain why the two graphs below represent the same graph. Then, draw a third figure that represents the same graph.

Below is the flight schedule for Delta airlines flights (edges) between six cities (vertices): New Orleans Los Angeles_ New York City, Chicago, Atlanta, and Las Vegas. Draw a graph representing this data_ Monday: New Orleans to LA, NYC to Las Vegas Tuesday: Chicago to Atlanta, NYC to LA…

1% Regular Septagon 20 What is the angle marked "a" in this figure? 145Â° 300Â° 500Â°

Math 210B Homework: Chapter 12 online Score: 0.33 of pt 12.1.9 Use a ruler, protractor; and compass to construct; when possible triang properties. Complete parts (a) through (c) (a) A triangle with sides of length 6cm, 3 cm, and 13 cm How many noncongruent triangles of this form can be…

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Stloment EG = Hf Rotations Given Given Not In The Real Complex Property: SS Steps 1, % Length = (Mfg {G = fG AeGf AHig

Text: https://www.mathxcon.com/StudentPlayer/Homework.aspx?homeworkid=32o Math 210B Homework: Chapter 10 Score: 0 of 1 pt 10.3-8 26 9A 4627 9 B. 1480 pc_ 1872 D; 4725 Click to select your answer and then click Check Answer All parts showing Type here to search

Compute the volume of a shape bounded by a parametric equation

mass of the upper half of the ball (Ifyou take the hemisphere to have its origin at (0,0,0) and its base in the XY-plane the z-coordinate ofthe center of mass is the "average value ofz" over the hemisphere, or the total moment divided by the volume:) Parametrize the upper hemisphere using…

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Length 1 Width 1 Rectangle is the length of the 1-dimensional rectangle.

Let circle with center O, and B be points with not AB. Let X be a point on the same side of OB as A and on the opposite side of O from B. Prove the following equality about degree measure âˆ D (AXB) = âˆ D (AOB).

Exercise 3. Evolutes and involutes (10 + 5 + 5 + 5 + 5 points) (a) The locus of the centres of curvature of a parametrized curve a(s) = (x(s), Y(s)) is called its evolute. Express the evolute of a as a parametrized curve Y(s) = (e(s), n(s)) solely in terms of x, Y, and their derivatives. (b)…

Find the farmer's distance between the newly divided north border L and the south interstate. The two plots of land are 15 meters apart.

The sides of a right-angled triangle have lengths of 12, 16, and 21. Find the bisector that intersects the hypotenuse; also find the segment that the bisector divides the hypotenuse into. The drawing shown in the accompanying diagram represents a right-angled roof truss, represented by…

In hyperbolic geometry, what is the possible range for the degree measure of the base angles of an isosceles triangle with a right angle? Sketch three different such triangles in the Poincare disk model, suggesting that the angle measure of the base angle indeed can attain any value in that…

10. The small square is inscribed inside the circle and the larger circle circumscribes the same circle. If A1 is the area of the large square and A2 is the area of the small square, what is the ration A1 / A2?

Refer to the Write Up directions found on the website and the date found on our calendar. You may use other paper and/or type your answer. Name: Section 11.2 Given the series, apply the Ratio Test to determine the Radius and interval of Convergence. Be sure to apply appropriate tests to…

17. A small heater has a rectangular filter that is 16 in. by 20 in. Another larger heater requires a similar filter that has a width of 48 in. What is the length of this larger filter?

Refer to the following figure for Exercises 15-18. Segment AC is a diameter; BC = 115°, ∠DOC = 25°, and OA = 8 cm. 15. Find the lengths (in cm) of AC and DC. Round to the nearest hundredth. 16. Find the lengths (in cm) of BC and AD. Round to the nearest hundredth. Answers: [Also, label the…

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Following the rules for working with measures, find the required values: 120 in 12.2 in 10.3 in 9.1 in The lateral surface area of the prism in the illustration above is in^2. If h = 11.2 in, what is the total surface area of the prism in in^2? Also, what is the volume of the prism in in^3?

Problem 1.4: In ABC, let F, E, and D be the feet of the perpendiculars drawn from the vertices A, B, and C. Let the corresponding altitudes and the sides extended to meet each other at the points M, N, and L. Prove that M, N, and L are collinear. INSTRUCTOR: M. BRAKALOVA YOUR NAME

Which of the plans for IProot Koulocorkio Dooe AABC = ADEF using the previous question? Based on the methods chosen. Use the distance formula to find AB and DE. Then, use similar triangles to find angle ZAWD and angle ZB = angle ZE. Use the distance formula to find BC and EF. Then, use the…

Lonsicer AABC with vertices at A(-3,3), B(-3, T), and C(3,3); and ADEF with vertices at D(2, 2), and E(2,2). Which method(s) work for proving the triangles are congruent? SSS or SAS only ASA only ASA only SSS, SAS, ASA SSS only ASA or SAS only SAS only

(a) What is the order of S4? (b) Obtain & nontrivial 4 X 4 matrix representation for this group: (c) Identify the classes of this group and show that the character of each of the matrices in part (b) is the same for each class_ (d) Identify the subgroup of S4 that corresponds to only the…

PARALLEL LINES CUT BY A TRANSVERSAL {Coloring Activity} 1 Find the value of x. 2 Find the value of x. 3 Find the value of x. 4 Find the value of y. 5 Find the value of y. 6 Find the value of y. 7 Find the value of y. 8 Find the value of y. 9 Find the value of y. 10 Find the value of x. 11 Find…

Free figures below. Now, how many have more than one line of reflection symmetry? 12 of them 8 of them of them

Additional problem 2* (Steiner chain) Let % and %' be two circles tangent to each other at some point A. Show that you can fill the region between % and %' with circles %n; for n â‚¬ Z, tangent to both % and %' and such that %n is tangent to %n+1 and %n-1. Hint: Invert in A. Suppose that % is a…

Additional problem 1* Let A; B; and 0 be three distinct points in R?, and let & be a circle with centre 0. Show that there exists unique generalised circle (i.e , & circle or line) through and B and orthogonal to % . Hint: Invert in A_ Show that such generalised circle intersects as well

6: Geulletr $ ABC with a hypotenuse. Calculate the sin A, cos A, and tan A for the right side equals 14, the shorter side equals 7, and the longer side equals 16, the hypotenuse. Angle A is the angle created by the shorter side and the hypotenuse, and Angle â‚¬ is the right angle. Draw the…

Arc length A circle has a radius of 5. An arc in this circle has a central angle of 162°. What is the length of the arc? Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.

Text: The text must be constructed on one figure; Hence the question. Using straightedge and compass only, construct the âˆš3 + 2 length segment (the length is given below). Write out all steps of how to construct the length. Here, that is the square root of square root of…

4. (6 pts) In the drawing below, DE is parallel to BC, and BD = 2AD. a) Is triangle ADE similar to triangle ABC? Explain. b) If the two triangles are similar, what is the scale factor? c) What is the ratio between the areas of triangle ADE and triangle ABC?

A certain circle can be represented by the following equation: x^2 + y^2 - 2y - 99 = 0 What is the center of this circle? What is the radius of this circle? units

A certain circle can be represented by the following equation: 22 +y? + 182 + 14y + 105 = 0 What is the center of this circle What is the radius of this circle units Do 4 problems Check

10 The small square is inscribed inside the circle and the larger circle circumscribes the same circle: If Al is the area of the large square and A2 is the area of the small square, what is the ration Al A22

1.) Use Brahmagupta'$ Formula to find the area of a square with sides of length 6 inches 2.) Use Brahmagupta' $ Formula to find the area of a rectangle with a length of 8 cm and a width of 6 cm: 3.) Find the length of the diameter of the circle in which quadrilateral ABCD is inscribed

28. Find the measure of 17 in Illustration_

(1,8) (5,-2) Which of the following is the distance of the line segment? 2+/34 6,7 2 /6 VTo

Exercises The following exercises illustrate the result above about invariant funetions of quadruples: They show that the invariants obtained by permuting the variables in the cross-ratio y = [p gr;s] are simple functions of y, such as 4/yandy -1. 5.8.1 If [p.4rs] =% show that [p,4:s,r] = Iy.…

Tonc ( FW = 0 (6)In the figure below, suppose two chords intersect at point V inside the circle. VM = 26, VK = 39, and VN = 19.5. Find JK. JK = 0 search Type here 3n 8 Hcld

Find each length below. (a) In the figure below, two chords intersect inside the circle at point E. Suppose that EM = 14, EK = 10.5, and EN = 21. Find JK. JK = (b) In the figure below, a tangent and a secant are drawn to a circle from exterior point U. Suppose that UC = 5.5 and UG = 11. Find…

Mon 22 of 30 (I point) Title: Tirie Rem F 19 Write an equation of the circle with center (7, 8) and radius r = 6.

Given quadrilateral ABCD with diagonal AC. If BC = 1 AB and AC = LDC, find DA if AB = 4, BC = 3, and DC = âˆš2.

A quarter circle with radius BC = 4 is given below. Semicircles are constructed with diameters AB and BC. Find the area of the region enclosed by the bold curves. [Hint: Write an area formula like we did in class for area example 2. At some point, you will also need to construct a few simple…

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Triangle ABC is & right triangle with the right angle at vertex B Find k; the y-value of point C_ Graph ABC. An algebraic solution must be given: (5 points) A(3,4), B(S,-3), C(-2,k)

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Find the lateral area of each cone to the nearest whole number.

On 7th April and B respectively. In the following figure, let BGA and PB LBDA be tangents to the circle O at points BCAD is shown that cyclic te 2 a=Y-

Find the area of a rhombus in terms of the lengths of its diagonals d, and d Will the same formula you derived in part (a) work for kites? Why or why not?

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16.5 Surface integrals of vector fields: Problem 2 Previous Problem Problem List Next Problem Compute the surface integral over the given oriented surface: F = (0, 4, 1) where the sphere x^2 + y^2 + z^2 = 220 outward-pointing normal is correct Submit Answer

21. Suppose m 8x 67 3x 14 Find the 1 of x

Look at quadrilaterals A' B' B A, B' C" C B, and their angle sum.

The formula for the area S of a circle of radius a in double elliptic geometry is S = 2Ï€a^2 cos. Show that S approaches the area of the double elliptic plane when a approaches Ï€k.

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Q2 - Find the parametric equation of a circle of radius R, centered at (x = a, y = 6), using the arc length as a parameter. Q3 - Find the unit tangent vector to the curve r(t) = [t, +2, +3] at the points where it cuts the plane 2x = 2 - 1.

10 ft 8 ft Hint: Circumference of a circle: C = ?d Find the perimeter of this figure to the nearest hundredth. Use 3.14 to approximate ?. P = [?] ft Notice that only half of the circle is included in the figure!

Expected Value You earn 1 point for each correct response on a multiple choice test and lose 0.5 point for each incorrect response. Each question has 4 answer choices. If a student just guesses, what is the expected value of the guess?

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Parabola is a curve that represents any portion of the directrix (focus) F(x, 6) and the point (x, y) on the parabola. The following steps work to find the equation of the parabola: Step 1: FP = DP Step 2: Vk = âˆš((x - (-8))^2 + (y - 6)^2) Step 3: 12t + 36 = x^2 + 6x + 64 Step 4: y = 2y +…

Parabola is a locus of F(2,9) and directrix of y = Dx, where D represents any point on the directrix. P(x, y) represents any point on the parabola. While the following steps provide a solution: Step 1: FP = DP Step 2: V(x-2) = (VG-2) - (VG-m) Step 3: 1 + 4 - 4 + 7 (8y + 81) = y (22v +…

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QUESTION 4 For AABC, RS BC . If AR = 5, RB = 2.5,and RS = 4, find BC a,6 bb.3 c 2 d,7.5

Given that ZM = ZQ, MP = 6, PR = 4, and NQ = 15, find P

Find the surface area and the volume of the cement block in the figure shown. What is the surface area of the cement block? 956 in.² What is the volume of the cement block?

Using a compass and straightedge only, construct the last vertex, write out all steps, and prove your result. Below, we are given vertex A and B and the incenter of triangle ABC. Using a compass and a straightedge, construct the last vertex C.

13 Congruence: What other information do you need in order to prove that two triangles are congruent?

Instructions (10 points): Draw any triangle AABC on your own paper: Use what you have learned in this unit to construct the Euler Line by finding the centroid, circumcenter and orthocenter of a triangle: Carefully label the intersection points and record your work as you finish each…

Show that the triangle whose vertices are P(- 4,4), Q(- 11, - 12), and R(3,4) is isosceles. Find the lengths of all three sides. PQ = (Round to three decimal places as needed.) QR = (Round to three decimal places as needed.) PR = (Round to three decimal places as needed.) Is the triangle an…

Mass of the upper half of the ball (If you take the hemisphere to have its origin at (0,0,0) and its base in the XY-plane, the z-coordinate of the center of mass is the "average value of z" over the hemisphere, or the total moment divided by the volume). Parametrize the upper hemisphere using…

Proof: 1. RS = UZ (Given) 2. RT = US (Given) 3. ST = TS (Reflexive Property of Equality) 4. RS = UI (Transitive Property of Equality) 5. RT = US (Given) 6. ST = TS (Reflexive Property of Equality) 7. A RST = AUT (SSS Congruence) 8. A RST e AUTS (Definition of Subset)

Based on the drawing, where can the sink be located along the countertop that is 50 units away from the stove and 15 units away from the small island? The location should minimize the perimeter, which should be below 26 units.

The sides of a right triangle are 6, 8, and 10. Find the altitude drawn to the hypotenuse. (A) 2.4 (B) 4.8 (C) 3.4 (D) 3.5 (E) 4.2

Euclidean geometry, find the value of x in the given diagram: 10 S(a(Ï€ { ^ ~'70440 | 35) 147 <

2.2.6 Show that if two triangles have two pairs of corresponding sides in proportion and the angles included by the proportional sides are congruent; then the triangles are similar: (SAS similarity) Hint: Use the converse of the Thales Theorem for triangles.

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Creen Chloe bought a swimming pool for her backyard that measured 8 feet across and 3 feet deep. She fills the pool half way to the top. Assuming that one cubic foot of water is 7.5 gallons of water, about how many gallons of water will Chloe put in the pool?

Chloe bought a swimming pool for her backyard that measured 8 feet across and 3 feet deep. She fills the pool half way to the top. Assuming that one cubic foot of water is 7.5 gallons of water, about how many gallons of water will Chloe put in the pool?

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Consider the tabletop template of the regular hexagon shown below: a. Draw all radii from the center of the circumscribed circle to each vertex of the hexagon. b. What is the measure of each of the central angles formed by the radii? Explain how you arrived at your answer. c. Classify the…

K / (5,, (3 Nor Aba *lRahm Nole: Figure not drawn to scale. The figure above shows right triangle ABC. Line contains points A and B and the point (3, 1). If the coordinates of point B are (5, ?) and if the measure of âˆ BAC is 60Â°, what is the value of y?

The floor of the bathroom area measures 2 square feet; the living room, kitchen, and bedroom are in the house. The north and south walls of the living room are parallel.

Find the measures of the interior angles of the following triangle. The interior angles measure 26Â° and...

Find the missing angle or angles. 56 62 0A 72 0 B. 34 OC. 54 0 D. 62 "

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Give the definition of the apothem. If a regular hexagon is inscribed in a circle of radius R, the sides of the regular hexagon have length R. What is the length of the apothem in such a regular hexagon? What is the area of such a regular hexagon? If a regular hexagon is circumscribed about a…

The circle graph shows how a family budgets its annual income. If the total annual income is $150,000, what amount is budgeted for Food? Housing 24% Savings 7% Leisure 13% Insurance 10% Food 17% Auto 13% Clothing 16%

Many people think that if you want to find the area of an irregularly shaped object (like a footprint) you could measure the perimeter by putting string around it, then reshape the piece of string into a regularly shaped object (like a rectangle) and then find the area based on the measure of…

y(n) = u(n) * sum(alpha^k from k=0 to n) = (1-alpha^(n+1))/(1-alpha) * u(n) When n -> infinity, y(n) = 1/(1-alpha) y(n) = x(n) * h(n) = sum(x(k)h(n-k) from k=-infinity to infinity) = sum(alpha^k u(n-k)u(k) from k=-infinity to infinity) = sum(alpha^k from k=0 to n) = (1-alpha^(n+1))/(1-alpha) *…

Assignment DJaic Period: Using degrees, find the amplitude and period of each function. Then graph: 1) Period: 180 degrees, Amplitude: 1, y = sin(20) 2) Period: 360 degrees, Amplitude: 2, y = sin(40) 3) Period: 360 degrees, Amplitude: 1, y = cos(40) 4) Period: 360 degrees, Amplitude: 2, y =…

2-icch bele i: drilled through Eleck (cube) of wocd thet picaalg 'ES Le3 @L 'sueli dde. How much wood is leftin the block after the bole i: deu can of tuna with height of - and diameter of 12 cm cost 950. Another can has : height of cm and diameter of 14 cm If the second cost $1.69,which is the…

7 in 4/10/2019 MAFS.912.6-C0.1.3 Trapezoid RSTU is shown. Write the trapezoid onto itself for the line that would map the MAFS.912.G-Co.1.3 Figure rhombus and Figure 2 is rectangle Neither unique square. Which transformation can be used to map Figure onto itself? Rotation of 90 degrees…

Taxicab Triangles Draw three right triangles on the graph. Measure their sides using taxicab distances. Hypotenuse (long side) Leg (short side) Leg (short side) Triangle Triangle Triangle Then mark dots on the graph. The Pythagorean Theorem does not apply to taxicab geometry. Why not come…

UIC SaTfle Distance Toi Given that there are the same two points X and Y, describe a rule for finding all the points' distance from X. 5. Find all points that are the same distance from G as from H.

Hexagon is graphed on the coordinate plane. Part A: Find the area of the hexagon. Part B: Find the perimeter of the hexagon. 5433402 Given triangle ABC with vertices (-8, 2), (-2, 2), and (-2, 8), determine which sequence of rigid transformations would map…

Consider the points in the following diagram. Ac5i7) 5451+/5-7/42 141/+ 6-1-3 ~I+h-41= 7 751+H- Il24 J54Iet S 5 - 3 ` I 2 ] 4 5 6E7 0 4 7 (zzV) Find all points that are the same distance from B. Find all points that are the same distance from C as from D. Find all points that are the same…

Find the volume of the region between the cylinder z = 5y^2 and the xy-plane that is bounded by the planes x = 0, x = 3, y = 0, and y = 3. The volume is (Type simplified fraction).

14. Which is NOT a true statement about a rhombus? RO = 28 cm, then RB = 14 cm. mZRHB = mZHRB RH = OH mZRMO = mZRHO 15. Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each other: Parallelogram, Rectangle, Rhombus,…

25. To the nearest meter; find the volume of the prism below: . 1235 m? 1140 m? 1080 m 190 m? 13m 19m " 1 10m 26_ A barn silo consists of & cylinder with _ hemisphere 'Yz sphere) on top_ What is the volume of the silo? 1390 m} 1524 m- 1657 m 2059 m" 25 m 8 m-

19. Find the closest value for x 12.6 16.1 20.4 25.6 20. The sketch of a stained glass window is shown in the shape of a semi-circle. Ignoring the seams, how much glass would be needed for the window? 61 f12 181 ft? 361 ft? 721 ft?

7 _ Find the number of diagonals in a hexagon b. d. 12 91 ' 8 The measure of a vertex angle in an isosceles triangle is 468_ What is the measure of one base angle in the triangle? : . - "3 " , "uc , <<: ` 230 460 3 670 920 "'

Welcome to the world of geometry! In this text, we will explore the concept of supplementary angles and polygons. Let's dive in! Given the following information: - Wlcn proves allb and Il m 23sini - Zazlo, 27e212 ZSe21O, L14 and Z1S are supplementary - Z6 = L9, L2 and Z14 are…

In the figure below, line a is parallel to line b. Find the measure of angle S if: the measure of angle 6 is 3x + 22 and the measure of angle 8 is x + 58. b. 76Â° d 104Â° 18 978

Find sides x and y in the triangle below. a. x=15, y=7.5 b. x=20, y=10 c. x=15√2, y=15 d. x=(30√3)⁄3, y=(15√3)⁄3 Find the measure of the missing angle "?". a. 24° b. 20° c. 35° d. 31° In the figure below a || b. Find m∠5 if:

Question 5: Use Voronoi construction on a representative part of the structure to estimate the average number of nearest neighbors about a disc.

Let AABC be a triangle, let Î± be the bisector of the angle ZCAB. Let P be the intersection of Î± and BC. Let R be the point on the line AB such that AR = AC, and let X = AP âˆ© RC. Let Q denote the intersection point between the line through B and X and AC. a) Show that the triangle AARC is…

A box is formed by cutting squares from the four corners of a 5"-wide by 7"-long sheet of paper and folding up the sides. Let x represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches). a. Write a formula that expresses V in…

Ifthe triangle is equiangular in the hyperbolic plane _ will that force it to be equilateral? If not, give constructed example: If ves, justify why

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The quadrilateral LMNO in the following figure is a parallelogram. M (a,b) N C' h M 0 (c, 0) L (0,0) Find the coordinates of vertex N based on the coordinates of the other vertices already listed in the figure. Using the given information and the results of part b, show that the diagonals of a…

Solve the triangle using the conventional system for labeling a right triangle, C is the right angle. a = 21.0 and c = 30.0 Remember to round your answers to the appropriate number of significant digits_ A = B = b =

Whether it is possible to tessellate? Determine the combination of regular S-gons that will tessellate the plane using only squares and regular T-gons. We know that a combination of squares and regular polygons will tessellate the plane. Explain why these 64-gons work, but regular octagons…

Prove that e is irrational: Steps to prove that if an n-gon is constructible, then a Zn-gon is constructible. And if GCD(a,b) = 1 and an a-gon is constructible, then a b-gon is constructible. Hint: Use the half-angle identity to prove that is constructible. Use the equation ax + by implies x…

Consider the cone $z^2 = x^2 + y^2$ between $z = 0$ and $z = 1$. (a) Find the surface area of this cone. (b) Find the volume of the region above this cone and inside the sphere of radius $\sqrt{2}$ centered at the origin that encloses the cone.

Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r?

Gt > G, Over 0 < q < r < $ < t, for geometric Brownian motion (Gt) â‰ 0, show that ratios and Gq are G, independent random variables.

Find the area and perimeter of the Norman window shown below: 10 10 & 8 f

(6) Sketch the ellipse 2 =1. Then fnd an cquation of its tangent line at the point (_4,0). Sketch the ellipee Then find equation of its tangent line the point Sketch the ellipse 634 @=1 = 1 Then find an equation of its tangent line at the point (2,3).

Given: mZT = 30, mZvUS = 1358 Prove mZS = 1058

Show that if M € Rk is an m-manifold and N € Rl is an n-manifold, then the product M x N = {(~,y) : x € M,y e N} € Rk+l is an (n + m)-manifold.

point) Find the minimum distance from the point (1,1,15) to the paraboloid given by the equation 2 = 22 + y?_ Minimum distance 5.94540564902 Note: If you need to find roots of a polynomial of degree > 3, you may want to use a calculator of computer to do so numerically. Also be sure that you…

Bicycle gearing allows the rider to control the speed and effort required to pedal. By adjusting the gear ratio, which is the number of teeth on the front and rear gears, the rider can make each pedal revolution turn the rear wheel a certain number of times. Suppose we have a bicycle with a…

Bicycle gearing allows the rider to control the speed and effort required to pedal. The gears on a bicycle are made up of teeth on the front and rear wheels. When the pedal is turned, it rotates the front wheel, which in turn rotates the rear wheel. The number of teeth on each wheel determines…

The supplement of an angle is 608 less than twice the supplement of the complement of the angle. Find the measure of the complement.

Arnex has a 309, 60", a 1508 , a 458, and a 1358 angle in his pocket. He takes out two of the five angles. Find the probability that The two angles are supplementary The two angles are complementary

The measure of the supplement of an angle is 308 less than five times the measure of the complement: Find two-fifths the mea- sure of the complement:

For 7.20, the crucial observation is that the circumcenter and orthocenter are the same point if and only if the angle bisectors are altitudes. You should justify this observation as part of your proof. The justification shouldn't take more than line two.

Five times the complement of an angle less twice the angle'$ supplement is 40:. Find the measure of the supplement.

Write a two-column proof; Given: [ 1L,2I=2 Prove: Ilt Complete the proof by filling in the blanks (1, 2, and 3). Proof: Statements Reasons 1. Given 1L,2I=2 2. L is congruent to itself Reflexive Property 3. m I! 3. Definition of congruent angles

10. Find mZRST. Give a reason for each step (informal proof). (3x)^9 (4x - 24)^9

Given: mLI = (3x+30), mLZ = (Sx-10), and x = 20 Prove: mLI || mLZ Statements: 1. mLI = 3x + 30 2. mLZ = Sx - 10 3. x = 20 4. mLI = 3(20) + 30 5. mLI = 90 6. mLZ = 5(20) - 10 7. mLZ = 90 8. mLI = mLZ 9. Therefore, mLI || mLZ Reasoning: Given…

The supplement of an angle is four times the complement of the angle. Find the measure of the complement:

Given: XY = 1, YW = AB = 1, BC = (2x)^(50) Find: mLDBC

The larger of two supplementary angles exceeds 7 times the smaller by 4 Find the measure of the larger angle.

Text: Given: ! || m Prove: mâˆ I + mâˆ 2 = 180Â° Proof: Statements Reasons 1. Given Given 2. âˆ I || âˆ 2 Definition of parallel lines 3. âˆ I + âˆ 2 = 180Â° Angle sum of a straight line

13. Given: mZI = (3x+30), mZ2 = (5x-10), and x = 20. Prove: mLI = mZ2. Statements: 1. mZI = 3x + 30 2. mZ2 = 5x - 10 3. x = 20 4. mZI = 3(20) + 30 5. mZI = 90 6. mZ2 = 5(20) - 10 7. mZ2 = 90 8. mZI = mZ2 Reasoning: Given

The measure of angle A is 415Â°. One of two complementary angles added to one-half the other yields 729. Find half the measure of the larger angle.

12_ Find the value of x $0 that m Iln. Give reason for each step (informal proof): (Gx + 522 (Sx - 12)8

11. Given: ? | m Prove: ZI = Z2 Statements Reasons

One of two complementary angles added to one-half the other yields 729_ Find half the measure of the larger.

10. Find mZRST. Give a reason for each step (informal proof). S/31)9 (4x 24)9_

Proof Statements Reasons [ 2 LLm _ 3. m || ! 1. Given 2. [2] 3. [3]

Find the missing length for each triangle a_ b_ 18

SLT24-29 Determine which practice problems make sure method! Mark any can prove the triangles congruent. Use congruence statements and tick marks for special cases. If congruent, write congruence statement. Are the triangles congruent? If yes, by which method? If yes, congruence statement: UILa…

Find the measure of the acute or right angle formed by intersecting lines s0 that C can bel mapped to C" using two reflections. The rotation (T,y) (-I, y) maps C to C"' The measure of the angle is

Let us recall the midline theorem of a triangle: the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to half of it. A quadrilateral which has two opposite sides parallel and the other two opposite sides not parallel is called a…

Prove that the midpoints of the sides of any quadrilateral are vertices of a parallelogram. Hint: the midline theorem.

The scale of two similar quadrilaterals. The perimeter of the small quadrilateral is 50 centimeters. What is the perimeter of the larger quadrilateral? If the dimensions of a rectangle with a perimeter of 24 inches are tripled, what will be the perimeter in inches of the new rectangle? If the…

Make sure to do the entire problem. Problem 7.6 is an "if and only if" statement. Hints and reminders: you have to write proofs in both directions. But Problem 7.4 also requires two directions. For example, so you will need to write proofs in both directions.

For example, you have to write proofs in both directions. But Problem 7 also requires two directions. Once you've figured out your answer, you need to explain why that kind of triangle has its orthocenter at vertex B. Then you need to explain what other kind of triangle does. Put differently,…

Perform the following series of rigid transformations on ∆ABC. Translate ∆ABC by moving it 5 units to the right and 2 units up. Draw the line y = -x and reflect ∆A'B'C' across the line. Rotate ∆A"B"C" counterclockwise about the origin by 270°.

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Near this sketch asserts that non-Euclidean geometry, the ratio of the circumference of a circle to its diameter, remains constant, unlike in Euclidean geometry. The following questions illustrate this fact: In Riemannian geometry, assume the Earth is a sphere with a radius of 1. Call some…

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