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Algebra Q&A Archive of March 29, 2025

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March 29 of 2025

Write the following in simplified radical form. \[ \sqrt[5]{u^{6}} \] Assume that the variable represents a positive real number. \( \square \) \( \sqrt[\square]{\square} \)
Write the following in simplified radical form. \[ \sqrt[4]{v^{9}} \] Assume that the variable represents a positive real number. \( \square \) \( \sqrt[4]{\square} \) \( \frac{\square}{\square} \) \( \square \) 5 Explanation Check Search
Write the following in simplified radical form. \[ \sqrt[3]{x^{14}} \] Assume that the variable represents a positive real number. \( \square \) Explanation Check
function by identifying the domain of each piece. \[ \begin{array}{l} f(x)=\left\{\begin{array}{ll} -x, & x<a \\ -1, & a \leq x<b \\ (x-3)^{2}-1, & x \geq b \end{array}\right. \\ a=\square \quad b=\square \end{array} \] Intro Done
Determine the domain of each piece. Domain of piece 1 : \( \square \) Domain of piece 2 : \( \square \) Domain of piece 3 : \( \square \) CONE
22. Which conversion factor is used to convert radians into degrees? \( \frac{90}{\pi} \) \( \frac{\pi}{360} \) \( \frac{\pi}{180} \) \( \frac{180}{\pi} \)
The mass of a hydrogen atom is \( 1.67 \times 10^{-24} \) grams. The mass of a carbon atom is \( 1.99 \times 10^{-23} \) grams. A molecule of methane contains 4 atoms of hydrogen and 1 atom of carbon. a) Calculate the mass of one molecule of methane, giving your exact answer in standard…
21. What is the circumference of the circle shown below? 119.32 inches 59.66 inches 6.05 inches 19 inches
Let \( g \) be the piecewise defined function shown. \[ g(x)=\left\{\begin{array}{ll} x+4, & -5 \leq x \leq-1 \\ 2-x, & -1<x \leq 5 \end{array}\right. \] Evaluate \( g \) at different values in its domain. \[ \begin{array}{l} g(-4)=\square \\ g(-2)=\square \\ g(0)=\square \\ g(3)=\square…
Question 1 1 pts What is the inpatient census for the following scenario? At the start of the week on Sunday, there were 150 inpatients. Throughout Monday, Tuesday, and Wednesday, \( 40 \% \) of the inpatients were discharged in total from on those three days combined. On Thursday 36 more…
The linear density expression for FCC [110] direction in terms of the atomic radius R is LD = 2√2R.
19. What is the \( \mathrm{m} / \mathrm{YXZ} \) ? \( 127^{\circ} \) \( 361^{\circ} \) \( 234^{\circ} \) \( 63.5^{\circ} \)
Question 4 1 pts What is the alternative hypothesis in this scenario? H1: the number of treats claimed by the company (the population) is less than the number of treats you find in your sample. H 1 : the number of treats claimed by the company (the population) is different from the number of…
18. The diameter of the window below is 4.2 feet. What is the radius? 1.4 feet 2.1 feet 4.2 feet 8.4 feet
14. Which of the following is the correct formula for calculating the diameter \( (D) \) of a circle? \( D=2 R \) \( D=2 \pi R \) \( D=2 \pi R^{2} \) \( D=2 R^{2} \)
What is the negative solution to \( 2 p^{2}+2 p-12-2 p^{2} \) ? The negative solution is \( \square \) 1
(b) Find the time taken by the liquid to cool to \( 40^{\circ} \mathrm{C} \). (c) Sketch the graph of \( \theta \) against t. (23. Solve the following equations. (a) \( 5^{x}>2500 \) (b) \( \mathrm{e}^{x}<11 \) (c) \( 0.8^{x} \geq 0.3 \) (d) \( 5^{x+1} \leq 4 \) (e) \( \mathrm{e}^{1-x}<2 \)
Fome Modules Grades The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters \( (\mathrm{m}) \) and two walls each of length 10 m . If the seating portion of the hall has an area of 180 square meters, what is the value of \( x \) ? 6
5. The diameter of a circle is 6 kilometers. What is the circumference? Use 3.14 as an approximation for \( \pi \). 37.68 km 1.19 km 18.84 km 12.00 km
2. Find the surface area of a cube with. sides 1.5 m
1. (JPE) Let \[ A=\left(\begin{array}{ccc} 4 & 4 & 1 \\ 3 & -2 & 7 \\ 0 & 3 & 1 \end{array}\right) \] Use Householder reflectors to find a QR factorization for the matrix \( A \), i.e., \( A=Q R \) where \( Q \) is an orthogonal matrix and \( R \) is an upper triangular matrix.
1. calculate the sufface area of a cube whose length is 6 cm
11. Solve the equation \( \log _{3}(x+4)+\log _{3}(x-2)-\log _{3}(2 x-1)=1 \). 12. Solve the equation \( 2 \log _{2}(x+1)-\log _{2}(3 x-1)=1 \)
10. Solve the equation \( \lg (3 x-2) \) 11. Solve the equation \( \log _{3}(x+4)+\log _{3}(x-2)-\log _{3}(2 x-1)=1 \). 12. Solve the equation \( 2 \log _{2}(x+1)-\log _{2}(3 x-1)=1 \) (13.) Solve the equation \( \lg (2 x+1)-\lg (x-4)+\lg 2=1 \). 14. Solve the simultaneous equations. \[ \log…
vi) an integer esmaller than both the integer. \[ \begin{array}{l} =-5 \text { and }-3,(-5)+(-3) \\ =-2 \text { and }-3,(-2)+(-3) \end{array} \] vii) an integer greater than both the integers. \[ \begin{array}{l} =7 \text { and } 5,7+5 \\ =16 \text { and } 2,16+2 \\ =9 \text { and }…
Que 1] Write a pair of integers whose sum is: i) a negative integers \( =8 \) and \( -10,8+(-10) \) \( =-3 \) and \( 2,(-3)+2 \) \( =-4 \) and \( 1,(-4)+1 \) ii) -9 \( =-10 \) and \( 1,(-10)+1 \) \( =-19 \) and \( 10,(-19)+10 \) \( =-8 \) and \( (-1),[(-8)+(-1)] \) iii) a positive integer \( =3…
Mathematics Assignment term 1 All craft 2025 Question 1 i. A German silver alloy consists of \( 60 \% \) copper, \( 25 \% \) zinc and \( 15 \% \) nickel. Determine the masses of the copper, zinc and nickel in a 3.74-kilogram block of the alloy. ii. If the compression ratio of a cylinder is \(…
12. Height A tree stands on a hillside of slope \( 28^{\circ} \) from the horizontal. from a point 75 feet down the hill, the angle of elevation to the top of the tree is \( 45^{\circ} \) (see figure). Find the height of the tree. here to search \( 60 \% \) 1097m 18was
Let \( S_{1} \) and \( S_{2} \) be bounded sets in \( \mathbf{R}^{\mathrm{n}} \); let \( f: S_{1} \cup S_{2} \rightarrow \mathbf{R} \) be a bounded function. Show that if \( f \) is integrable over \( S_{3} \) and \( S_{2} \), then \( f \) is integrable over \( S_{1}-S_{2} \),…
Que 1] A number line is shown below: Write the integers represented by \( A, B, C, D, E, F, H \) and \( J \). \[ \begin{array}{l} \Rightarrow A=-4 \\ B=-3 \\ C=-2 \\ D=-1 \\ E=0 \\ F=1 \\ H=3 \\ J=5 \end{array} \]
(3) If Median of the following data is 240 , then, Find the value of "f"? \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline C.I & \( 0-100 \) & \( 100-200 \) & 200 & 300 & 400 & 500 & 600 \\ freq. & 15 & 17 & f & 12 & -400 & -500 & -600 \\ -700 \\ \hline \end{tabular}
15. The diagram below shows a lawn (unshaded) surrounded by a path of uniform width (shaded). The curved end of the lawn is a semicircle of diameter 10 m . Calculate the total area of the path.
Back Question 3 AVG. ACCURACY: \( 67 \% \) AVG. TIME \( 2: 31 \) Chapter 5 Roots and Exponents A A \( \square \) If \( x \) and \( y \) are common fractions and \( \left(2^{8 x}+2^{8 x}\right)\left(3^{10 y}+3^{10 y}+3^{10 y}\right)=\left(\frac{1}{2}\right)^{2 x}\left(\frac{1}{3}\right)^{-5 y}…
9. A spinner of radius 7.5 cm is divided into six equal sectors. Calculate the area of each sector.
Chapter 5 Roots and Exponents A A If \( x \) and \( y \) are positive integers and \( \frac{1}{x}>\frac{1}{y} \), which of the following must be true? \( \left(\frac{1}{x}\right)^{2}<\left(\frac{1}{y}\right)^{2} \) \( x>y \) \( y^{2}>x^{2} \) \( x y<1 \) \(…
Back Question 1 AVG. ACCURACY: \( 44 \% \) AVG. TIME: 1:04 Chapter 19 Functions and Sequences A A The function \( f(n) \) equals the number of unique prime factors of \( n^{2} \). If \( m \) is any prime number, which of the following is equal to \( f(m) \) ? m \( \frac{m}{m} \) \(…
12. Which of the following statement is the conclusion of the arrangement below? If the two angles are congruent to the same angle, then the two angles are congruent. If \( \angle \mathrm{A} \) is complementary to \( \angle \mathrm{C} \) and \( \angle \mathrm{B} \) is complementary to C , then…
Determine whether the geometric series given in Problems 3-22 converges or diverges, and find the sum of each convergent series. 5. \( \sum_{k=0}^{\infty} \frac{2}{3^{k}} \) 9. \( \sum_{k=0}^{\infty} \frac{(-2)^{k}}{5^{2 k+1}} \) 11. \( \sum_{k=1}^{\infty} e^{-0.2 k} \) 15. \(…
(B) \( S 5 A \) C. SAS D. ASA 32. Which of the following conditions will make \( \triangle S O P \cong \triangle A C E^{-} \) A. If \( \overline{S O} \cong \overline{A C}, \overline{S P} \cong \overline{A E} \) and \( \angle S \cong \angle A \) B. If \( \overline{S O} \cong \overline{A C},…
Question 1 (1 point) A hot metal ball is dropped into water which is maintained at a constant temperature. The temperature of the ball as a function of time is shown in the table below. Calculate the best estimate of the rate of cooling (dT/dt) at \( \mathrm{t}=0 \). Give your answer to 2…
Question 1 (1 point) A hot metal ball is dropped into water which is maintained at a constant temperature. The temperature of the ball as a function of time is shown in the table below. Calculate the best estimate of the rate of cooling (dT/dt) at \( \mathrm{t}=0 \). Give your answer to 2…
Question 1 (1 point) A hot metal ball is dropped into water which is maintained at a constant temperature. The temperature of the ball as a function of time is shown in the table below. Calculate the best estimate of the rate of cooling (dT/dt) at \( \mathrm{t}=0 \). Give your answer to 2…
\( \left(2+1 \frac{1}{2}\right) \)
Simplify, \[ \left(v^{\frac{3}{8}}\right)^{2} \] Write your answer without parentheses. Assume that the variable represents a positive real number. \( \square \)
Simplify. \[ \left(x^{\frac{7}{6}}\right)^{\frac{8}{3}} \] Write your answer without parentheses. Assume that the variable represents a positive real number.
(d) Rajah 9.3 manurijukkan sebulir peluru dilembak keluar daripada sepucuk plsion dengan halaju \( 100 \mathrm{~m} \mathrm{~s}^{-1} \) Diagram 9.3 shows a bullet is shot out from a gun with a valocity of \( 100 \mathrm{~m} \mathrm{~s}^{-1} \). Jisim pistol 200 g Gun mass 200 g Rajah…
For numbers 45-48, use the incomplete Two - column proof of the two triangles below to answer the questions that follow. Below is the figure and the given congruent parts of the two triangles. Given: \( \angle 1 \cong \angle 2 \) \[ \begin{array}{l} \angle 3 \cong \angle 4 \\ A D \cong F…
1. Find the point-slope form of the equation of the line passing through the points \( (-6,-4) \) and \( (2,-5) \). A \( y+5=\frac{1}{8}(x+6) \) B \( y+4=\frac{1}{8}(x+6) \) C \( y+4=\frac{1}{8}(x-2) \) D \( y+4=\frac{1}{8}(x+6) \) 2. Find the slope of the line that passes through the pair of…
10. In order to give gr 5 rifabutin to a patient, how many capsules should be given? 11. A doctor orders tetracycline elixir qid for a child weighing 60 lb at a dosage of \( 8 \mathrm{mg} / \mathrm{kg} / \) day in equally divided doses. How many mg would 1 dose contain? The tetracycline in…
Question 6 of 10 possible This question: 1 point(s) possible Subn Find \( x \) for the following equation. \[ 5^{7 x+5}=3 \] \[ x=-0.617 \] (Do not round until the final answer. Then round to three decimal places as needed. Use a comma to separate as needed.) Time Remaining: 00:09:38 Next
This quiz: 10 point(s) possible Question 2 of 10 This question: 1 Submit quiz point(s) possible A supply equation and a demand equation for a product are given below. If \( p \) represents price per unit in dollars and \( q \) represents the number of units per unit of time, find the…
13. Discs of radius 4 cm are cut from a rectangular plastic sheet of length 84 cm and width 24 cm . a) How many complete discs can be cut out? Find b) the total area of the discs cut c) the area of the sheet wasted.
4. What is the experimental probabuit A. \( \frac{1}{6} \) B. \( \frac{1}{5} \) C. \( \frac{1}{4} \) 5. What is the experimental probability of rolling a 1 ? A. \( \frac{1}{5} \) B. \( \frac{1}{10} \) C. \( \frac{1}{15} \) D. \( \frac{1}{30} \) activity a Direction: Determine the experimental…
Find an equation of the line that passes through \( (-5,-3) \) and that is parallel to \( 2 x+9 y+18=0 \). Give the answer in slope-intercept form. The equation of the line in slope-intercept form is \( y=\frac{-2}{9} x-\frac{37}{9} \). (Simplify your answer. Use integers or fractions for any…
ACTIVITY 3: TEST YOUREELF Direction: Determine the experimental probability. Khian rolled two dice 10 times and recorded the sum of the numbers on the top faces. The results are shown below. \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline Outcome (Sum) & 4 & 7 & 12 & 3 & 9 & 8 & 10 \\ \hline…
Profiles Tab Window Help Quiz 2 tudent/PlayerTest.aspx?testid \( =270495336 \) \& centerwin \( = \) yes Artem Shiik Question 10 of 10 This quiz possible This que point(s) p If \( f(v)=\frac{1}{v^{2}+3} \) and \( g(v)=\sqrt{v+2} \), find \( (f \circ g)(v) \) and \( (g \circ f)(v) \). \( (f…
ACTIVITY I: PRACTICE Direction: Analyze the problem and answer the questions that follow. A spinner has three unequal sections: red, blue and green. The table shows the results of Miko's 20 spins. Find the experimental probability of landing on each color. Write \begin{tabular}{|c|c|} \hline…
\( \left(\frac{2}{5}\right)^{2}= \)
Chapter 3 Linear and Quadratic Equations A A \( 3^{10}-2^{10} \) is a multiple of all of the following numbers except: 5 25 55 75 211 Show Solution Related tags: The difference of squares
Answer: \( \qquad \) 5. Calculate volume of the truncated cone. Use \( \pi=\frac{22}{7} \)
Chapter 4 Properties of Numbers A A If \( n! \) and \( (n+1) \) ! have the same units digit, then \( n \) can be which of the following? I. \( n=10 \) II. \( n=1 \) III. \( n=0 \) I only II only III only I and III I, II, and III
3. Calculate surface area of the open cylinder. Use \( \pi=3.14 \). Working out:
2. Calculate the surface area of the rectangular prism. Working out: Answer:
Which of the following graphs is NOT useful for showing change over time or comparing two or more items? pictograph line graph bar graph pie graph
\( \qquad \) are visuals consisting of vertical or horizontal bars that represent specific sets of data. Line graphs Diagrams Bar graphs Pie graphs
MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER 1. Which of the following numbers has terminating decimal expansion? a) \( \frac{37}{45} \) b) \( \frac{21}{2^{3} 5^{6}} \) c) \( \frac{17}{49} \) d) \( \frac{89}{2^{2} 3^{2}} \)
\( \qquad \) are bar graphs that use pictures instead of bars. Line graphs Pie graphs Pictographs Visual graphs
9. A spinner of radius 7.5 cm is divided into six equal sectors. Calculate the area of each sector.
Suppose we want to choose 5 colors, without replacement, from 15 distinct colors. (a) How many ways can this be done, if the order of the choices is relevant? \( \square \) (b) How many ways can this be done, if the order of the choices is not relevant? \( \square \)
9. A spinner of radius 7.5 cm is divided into six equal sectors. Calculate the area of each sector.
6. Complete the equivalent fraction by filling in the box. \[ \frac{19}{7}=\frac{76}{\square} \] Working out:
Which place value model shows \( 1,671 ? \) Choose 1 answer: (A) (B) (c)
\( 2^{2} \frac{\frac{1}{4}}{-1 \frac{1}{2}} \)
Khan Academy Drag the vertex of the angle to place the vertex at point A. Drag another point on the angle to make one of the rays go through point \( B \). Make the other ray go through one of the unlabeled black points to create a right angle. The arc symbol near the vertex will show the…
7. Express \( 16 / 3 \) as a decimal correct to 4 decimal places. Working out:
Drag the vertex of the angle to place the vertex at point \( A \). Drag another point on the angle to make one of the rays go through point \( B \). Make the other ray go through one of the unlabeled black points to create an obtuse angle. The arc symbol near the vertex indicates the angle…
Math 030-1 UNIT 6 ASSIGNMENT Trigonometry Equations Problem ( Total: 12 marks) 1. a) Algebraically solve sec²? - 2tan? = 3. State the general solution to the nearest degree. (Hint: to solve a quadratic equation, either factor if possible or use the quadratic formula.) (3 marks) b) Explain…
How many vertices does the following shape have? \( \square \)
How many faces does the following shape have?
How many edges does the following shape have?
How many vertices does the following shape have?
How many faces does the following shape have?
4. Find the GCF of 40 and 120 . Working out:
We've updated our Terms of Service. Please review it now. Khan Academy 2 Identify parts of 3D shapes How many edges does the following shape have? \( \square \) Related content \( \square \) Counting faces and edges of 3D shapes \( 3: 47 \)
Assessment 1 mymodules.dtls.unisa.ac.za/mod/quiz/attempt.php?attempt=25259175\& \( \mathrm{cmid}=1094880 \) \( A \cong 150 \) Dashboard myModules myAdmin Unisa Library C. Since \( \triangle H I J / / / \triangle S T R \) \[ \begin{array}{l} \frac{H J}{12}=\frac{4}{10}=\frac{6}{T R} \\ H J=4.8…
ㅇ- \( _{\text {- }} \quad \) khanacademy.org/math/7th-grade-found We've updated our Terms of Service. Please review it now. Khan Academy Identify parts of 3D shapes How many vertices does the following shape have? \( \square \) Related content \( \square \) Counting faces and edges of 3D…
11:15 Grade Suno Dasht Chao: Ident Parts -- khanacademy.org/math/7th-grade-foundation (i) We've updated our Terms of Service. Please review it now. Khan Academy Level 7 \( \square \) Identify parts of 3D shapes How many faces does the following shape have? \( \square \) Related…
8. Write \( 0.416=666667 \) correct to 3 significant figures. Working out: significiant figures
2.2.4 Quiz: Exterior and Remote Interior Angles Which of the following are exterior angles? Check all that apply. A. \( \angle 4 \) B. \( \angle 2 \) C. \( \angle 5 \) D. \( \angle 1 \) E. \( \angle 6 \) F. \( \angle 3 \) PREvious
\( =\frac{1}{2} \log _{10} 16-2 \log _{10}\left(\frac{9}{5}\right)+\log _{10} a^{2} \)
8. Write \( 0.416-666657 \) correct to 3 significant figures. Working out: Answer: \( \qquad \)
○- www-awy.aleks.com/alekscgi/x/lsl.exe/1o_u-IgNsIkr7j8P3jH-IBjnuwZGiweFMYphv4tCLy6BMpSg0NHO-bYrWEkbUH6v227qTj2fBu6zSUn2DjC-1... Relaunch to update Undergrad Entrance... Amazon.com Thank... New folder Adobe Acrobat All Bookmarks Sec 10.3, 10.4 Quiz Question 5 of 5 (1 point) | Question Attempt:…
GR 11 GENERAL MĀTHEMATICS M1 8. Write \( 0.416-666657 \) correct to 3 significant figures. Working out: Answer: \( \qquad \)
Modules \( 0 / 1 \) pts Grades 18 A concrete block had a portion removed from its center. both the block and the portion removed are in the shape of a right rectangular prism, as shown in the figure. the dimensions of the portion of concrete removed are 2 centimeters ( cm ) 5 cm by 5 cm . what…
9. At first, Mr Tan's money was twice of Mrs Tan's money. Then Mr Tan gave \( \frac{1}{3} \) of his money to Mrs Tan. What is the ratio of Mr Tan money to Mrs Tan? Mr. Mrs \( x_{3} \) \[ \frac{1}{3} \times b \] \( +2 \) \( 4: 5 \) (ams)
9. A spinner of radius 7.5 cm is divided into six equal sectors. Calculate the area of each sector.
Reflect on your philosophy of guiding young children’s positive behaviors. How is your professional philosophy similar or different from how you were guided as a child? How do you constructively deal with young children’s challenging behaviors?
9. Express 12000 in Standard form. Working out:
\( (-3)^{-1}-(-1)^{-3}-\left(1-\frac{1}{2}\right)^{-2}+\left(5: \frac{5}{6}\right)^{-1}-\left(-1-\frac{1}{8}\right)^{-1} \)
Itts.unisa.ac.za/mod/quiz/attempt.php?attempt \( =252591758 \mathrm{cmid}=1094880 \) Dashboard myModules myAdmin Unisa Library Clear my choice (i) Determine roots in the equation \( 13 x^{2}-8=0 \). Leave your final answer to correct THREE SIGNIFICANT. FIGURE (ii) Leave the number 20468 to…
YEA E. \( \angle S T R=\sin ^{-1}\left(\frac{10^{2}+12^{2}}{15}\right) \) Clear my choice Which of the following equations will determine the length of side \( d \) of the triangle shown in the Figure below? A. \( d^{2}=(6 m)^{2}+(8 m)^{2}+2(6 m)(8 m) \sin \left(40^{\circ}\right) \) B. \(…
127 Question 9 1 pts Two right circular cylinders, cylinder \( X \) and cylinder \( Y \), have the same height, but the radius of the base of cylinder \( X \) is twice the radius of the base of cylinder \( Y \). What is the ratio of the volume of cylinder \( X \) to the volume of cylinder Y…
chocolate cherries sprinkles nuts (mealum, strawderry, sprinkies) (medium, strawberry, nuts) (medium, chocolate, cherries) (medium, chocolate, sprinkles) (medium, chocolate, nuts) (a) How many outcomes are there? \( \square \) outcome(s) (b) How many outcomes have cherries or nuts being…
Question 1 of 10 Which is a true statement about an exterior angle of a triangle? A. It is formed by two segments that are not sides of the triangle. B. It is formed by two segments that are sides of the triangle. C. It forms a linear pair with one of the interior angles of the triangle. D. It…
10. Write \( 2.36 \times 10^{-3} \) as a decimal number (ordinary form). Working out:
Question 6 1 pts To study amoebae in pond water, a student completely filled two cube-shaped containers with samples of pond water. When filled, the first container held 27 cubic cerrtimeters of pond water. The length of each side of the second container was twice the length of each side of…
Assessment 1 Is.unisa.ac.za/mod/quiz/attempt.php?attempt=25259175\&cmid=1094880 Dashboard myModules myAdmin Unisa Library Member \( A B \) rotates \( 150^{\circ} \) clockwise from the original position in the Figure below. Determine the angle \( \angle B C B^{\prime} \). (Hint: Use length \( A…
17. If Worker \( X \) was to sweep the corridors of the flat by himself, he would take 2 h . If Worker Y was to sweep the corridors of the flat by himself, he would take \( 1 \frac{3}{4} \mathrm{~h} \). (a) What fraction of the flat can Worker \( X \) sweep in 1 h ? (b) What fraction of the…
Note: Figure not drawn to scale. The rectangular mirror shown above has width 3 feet and length 5 feet and is surrounded by a mosaic border with a width of \( x \) feet. If the area of the mirror with the border is 35 square feet, what is the width \( x \), in feet, of the border? 1 2 3 5
25. Three pipes can be used to fill up a swimming pool with water. It takes 9 minutes for Pipe A to fill up the pool while 6 minutes for Pipe B. A third pipe, Pipe C, takes 4 minutes to empty the pool. How long would it take to fill the swimming pool given these conditions? (A) 10 minutes (B)…
The sum of money of Billy and Zander is 4,230 . If two-thirds of Billy's money is equal to five-sixth of Zander's money, how much money does Billy have? (A) 2,350 (C) 2,820 (B) 3,525 (D) 1,180
https://k12instructure.com/courses/1848303/quizzes/3072554/take Basics 7 , Quizzes > VOLUME, AREA, \& SURFACE AREA Home Modules VOLUME, AREA, \& SURFACE AREA Questions Started: Mar 29 at 8:16am Grades 17 Quiz Instructions Question 1 1 pts The surface area, \( S \), of a cylinder with a…
保 k). Spring 2025, Ivanova Donna Cornish 2 I 03/29/25 10:21 AM Question 23 of 24 This quiz: 100 point(s) possible This question: 4 Resume later point(s) possible Submit quiz For the following expression, state the exponent shown and its corresponding base. \[ -8^{2} \] The base is \( \square…
nt/PlayerTest.aspx?testld \( =269805872 \) 2 centerwin \( = \) yes Spring 2025, Ivanova Donna Cornish 03/29/25 10:22 AM This quiz: 100 point(s) possible Resume Question 24 of 24 This question: 4 point(s) possible Submit Two numbers total 26 and have a difference of 6 . Find the two…
8. A triangle has one vertex at the origin \( O(0,0) \), another at the point \( A(2 a, 0) \) and the third at \( \left(a, a /\left(1+a^{3}\right)\right) \). What are the largest and smallest areas this triangle can have if \( 0 \leq a<\infty \) ? 9. The product of two numbers \( x, y \) is 16…
Actuity \# 1 125 I. Complete each propontion 1. \( \frac{6 N}{6 H}=\frac{6 M}{?} \) 2. \( \frac{N M}{H_{J}}=\frac{?}{6 J} \) 3. \( \frac{6 \mathrm{~J}}{?}=\frac{6 \mathrm{H}}{6 \mathrm{~N}} \) 4. \( \frac{6 N}{N H}=\frac{6 M}{?} \) 5. \( \frac{?}{M N}=\frac{6 H}{6 N} \) II. Find the value of \(…
oft Edge m/Student/PlayerTest.aspx?testld=269805872\&centerwin \( = \) yes 12-wk), Spring 2025, Ivanova Donna Cornish Question 22 of 24 This quiz: 100 p possible This question: 4 point(s) possible Find the product. \[ (7 x-5 y)^{2} \] \[ (7 x-5 y)^{2}= \] \( \square \) View an example Textbook
Donna Cornish Question 19 of 24 This quiz: 100 point! possible This question: 4 point(s) possible Multiply. \[ (p+13 q)(p-13 q) \] A. \( p^{2}+26 p q-169 q^{2} \) B. \( p^{2}-A 69 q^{2} \) C. \( p^{2}-26 q^{2} \) D. \( p^{2}-26 p q-169 q^{2} \)
Donna Cornish a l 03/29/25 Question 16 of 24 This quiz: 100 point(s) possible This question: 4 \( R \) point(s) possible St Find the following product. \[ (3 x+7)^{2} \] \[ (3 x+7)^{2}= \] \( \square \) View an example Textbook Next
(11) Onlvias Practice Question (2017) The age of Mr. X last year was the square of a number and it would be cube of number next year. what is the least number of years he must wait for his age to become the cube of a number again? A. 42 B. 38 C. 25 D. 16
Donna Cornish \( 03 / 29 / 2 \) This quiz: 100 point(s) Question 14 of 24 possible This question: 5 point(s) possible Solve the system by either the addition method or the substitution method. \[ \left\{\begin{array}{r} x+\frac{1}{12} y=\frac{1}{3} \\ 5 x+2 y=2 \end{array}\right. \] Select…
\( \lim _{n \rightarrow \infty}\left(\frac{a-1+\sqrt{b}}{a}\right)^{n} \)
dent/PlayerTest.aspx?testld=269805872\&centerwin=yes ), Spring 2025, Ivanova Donna Cornish This quiz: 100 point(s) Question 13 of 24 possible This question: 4 point(s) possible Multiply. \[ (x-8)^{3} \] \[ (x-8)^{3}= \] \( \square \) (Simplify your answer.) View an example Textbook
25 radius 0.84 m 14. The diagram shows a framework for a target. The radius of the outer circle is 30 cm and the radius of the inner circle is 15 cm . Calculate the total length of wire needed for the whole framework. Area of a circle The area of a circle of radius \( r \) is given by \( A=\pi…
This quiz: 100 point(s) Question 10 of 24 possible This question: 4 point(s) possible Simplify the following expression. \[ (-3)^{-2} \] \( (-3)^{-2}= \) \( \square \) (Type an integer or a simplified fraction.) fiew an example Textbook
Ige udent/PlayerTest.aspx?testld=269805872\&centerwin=yes k), Spring 2025, Ivanova Donna Cornish Question 9 of 24 This quiz: 100 poin possible This question: 4 point(s) possible Simplify the following expression. \[ \left(-\frac{1}{4}\right)^{-5} \] \( \left(-\frac{1}{4}\right)^{-5}= \) \(…
13. An old-fashioned type of bicycle is shown. In a journey the front wheel rotates completely 156 times. How far does the bicycle travel?
yerTest.aspx?testld=269805872\&centerwin=yes g 2025, Ivanova Donna Cornish 03/29/25 This quiz: 100 point(s) Question 7 of 24 possible This question: 4 point(s) possible Re Solve the system of equations by the substitution method. \[ \left\{\begin{array}{l} 35 x+7 y=57 \\ -5…
This quiz: 10 Question 6 of 24 possible This questior point(s) possib Simplify the expression. Assume that all bases are not equal to 0 . \[ 11^{0}+5^{0}+y^{0} \] \[ 11^{0}+5^{0}+y^{0}= \] \( \square \) View an example Textbook
ing 2025, Ivanova Donna Cornish e | 03/29/25 9:44 Question 5 of 24 This quiz: 100 point(s) possible This question: 4 Resume point(s) possible Submit Solve the system of equations by the addition method. \[ \left\{\begin{array}{l} -3 x-2 y=-35 \\ -5 x+3 y=-14 \end{array}\right. \] Select the…
Question 5 of 24 This quiz: 100 point(s) possible This question: 4 point(s) possible Solve the system of equations by the addition method. \[ \left\{\begin{array}{l} -3 x-2 y=-35 \\ -5 x+3 y=-14 \end{array}\right. \] Select the correct choice below and, if necessary, fill in the answer box to…
Donna Cornish \& 1 03/29/259.41 AM Question 4 of 24 poss terms. point(s) possible \[ \frac{x^{3}-64}{x-4} \] Submit quiz \[ \frac{x^{3}-64}{x-4}= \] \( \square \) an example Textbook Next
Q6. In how many ways can the letters of the word "BALLOON" can be arranged? (2 marks)
1/Student/PlayerTest.aspx?test/d=269805872\%centerwin =yes -wk), Spring 2025, Ivanova Donna Question 3 of 24 This qu possible This que Find the quotient using long division. point(s) pc \[ \frac{15 x^{2}+27 x+9}{5 x+4} \] \[ \frac{15 x^{2}+27 x+9}{5 x+4}= \] \( \square \) example Textbook
m/Student/PlayerTest.aspx?testld \( =269805872 \& \) centerwin \( = \) yes 12-wk), Spring 2025, Ivanova Donna Cornish a | 03/29/25 9:25 A Question 2 of 24 This quiz: 100 point(s) possible This question: 5 point(s) possible Resume Write a system of equations in \( x \) and \( y \) describing…
This quiz: 100 Question 1 of 24 possible This question: 4 point(s) possible Divide. \[ \frac{-6 x^{7}+2 x^{4}-8}{2 x^{2}} \] \[ \frac{-6 x^{7}+2 x^{4}-8}{2 x^{2}}= \] (Simplify your answer. Use positive exponents only.) View an example Textbook earch
Answer \[ x= \] \( \square \)
12. The minute hand of a clock is 14.4 cm long. How far does the tip of the minute hand move between \( 12: 00 \) and \( 12: 15 \) ?
Q4. Find the number of ways in which 7 people can be seated on a round table. (2 marks)
1. \( 5,845+24,768-9,651-7,325= \) (A) 13,637 (B) 13,647 (C) 20,962 (D) 23,288
< Question 19 of 21 This quiz: 100 point(s) possible This question: 5 point(s) possible Rest Find the domain and range of the function graphed. Subn A. domain: \( [5, \infty) \); range: \( (-4, \infty) \) B. domain: \( (-\infty, \infty) \); range: \( 1-4 \) C. domain: \( (-\infty, \infty) \),…
11. A running track has two semicircular ends of radius 34 m and two straights of 93.2 m as shown. Calculate the total distance around the track to the nearest metre.
Question 18 of 21 This quizi 100 point(s) posalble This question: 4 poini(s) possible Use the graph of f below to find f(0). \[ (0) \equiv \] \( \square \) A View an example Get more help . Search
Find \( h(-5), h(0) \), and \( h(5) \) for the following function. \[ h(x)=5 x^{2}+4 \] \[ h(-5)= \] \( \square \) \( \mathrm{h}(0)=\square \) (Simplify your answer.) \( \square \) \( h(5)=\square \) (Simplify your answer.) \( \square \) View an example Get more help - Search
Donna Cornish \( \& \) | 03/29 Question 16 of 21 This quiz: 100 point(s) possible This question: 4 point(s) possible Determine whether the graph is the graph of a function. \( s \) Is the graph the graph of a function? No Yes example Get more help - Next
\[ \begin{array}{l} -4 k^{2}+20 k+23=0 \\ k_{1,2}=\frac{-20 \pm \sqrt{400-368}}{8}=- \end{array} \] \[ 4 k^{2}+20 k+23=0 \]
Determine if the given relation is also a function. \[ \{(0,5),(0,-2),(0,9)\} \] Is the relation a function? Yes No w an example Get more help .
Question 13 of 21 Find an equation of the horizontal line through \( (9,4) \). The equation is \( \square \) (Type your answer in standard form.)
10. How many complete revolutions does a cycle wheel of diameter 60 cm make in travelling 400 m ?
wk), Spring 2025, Ivanova Donna Cornish 03/29/ This quiz: 100 point(s) Question 12 of 21 possible This question: 5 point(s) possible Find an equation of the vertical line through \( (-3,9) \). The equation is \( \square \) (Type your answer in standard form.) View an example Get more help…
2025, Ivanova Donna Cornish 03/29/25 8:58 AM Question 11 of 21 This quiz: 100 point(s) possible This question: 5 Resume lat point(s) possible Submit quil Find an equation of the line passing through the pair of points \( (2,3) \) and \( (-4,-4) \). Write the equation in the form \( A x+B y=C…
\( =2698058648 \) centenwin zyes Donna Cornish Question 10 of 21 \( A x+B y=C \). This quiz: 100 point(s) possible This question: 5 point(s) possible Resume Submit qu \[ m=\frac{3}{2},(9,-8) \] 5 Choose the equation of the line in the form \( A x+B y=C \) A. \( 3 x+2 y=43 \) B. \( 3 x-2 y=43…
\( (2 y-7)^{2}+(y-6)^{2}=2 \)
Determine whether this pair of lines is parallel, perpendicular, or neither. \[ \begin{array}{l} 7+2 x=4 y \\ 4 x+2 y=5 \end{array} \] Choose the correct answer below. A. These two lines are neither parallel nor perpendicular. B. These two lines are parallel. C. These two lines are…
This question: 5 point(s) possible -ind the slope of the line. \[ 7 x-2 y=14 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. The slope of the line is \( \square \) (Type an integer or simplified fraction.) B. The slope of the line is…
Find the slope of the line that passes through the given points. \( (-4,-5) \) and \( (-1,-6) \) Select the correct choice below and, if necessary, fill in the answer box within your choice A. The slope is \( \square \) . (Type an integer or a simplified fraction.) B. The slope is undefined. w…
10. Which of the following is not a criterion for congruence of triangle? (a) SAS (b) SSA (c) ASA (d) \( 5 s s \) 11. If \( \triangle A B C \cong \triangle P Q R \), then which of the following is not true? (a) \( -A C=P R \) (b) \( B C=P Q \) ( \( \delta \) ) \( Q R=B C \)
10. Which of the following is not a criterion for congruence of triangle? (a) SAS (b) SSA (c) ASA (d) \( 55 s \)
3 A supermarket sells 110 g tubes of toothpaste for \( \$ 3.19 \), and 160 g tubes of toothpaste for \( \$ 3.99 \). a Calculate the price per 10 g for each size tube. b Which size tube is better value for money? c. The supermarket offers a " 3 for 2 " deal where if you buy two 110 g tubes of…
9 In figure \( A B \| C D \), the value of \( x \) is (a) \( 75^{\circ} \) (b) \( 40^{\circ} \) (c) \( 65^{\circ} \) (d) \( 35^{\circ} \)
Q2. The marks obtained by 50 students in a math exam are grouped as follows: \begin{tabular}{|l|l|} \hline \begin{tabular}{l} Cass interval \\ (marks) \end{tabular} & Frequency (f) \\ \hline \( 10-20 \) & 5 \\ \hline \( 20-30 \) & 8 \\ \hline \( 30-40 \) & 12 \\ \hline \( 40-50 \) & 6…
Q1. The marks obtained by the 10 students in a math's tests are: \[ 45,50,55,60,65,70,75,80,85,90 \] a). Find the mean of the marks. (1 mark) b). Calculate the standard deviation. (2 marks)
\( x^{2}-3 x-10=0 \)
\( \begin{array}{l}x^{2}-3 x-10=0 \\ (x+5)(x-2)\end{array} \)
\( \begin{array}{l}-8 p+20 q=-16 \\ -20 p-8 g=-156\end{array} \)
3. Let \( v_{1}, v_{2}, v_{n} \) be vectors in a Space \( v \) and Let their span be \( \omega=\operatorname{Span}\left[v_{1}, v_{2}, v_{1}\right] \) Show that \( w \) is a subspace of \( v \).
2. Let \( T: \mid R^{2} \rightarrow \mathbb{R}^{2} \) be a linear transformation such that \( T(v)=\binom{1}{2}, T\left(v_{2}\right)=\binom{4}{2} \) and let \( v_{1}=\binom{1}{1} \) and \( V_{2}\binom{2}{1} \) and \( \omega=\binom{5}{7} \) Express \( T(w) \) in terms of \( v_{1} \) and \( v_{2}…
GR 12 GENERAL MATHEMATICS M2 TOPIC TEST 1 0 Suss Substitute for \( A, P \) and \( T \) in the formula \( A=P(1+r)^{T} \); given that \( A=1000000 \), \( \therefore P=10000 \) and \( T=2 \), and express as quadratic equation. (1 mark)
2. Show that the Linear Span qo set of vectors \( x, x, x, b, x \) a vector subspace of vector spale \( v \)
Calculate the amount (principal) that must be invested at \( 6 \% \) p.a. interest compounded annually to have K5 000 at the end of 4 years. (1 mark) Answer: \( \qquad \) A new Mazda BT-50 costs K96 990 now. The price increases at the same rate as inflation. If the rate of inflation is \( 5.5…
\( A=3500(101565)^{28} \) Answer: \( A=5386 \cdot 5 \) Calculate the simple interest on K5 000 at a rate of \( 8 \% \) p.a. over 4 years. (1 mark) \( \qquad \) \( \qquad \) 8. Calculate the amount (principal) that must be invested at \( 6 \% \) p.a. interest compounded annually to have K5 000…
[ N \( \circlearrowleft \) [ 15 II ) II v [ urses/159/quizzes/892/take/questions/2590 Which of the following sentences does NOT correctly use a fractio expression to indicate proportion? The theater was two-half full last night. Three-eighths of the cake was left untouched. Half the employees…
GR 12 GENERAL MATHEMATICS M2 TOPIC TEST 1 Apply logarithm to evaluate T given \( 644204=400000(1+10 \%)^{\top} \), by first simplifying the equation. (1 mark) Answer: \( \qquad \) 6. Use the compound interest formula to calculate the amount of a fixed term investment of K3 500 over 7 years at…
Part 2: A) Construct a difference 1) \( 6,9,14,26,50,91 \), ?
organized Additional Activities Solve the following. Write your answers on a separate sheet of paper. 1. Jessie is making a circular tablecloth for an art project. She wants half of the table cloth to be made of plain-colored fabric and half to be made of printed fabric. If the diameter of the…
Write the given equation in the form of \( a x+b y+c=0 \). \[ -2 x+4 y=7 \] \[ a=-2 \] \[ b= \] \( \square \) \( c= \) \( \square \)
Andrei wants to fill a glass tank with spherical marbles and then fill the remaining space with water. The variable \( w \) models the amount of water (in liters) Andrei uses if he uses \( n \) marbles. \[ w=32-0.05 n \] What is the volume of each marble? \( \square \) liters
How many solutions does the system have? You can use the interactive graph below to find the answer. \[ \left\{\begin{array}{l} 12 x+9 y=-36 \\ 4 x+3 y=-12 \end{array}\right. \]
Write an equation that represents the line. Use exact numbers.
Write the given equation in the form of \[ a x+b y+c=0 . \] \[ x=4 y \] \[ a=1 \] \[ b= \] \( \square \) \( c= \) \( \square \)
\[ a x+b y+c=0 . \] \[ 2=3 y \] \[ b=3 \] \[ a= \] \[ c= \] \( \square \)
Q.13. When a positive integer is divided by \( d \), the remainder is 15 . When ten times of the same number is divided by \( d \), the remainder is 6 . The least possible value of \( d \) is: SSC CGL 5 /03/2020 (Afternoon) (a) 9 (b) 12 (c) 16 (d) 18
The sum of the number of factors of the number \( N \) and \( N^{2} \) is 34 . How many such distinct numbers \( N<150 \) exist? (2010
Q.10. Which of the following numbers will completely divide \( 7^{81}+7^{82}+7^{83} \) ? SSC CHSL 17/03/2020(Morning) (a) 399 (b) 389 (c) 387 (d) 397
6:34 Course challenge You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that…
\( d \div 6 \)
Try It! Quipper Given \( f(x)=x^{3}+x^{2} \), solve for \( f^{\prime}(1) \). Interpret what this value means.
6:31 Course challenge You might need: 囲 Calculator What is the length of \( \overline{A C} \) ? \( \square \) units (A) Do 30 problems Skip Check
function f(x) shows the graphof the \( 0 \leq x \leq 5 \). \( f(x)=|2 x-1| \), forthe domain State (a) the value of (b) the (b) the range of \( f(x) \) corresponding to the Ans: (a) \( 1=1 \quad\left[3 \mathrm{marks}_{s]}\right. \) \( f(x)=\mid 2 x-11 \) \( 1.12 x-1 \) i) \( z_{n-1}…
12. Use Structure Point \( B \) has coordinates \( (2,1) \). The \( x \)-coordinate of point \( A \) is -10 . The distance between point \( A \) and point \( B \) is 15 units. What are the possible coordinates of point \( A \) ?
2. A company sells bags of coffee, and the weight of each bag is normally distributed with a population mean of 500 grams and a standard deviation of 15 grams. The company takes random samples of 36 bags of coffee to monitor the average weight. a) What is the mean of the sampling distribution…
6:21 Course challenge A polynomial \( p \) is graphed. What could be the equation of \( p \) ? Choose 1 answer: (A) \( p(x)=(x+3)(x+1)^{2}(2 x-1) \) (B) \( p(x)=(x+3)^{2}(x+1)^{2}(2 x-1) \) (C) \( p(x)=(x+3)^{2}(x+1)(2 x-1) \) (D) \( p(x)=(x+3)(x+1)(2 x-1)^{2} \) (A) 27 of 30 Skip Check
6:20 Course challenge Consider the polynomial function \[ h(x)=x^{6}-3 x^{5}-17 x^{3} \] What is the end behavior of the graph of \( h \) ? Choose 1 answer: (A) As \( x \rightarrow \infty, h(x) \rightarrow \infty \), and as \( x \rightarrow-\infty \), \( h(x) \rightarrow \infty \). (B) As…
6:19 Course challenge You might need: 囲 Calculator Angle \( A \) is circumscribed about circle \( O \). What is the measure of \( \angle A \) ? \( \square \) 。 (A) 24 of 30 Skip Check
6:19 Course challenge You might need: 㘣 Calculator A certain circle can be represented by the following equation. \[ x^{2}+y^{2}-2 x-10 y+17=0 \] What is the center of this circle? \( \square \) \( \square \) What is the radius of this circle? \( \square \) units (A) 22 of 30 Skip Check
7. Prepare regret table from the given conditional profit table: \begin{tabular}{|c|c|c|c|c|} \hline \multirow{2}{*}{ Event (Demand) } & \multicolumn{4}{|c|}{ Act (Purchase) or Decision Alternatives } \\ \cline { 2 - 5 } & 25 & 26 & 27 & 28 \\ \hline 25 & 50 & 42 & 34 & 26 \\ 26 & 50 & 52 & 44…
3. The age of Toni's dad is six times his age and the age of Toni's mom is two less than the age of his dad. 3 years ago, the sum of the ages of Toni's parents is equal to five times Toni's age in 5 years plus his age three years ago. Find the age of Toni's parents 2023 Edition - All Rights…
What is the arc measure, in degrees, of minor arc \( \overparen{A C} \) on circle \( P \) below?
8. Dia gram above shows the graph of the function \( f(x)=|2 x-1| \), for the domain \( 0 \leq x \leq 5 \). State (a) the value of \( t \), (b) the range of \( f(x) \) corresponding to the given domain. [3 marks] Ans: (a) \( t=\frac{1}{2} \), (b) \( 0 \leq f(x) \leq 9…
4. Pmi : 12. Given that \( f: x \rightarrow x+-5 \), find (a) \( f(3) \) (b) the vatue of \( k \) such that \[ 2 f^{-1}(k)=f(3) \] [3 marks] Ans: (a) 8, (b) \( k=9 \) \[ \text { Let } y=f(x) \] \[ \begin{array}{rl} f f(b)=3+5 & \text { fet } y=+ \text { y } \\ =8 & y=x+5 \end{array} \] b) \[ 1…
The linear density expression for FCC [110] direction in terms of the atomic radius R is LD = 2√2R.
Math 030-1 UNIT 6 ASSIGNMENT Trigonometry Equations Problem ( Total: 12 marks) 1. a) Algebraically solve sec²? - 2tan? = 3. State the general solution to the nearest degree. (Hint: to solve a quadratic equation, either factor if possible or use the quadratic formula.) (3 marks) b) Explain…
Reflect on your philosophy of guiding young children’s positive behaviors. How is your professional philosophy similar or different from how you were guided as a child? How do you constructively deal with young children’s challenging behaviors?
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