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Algebra Q&A Archive of August 28, 2025

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August 28 of 2025

Which is a composite number? 81 61 41 71

An architect has a 1:30 scale drawing of the floor plan for a new house. The floor plan shows that the dimensions for the master bedroom are $ 5 \frac{3}{4} $ inches wide by $ 6 \frac{1}{2} $ inches long. What are the actual dimensions of the master bedroom? $ 35 \frac{3}{4} $ inches…

INSTRUCTIONS Convert the following units: D. Weight (3 items) E. Time (2 items) 9. Convert 2.5 kg to grams. 12. Convert 3 hours to seconds. 10. Convert 3000 g to kilograms. 13. Convert 2 years to days. 11. Convert 50 pounds to F. Temperature (2 items) kilograms. 14. Convert \( 25^{\circ}…

INSTRUCTIONS Convert the following units: A. Length (3 items) 1. Convert 5 km to meters. C. Volume (3 items) 2. Convert 250 cm to meters. 6. Convert 1.5 L to mL . 3. Convert 12 inches to 7. Convert 3. $ \mathrm{m}^{3} $. to liters. centimeters. B. Area (2 items) 8. Convert 10 gallons (US) to…

CLASS - VII, SUBJECT - MATHEMATICS CHAPTER 4(EXPONENTS AND POWERS) WORKSHEET, (BASIC LEVEL) Choose the correct option ( $ 10 \times 1=10 $ ) $ 1.8^{3} \times 8^{4} $ is equal to a. $ 8^{12} $ b. $ 64^{7} $ c. $ 2^{21} $ d. none of these 2. Which of the following is not equal to \( 3…

ole: Tutorial 33 of 35 Save \& Ext What is the solution of this equation? \[ -6+5 x=6 x-7 \] Enter the correct answer. DONE.

Variable: Tutorial VAXNICiThc3NpZ25tZW50LZE 32 of 35 Save \& Exit What is the solution of this equation? \[ -2 y+13=17 \] Enter the correct answer. DONE

31 of 35 Save \& Ext What is the solution of this equation? \[ 8+\frac{1}{3} x=-1 \] Enter the correct answer. DONE

What is the solution of this equation? \[ \frac{1}{2} a=-5 \] Enter the correct answer. DONE

ble: Tutorial 28 of 35 Save \& Ext What is the solution of this equation? \[ w-7=13 \] Enter the correct answer. DONE

the Variable: Tutorial 25 of 35 Save \& Exit \[ -16=\frac{1}{2} s-20 \] $ r $ answer by What is the solution of the equation? the original Click on the correct answer. 4 72 8

ble: Tutorial 24 of 35 Save \& Exit \[ s=-4 s+30 \] What is the solution of the equation? Click on the correct answer. \[ \begin{array}{c} s=-6 \\ s=6 \\ s=-10 \end{array} \]

ariable: Tutorial 23 of 35 Save \& Exit \[ \frac{1}{4} z-9=1 \] What two steps could you use to solve the equation? Click on the correct answer. First subtract 9 from both sides. Then multiply both sides by 4 . First add 9 to both sides. Then multiply both sides by 10 . First add 9 to both…

of 35 Save \& Exit \[ 7 x=-2 x-18 \] What two steps could you use to isolate $ x $ ? Click on the correct answer. First subtract $ 7 x $ from both sides. Then subtract 18 from both sides. First add $ 2 x $ to both sides. Then divide both sides by 9. First add $ 2 x $ to both sides.…

riable: Tutorial 18 of 35 Save \& Exit \[ 2 x=14 \] What could you do to isolate the variable? Click on the correct answer. Multiply both sides by 2 . Divide both sides by $ 2 x $. Divide both sides by 2 .

Iutorial 16 of 35 Sav \[ 5 x+4=-11 \] What could you do to further isolate the variable? Click on the correct answer. Subtract $ 5 x $ from both sides. Subtract 4 from both sides. Add 4 to both sides.

iable: Tutorial 14 of 35 Save \& Exit \[ 2 x+4=-3 x-11 \] What could you do first to isolate the variable? Click on the correct answer. Subtract $ 3 x $ from both sides. Add $ 2 x $ to both sides. Add $ 3 x $ to both sides.

riable: Tutorial 12 of 35 Save \& Exit \[ 3 x+5=2 x+7 \] How will the equation look if you subtract $ 2 x $ from both sides? Click on the correct answer. \[ 3 x+5=7 \] \[ 5 x+5=7 \] \[ x+5=7 \]

8 of 35 Save \& Exi Solve the equation for $ x $. \[ x+7=13 \] Enter the correct answer.

d) Consider the binary operation $ a * b=a+b-2 a b $, where $ a $ and $ b $ are real numbers. (i). Is * commutative? Justify your answer (ii) Compute $ 3^{*}\left(2^{*} 1\right) $

You begin climbing Mt Whitney ( 4420 m ) from your campsite, where the elevation is 2240 m and the temperature is $ 23^{\circ} \mathrm{C} $. Using the environmental lapse rate, what would you expect the temperature to be when you arrive at the top? View Available Hint(s) \( 10^{\circ}…

What is the area, in square inches, of the shape below?

The function $ f(x)=\frac{5}{x+7} $ and $ g f(x)=\frac{x-3}{x+3} $ What is the value of $ g(1) $

10. The digit in the units place of the cube of 47 is (a) 9 (b) 7 (c) 3 (d) 1 11. The least possible value of $ A $ for which $ 90 \times \mathrm{A} $ is a perfect cube is (a) 200 (b) 300 (c) 500 (d) 600

POSSIBLE POINTS: 25 Using the picture, give an example for each of the following descriptions. Number each answer. 1. A line of intersection of two planes 2. The point of intersection of two lines 3. Three coplanar points 4. Three collinear points B I $ \underline{\mathrm{v}} $ 0 / 10000…

3. Translate pre-image coordinates using the rule and ( $ \mathbf{x} $-11), then reflect over the $ \mathbf{x} $-axis. Pre-Image Coordinates: $ A(8,0) B(-1,9) C(-1,0) $ Post Image Coordinates: A' $ \qquad $ B' $ \qquad $ C' $ \qquad $ A" $ \qquad $ B" $ \qquad $ C" \( \qquad…

4 Determine the remainder that would occur if $ \left(4 x^{3}-5 x^{2}+7 x-3\right) $ were divided by $ (x-3) $

Relation Between Multiplication and Division When we multiply two numbers, we get the product. This product can be divided by any of its factors. Example: Remember - Multiplication and division are inverse operations. For every multiplication fact, we have two division facts. Multiplication…

Divide: (a) $ 5 \longdiv { 2 5 } $ (b) $ 6 \longdiv { 4 8 } $ (c) $ 7 \longdiv { 6 3 } $ (d) $ 9 \longdiv { 4 5 } $ (e) $ 6 \longdiv { 3 6 } $ (f) $ 7 \longdiv { 4 2 } $ (g) $ 6 \longdiv { 5 4 } $ (h) $ 8 \longdiv { 3 2 } $

100 Morefaces, vertices and edges Thinkl Look at these nets of geometric solids. How many faces, vertices and edep. does each solid have? 1. Write labels with arrows pointing to the geometrical figures which you can see in each object, and write down how many of each the object contains. 3…

Formative tests Abisana Rakeshkumar 3. Exemplar example problems III 1 2 3 Question: 2 m . 1. Arnav buys a book costing Rs. 600 . If the rate of sales tax is $ 7 \% $, then the total mount payable $ y $ him is Rs. 642 . $ \square $ 2. After allowing a discount of $ 15 \% $ on the…

Formative tests Abisana Rakes imar 2. Exemplar example problems 1 2 3 Question: 2 m . Amna purchased a toy for Rs. 660 including sales tax. If the rate of sales tax is $ 10 \% $, then the selling price of the toy is Rs. $ \square $ . Send answer! Copyright © 2025 YaClass Tech Private…

Question 30 1 pts When we divide monomials, the quotient can have a negative exponent. What should at a den A. Remove the negative sign in the exponent to make it positive. B. Treat the quotient obtained as the that answer. C. Get the pase wentive the and then D. Dopy hify , divide the…

1 pts Question 27 What is the quotient when $ x^{4}-2 x^{3}-3 x^{2}-4 x-8 $ when divided by $ x-2 ? $

1 pts Question 26 What must be subtracted from $ 4 x^{3}-7 x^{2}+3 x-5 $ to get zero? A. $ 4 x^{3}-7 x^{2}+3 x-5 $ C. $ 4 x^{3}+7 x^{2}+3 x-5 $ B. $ 4 x^{3}-7 x^{2}-3 x+5 $ D. $ -4 x^{3}+7 x^{2}-3 x+5 $ $ \square $ Next Previous

Question 25 1 pts Perform the indicated operations: $ \left(20 v^{2}-9 v^{3}\right)-\left(7 v^{3}-10 v^{4}-14 v^{2}\right) $ A. $ 10 v^{4}-16 v^{3}+34 v^{2} $ B. $ -10 v^{4}-16 v^{3}+34 v^{2} $ C. $ 10 v^{4}-2 v^{3}+34 v^{2} $ D. $ 10 v^{4}-16 v^{3}+6 v^{2} $

https//www-awu.aleks.com/alekscy Real Numbers Addition or subtraction of fractions Add. \[ \frac{2}{9}+\frac{11}{12} \] Write your answer as a fraction in s $ \square $ $ \square $

5. Write cubes of five natural numbers which are multiples of 3 and verify the following: 12. 'The cube of a natural number which is a multiple of 3 is a multiple of $ 27^{\prime} $.

4. A train travels 700 metres in 35 seconds. What is its speed in $ \mathrm{km} / \mathrm{hr} $ ?

Add and reduce. 1. \begin{tabular}{rrrrr} $ \frac{3}{4} $ & $ \frac{2}{3} $ & $ \frac{7}{8} $ & $ \frac{5}{6} $ & $ \frac{5}{9} $ \\ $ +\frac{1}{2} $ & $ +\frac{5}{6} $ & $ +\frac{3}{4} $ & $ +\frac{1}{3} $ & $ +\frac{2}{3} $…

1 pts Question 23 What is the sum of $ 10 x^{2}-12 x+2 $ and $ 12 x^{2}-5 x-9 $ ? C. $ 22 x^{2}-7 x-7 $ A. $ 22 x^{2}+17 x-7 $ D. $ 22 x^{2}-17 x-7 $ B. $ 22 x^{2}-7 x-11 $ Next *

On Saturday mornings, Zach volunteers at the hospital where his mother works. One Saturday, he answers phone calls at the information desk while the receptionist is away. Then he spends 20 minutes delivering flowers to patients' rooms. In all, Zach volunteers at the hospital for 60 minutes that…

Question 21 1 pts Two sides of a triangle are $ (x+2) \mathrm{cm} $ and $ (2 x-3) \mathrm{cm} $. If the perimeter is $ (5 x+7) \mathrm{cm} $, what is the third side?

Question 19 1 pts What must be multiplied to $ (x+3) $ to get $ \left(x^{3}+x^{2}-3 x+9\right) $ ? A. $ x^{2}-2 x+3 $ B. $ x^{2}+2 x+3 $ C. $ x^{2}-2 x-3 $ D. $ x^{2}-2 x+18 $

Question 17 1 pts Which of the following expressions does not belong to the group? A. $ (a+b)^{2} $ C. $ (a+b+p)^{2} $ B. $ a(b+c) $ D. $ (a+b)^{3} $ $ \square $ Previous Next

Use small letter for variables Question 18 1 pts The expression $ 4 x^{2}-36 x+k $ is the expanded form of $ (2 x-9)^{2} $. What is the value of $ k $ ? A. -81 C. 18 B. -18 D. 81 $ \square $

EXAMPLE 1. $ \frac{1}{1^{2}}+\frac{1}{2^{2}}-\frac{1}{3^{2}}-\frac{1}{4^{2}}+\frac{1}{5^{2}}+\frac{1}{6^{2}}-\cdots $ is absolutely converger

5. $ \frac{-\frac{3}{2} \sqrt[4]{15}}{-\frac{1}{6} \sqrt[4]{5}} $

Part 2: Find the product of the expressions. 6.) $ \left(6 x^{2}\right)\left(4 x^{2}\right) $ 7.) $ \left(3 x^{3} y^{2}\right)\left(-6 y^{5}\right) $ 8.) $ \left(5 p^{3}\right)\left(-m^{2} p^{2}\right) $ 9.) $ \left(10 g^{3} h^{5} v^{6}\right)\left(11 g h^{8}\right) $ 10.) \( \left(4…

10. Which of the following is the equation of a line that passes through $ (-2,-1) $ and $ (-4,-3) $ ? A. $ y=\frac{1}{2} x+1 $ B. $ y=x+1 $ C. $ y=\frac{1}{2} x-1 $ D. $ y=x-1 $ MacBook Air

8. Which of the following is equivalent to the expression $ (3 a b)(-5 a b) $ ? A. $ -2 a b $ B. $ -2 a^{2} b^{2} $ C. $ -15 a b $ D. $ -15 a^{2} b^{2} $

Simplify each expression for $ x=4 $. a. $ -5 x^{-4} $ b. $ 7 x^{-3} $ 17. Evaluate each pair of expressions. a. $ (-3)^{-8} $ and $ -3^{-8} $ b. $ (-3)^{-9} $ and $ -3^{-9} $ e Precise To win a math game, Lamar has to pick a card with an pression that has a value greater than 1 .…

Student Profile bil. 8/26/25-25f) 121. Quizzes - 25F/ My Sign-Ins I How to do 9/F Solution 3483 ISA Modity M x .edu/d21/lms/quizzing/user/attempt/quiz_start_frame_auto.d2|?ou=20235118isprv=8iqi=47283258cfq|=18idrb=08from08=02inProgress=0 Pre-Assessment Page 1: \begin{tabular}{|l|l|l|} \hline…

(1) $ \triangle A B C, M C(B C), 2 B M=3 C M \frac{\text { AABM }}{\text { AACM }}= $ ?

AUG25-P176 Student Profile bri. 8/26/25-25F learning.suny.edu/d2t/ms/quizzing/ My Sign-Ins | How to do 9/3 Pre-Assessment Question 23 (1 point) Find the product. \[ (4 z-1)(5 z-6) \] $ 20 z^{2}+6 $ $ 9 z^{2}-7 $ $ 20 z^{2}-19 z+6 $ $ 20 z^{2}-29 z+6 $ Question 24 (1 point) Multiply.…

Student Profile BIL 8/26/25-251 pric Quizzes - 258 My Sign-ins | How to do 9 Pre-Assessment 10 11 12 Question 22 (1 point) 13 14 15 Multiply. $ 5 x^{6}\left(2 x^{6}-10 x^{2}-4\right) $ 16 17 18 $ 10 x^{6}-50 x^{2}-20 $ 19 20 21 $ 10 x^{12}-50 x^{8}-20 x^{6} $ \( 10 x^{12}-50 x^{8}…

Pre-Assessment 0.00027 10 11 12 13 14 15 $ \checkmark $ 16 17 18 楼 $ \checkmark $ 19 20 21 -- 22 23 24 -- -- -- 25 26 27 -- 28 29 30 -- 31 -- Quiz Information Question 20 (1 point) Add the polynomials. $ \left(7 y^{6}-5 y^{5}+5 y\right)+\left(6 y^{6}-3 y^{5}-8 y\right) $ \( 13 y^{12}-8…

Order the following from least to greatest: $ 2 \sqrt{5} $ 455\% $ \frac{40}{9} $ $ 4.4 \overline{6} $ $ 4 \frac{2}{5} $

ding.suny.edu/d2/M/ms/quizzing/user/attempt/quiz_start_frame_auto.d2|?ou=20235118isprv=8qi=4728325\&cfql=18: Pre-Assessment Question 16 (1 point) $ \checkmark $ Saved Express in simplest form. \[ y^{6} \cdot y^{10} \] $ y^{60} $ $ 2 y^{60} $ $ y^{16} $ $ 2 y^{16} $ Question 17 (1…

SOLVE NUMERICALLY THEN WITH ALGEBRA A farmer wants to build a rectangular pen using 40 meters of fencing. One side is along a wall and doesn't require fencing. What dimensions would give the following areas (try solving numerically and algebraically): 150,182 , and 192 . What do you think is…

Question 10 1 pts When the preset and clear inputs to a JK flip-flop are HIGH, which of the following statement is true? The Q output is immediately cleared The Q output is an ambiguous state The flip-flop is free to respond to its J, K, and clock inputs The Q output is immediately set to 1

7. Tushar spent $ 2 \frac{1}{4} $ hrs. for completing his homework while Sunny took $ \frac{9}{5} \frac{12}{5} $ hrs. Who took more time for completing the homework ? 8. Ms. Aruna bought $ 15 \frac{1}{4} \mathrm{~kg} $ of apples and Ms. Meena bought $ 15 \frac{2}{3} \mathrm{~kg} $ of…

a) Find $ \lambda $ for which the matrix $ \lambda I-A $ is a singular matrix if where $ I $ is an identity Matrix given that $ A=\left(\begin{array}{lll}3 & 2 & 4 \\ 2 & 0 & 2 \\ 4 & 2 & 3\end{array}\right) $ (5 marks)

5-P176 Student Profile 8/26/25-25f (1). Quizzes : 25 F My Sign-Ins | How to do 9 ) Pre-Assessment Page 1: 1 2 3 4 5 6 $ \checkmark $ 7 8 9 $ \checkmark $ 10 11 12 $ \checkmark $ 13 14 15 -- 16 17 18 -- 19 -- 20 -- 21 -- 22 23 24 -- -- 25 26 27 -- -- Question 15 (1 point) Simplify…

For a D flip-flop with inputs $ \mathrm{A}, \mathrm{B} $ and output Y , which expression is true assuming Y is initially 0 ? When $ \mathrm{A}=1 $ and $ \mathrm{B}=0 $, and CLK $ =1 $ then, $ \mathrm{Y}=1 $ When $ \mathrm{A}=1 $ and $ \mathrm{B}=1 $, and \( \mathrm{CLK} \uparrow…

$ c^{2} d x^{13} $ 9. From school A our of 650 snutem then 25,7 less number of apples? $ \frac{12}{12} \cdot \frac{}{12} $ $ \frac{7}{12}, \frac{9}{12} $ selected for essay writing and from $ B $ our of 759 scridents. 300 weres alent like 20 seles of 759 smidents 3 pers selested? 大 \(…

The following 4 input K -map (where A is LSB and D is MSB ) can also be represented by the function: \begin{tabular}{ccccc} & C $ ^{\prime} $ D $ ^{\prime} $ & C $ ^{\prime} $ D & CD & CD $ ^{\prime} $ \\ \hline A $ ^{\prime} $ B $ ^{\prime} $ & 0 & 0 & 0 & 0 \\ \hline A \(…

(e) Petros' dicam car eureatly custs R350 DOX. He bas inheried a large sum of money and decided to set aside enough to be able to huty the car in 3 years' time. However, the ear will cost more by then: inflation must be calculated at $ 8 \% $ p.a His savings account offers $ 3,5 \% $ p.s.…

9. From school A out of 650 students, 250 were selected for essay writing and from another school B out of 750 students, 300 were selected. From which school, more students were selected?

a) Find $ \lambda $ for which the matrix $ \lambda l-A $ is a singular matrix if where $ l $ is an identity $ M $ \[ A=\left(\begin{array}{ll} 4 & 1 \\ 3 & 2 \end{array}\right) \]

176 Student Profile 8/26/25-25F prl. Quizzes - 25F/ My Sign-Ins | How to do 9/e Solution 3483 JSA_Modify .suny.edu/d2//ms/quizzing/user/attempt/quiz_start_frame_auto.d2lใou=2023511\&isprv=\&qi=4728325\&cfq|=18dnb=0\&fromQB=02inProgress=0 Pre-Assessment Page 1: \( \checkmark…

(4) If $ \left(\begin{array}{rrr}4 & 3 & m \\ -2 & 0 & 5\end{array}\right)\left(\begin{array}{rr}3 & -2 \\ 1 & 0 \\ 4 & n\end{array}\right)=\left(\begin{array}{rr}11 & -13 \\ 14 & 29\end{array}\right) $,

\( \begin{array}{l}\left.H_{w}=\left[H_{3} \mathrm{O}^{+}\right] \cdot\left[\mathrm{OH}^{-}\right]=\mid 1,00 \cdot 10^{-8}+x\right) \cdot x=10^{-4} \\ \quad 1,00 \cdot 10^{-8} x+x^{2}-10^{-4}=0 \\ x^{2}+1,00 \cdot 10^{-8} x-10^{-4}=0 \\ D=\left(-1,00 \cdot 10^{-8}\right)^{2}+4 \cdot 1…

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours as shown. If each piece measures $ 10 \mathrm{~cm}, 30 \mathrm{~cm} $ and 30 cm , find the total area of the cloth required for the umbrella.

If each side of a triangle is changed to $ x $ times the original, by what factor does the area change? The area also becomes $ x $ times the original. The area becomes $ x^{2} $ times the original. The area doesn't change. The area becomes $ \sqrt{x} $ times the original.

If each side of a triangle is tripled, by what factor does the area increase? $ \square $ times

8:21 AM Thu Aug 28 $ 37 \% $ f1.apps.elf.edmentum.com Previous 1 Next Dividing a Line Segment: Mastery Test Submit Test Tools Info 1 Select the correct answer from each drop-down menu. A square is constructed on side $ \overline{A D} $ of quadrilateral $ A B C D $ such that \(…

8:22 AM Thu Aug 28 $ 37 \% $ f1.apps.elf.edmentum.com Dividing a Line Segment: Mastery Test Try Ace AI STEM Tutor by Numerade Previous 2 Next Dividing a Line Segment: Mastery Test Submit Test Tools Info Consider the directed line segment $ A B $. If point C divides the line segment in the…

- Find the volume of the box determined by \[ \mathbf{u}=2 \mathbf{i}+\mathbf{j}, \mathbf{v}=2 \mathbf{i}-\mathbf{j}+\mathbf{k}, \mathbf{w}=\mathbf{i}+2 \mathbf{k} \]

Quaution 1 1.1 Two motrices are equal if they have the rame dimmsions and their cressipanding enriver are equal 1.7 The product 18 of two motrices $ A $ and $ B $ is defined only when the number of adumes in $ A $ is equal to the number of tows. in $ B $. Question…

Each side of a triangle is doubled. By what factor does the area increase? Let's assume the sides to be $ a, b $, and $ c $. If each side is doubled, the sides will become $ 2 a $, $ \square $ $ b $, and $ \square $ .

A farmer needs to buy some fertilizer packets for his rice field. Each packet covers an area of 400 m 2 If his field is in the form of a triangle, whose sides measure $ 600 \mathrm{~m}, 800 \mathrm{~m} $ and 1 km , how many packets should he buy to cover the entire field?

20 Carı punca punca bagi persamaan kuadratik $ (2 x-1)^{2}=3 x-2 $ Find the mona of the quadratic degration $ (2 x-1)^{2}=3 x-2 $ A $ x=-\frac{3}{4} \cdot x=1 $ C $ x=\frac{3}{4}, x=1 $ B $ x=\frac{3}{4}, x=-1 $ D $ x=-\frac{3}{4}, x=-1 $

A traffic sign board is in the form of an equilateral triangle, whose side measures 12 in. Find the cost of painting it on both sides, if painting costs ₹ $ 10 / \mathrm{in}^{2} $. Take $ \sqrt{3} \approx 1.73 $.

A traffic sign board is in the form of an equilateral triangle, whose side measures 12 in . Find the cost of painting it on both sides, if painting costs ₹ $ 10 / $ in $ ^{2} $. Take $ \sqrt{3} \approx 1.73 $.

The perimeter of an isosceles triangle is 32 cm . If the ratio of the equal side to the unequal side is $ 5: 6 $, find the area of the triangle. $ \square $ $ \mathrm{cm}^{2} $

We obtained the sides as $ 0.9 \mathrm{~km}, 1.2 \mathrm{~km} $ and 1.5 km . We can finally use the Heron's formula to find the area of the field. \[ \mathrm{A}=\square \mathrm{km}^{2} \]

QUESTION 17 Write a mathematical equation for each of the following statements. a) The sum of a number $ y $ and twices the number is 15 . $ \qquad $ \[ S=y+30 \] (L mark) b) Yout weekly paycheck is $ 2,5 \% $ more than Peter. The total sum of your paychcoks is K1200. Find the amount of…

ABCDEFGIt represents a frustrum with a square base of 12 cm . If the original slanting edge was 44 cm . Task a) Calculate the original height of the pyramid b) Calculate the total surface area of the frustium c) Calculate the volume of the frustrum.

(e) Petros' dicam car eureatly custs R350 DOX. He bas inheried a large sum of money and decided to set aside enough to be able to huty the car in 3 years' time. However, the ear will cost more by then: inflation must be calculated at $ 8 \% $ p.a His savings account offers $ 3,5 \% $ p.s.…

QUESTION TWO a) Find $ \lambda $ for which the matrix $ \lambda I-A $ is a singular matrix if where $ I $ is an identity Matrix given that $ A=\left(\begin{array}{ccc}1 & 0 & 2 \\ 0 & -1 & -2 \\ 2 & -2 & 0\end{array}\right) $ (5 marks)

What is the length of $ B D $ ?

d) (i) Find the inverse of the matrix $ A=\left(\begin{array}{ccc}3 & -1 & 2 \\ 1 & 1 & 1 \\ 2 & 2 & -1\end{array}\right) $ (ii) Use your inverse above to solve the system of linear cyuations \[ \begin{array}{c} 3 x-y+2 z=4 \\ x+y+z=2 \\ 2 x+2 y-z=3 \end{array} \]

$ 4 x^{2}-20 x-200 $

If the perimeter of an equilateral triangle is 120 cm , then find its area. $ \square $ $ \mathrm{cm}^{2} $ Hint:

PRACTICE: SOLVING BASICS Question 15 of 16 (1 point) I Question Attempt: 1 of Unilmited SHAMAR Español 4 5 6 7 8 9 10 11 $ \checkmark 12 $ 13 14 15 16 Solve for $ w $. \[ 68-w=221 \] \[ w=[1] \] 5 $ \times $ Check Save For Later Submit Assignment 2025 McGraw Hill LLC. All Rights…

1/408/2005 ABCDEFGH represents a fustrum with a square base of 12 cm If the original slanting edge was 44 cm . Task a) Calculate the original height of the fyramid b) Cakulate the total surface area of the frustium 2) Calculate the rolume of the frustrum.

PRACTICE SOLVING BASICS Question 14 of 16 ( 1 point) - Question Attempt: 1 of Unilmited SHAMAR Español 4 5 6 7 8 9 10 11 12 13 14 15 16 Solve for $ u $. \[ 264=-u+33 \] ? \[ u=\llbracket \] 5 $ \times $ Check Save For Later Submit Assignment C 2025 McGraw Hillic. All Riohts Reserved,…

An isosceles triangle has a semi-perimeter of 25 cm and each of the equal sides is 15 cm . Find the area of the triangle. $ \square $ $ \mathrm{cm}^{2} $ Hint: Recall that if $ a, b $, and $ c $ are the sides of a triangle, then using Heron's formula we can calculate its area…

$ x^{2}+19 x+18 $

$ 5 x y \times\left(2 x^{3}-3 x y\right), x=4, y=-5 $

d) Consider the binary operation $ a * b=a+b-2 a b $, where $ a $ and $ b $ are real numbers. (i). Is * commutative? Justify your answer (ii) Compute $ 3^{*}\left(2^{*} 1\right) $

$ 49 x^{2}-16 $

If $ \sqrt{14} \approx 3.742 $, then what is the approximate value of $ \frac{5}{\sqrt{14}-3} ? $ $ \square $ (Round off the value to 3 decimal places.)

If $ \sqrt{10} \approx 3.162 $, then what is the approximate value of $ \frac{40}{\sqrt{10}}-2 ? $ $ \square $ (Round off the value to 3 decimal places.)

Express $ \frac{14}{\sqrt{6}} $ as a fraction with rational denominator. (Express the answer in simplest form.)

BINARY OPERATIONS 1. Define an operation *on the set of real numbers by $ a * b=b^{a} $ i). Is a binary operation on the set of real numbers ? Give reason for your Answer. ii). Is the operation commutative? iii). Evaluate $ (3 \cdot 2) \cdot-2 $ 2. Consider the binary cperation \( a \cdot…

MATHEMATICS 2. In the Fig.6.7, if $ \angle \mathrm{GDH}=\mathrm{x}, \angle \mathrm{DHK}=, 180^{\circ}-\mathrm{y} $ and $ \angle \mathrm{ABG}=(\mathrm{x}+\mathrm{y}) $, then show AB in CD . Fig. 6.7

1. $ 36.03 \mathrm{~m}=\square \mathrm{cm} $ 2. $ 5145800 \mathrm{~cm}= $ $ \qquad $ m 3. $ 4.35 \mathrm{~m}= $ $ \qquad $ mm 4. $ 143000 \mathrm{mg}= $ $ \qquad $ g 5. $ 15.49 \mathrm{~km}= $ $ \qquad $ dm 6. 7.17 dam $ = $ $ \qquad $ mm 7. $ 368 \mathrm{~mm}= $ \(…

If $ x+y=m+n $ and $ x=n $, then which of the following is true according to Euclid's axiom? \[ x=y \] \[ y=m \] \[ y=-m \] \[ m=n \]

150. $ A $ and $ B $ invested in the ratio $ 3: 2 $ in a business. If $ 5 \% $ of the total profit goes to charity and A's share is Rs. 855, then the total profit is: a) Rs. 1200 b) Rs. 1350 c) Rs. 1500 d) Rs. 1750

The first three terms in the expansion of $ \left(1+\frac{x}{p}\right)^{n} $ in ascending powers of $ x $ are $ 1+x+\frac{9}{20} x^{2} $. Find the values of $ n $ and $ p $. and state the range of values of $ x $ for which the expansion is valid. (5 marks

1. \[ 36.03 \mathrm{~m}=\quad \mathrm{cm} \] $ \square $ 2. $ 5145800 \mathrm{~cm}= $ $ \qquad $ m $ \square $ 3. $ 4.35 \mathrm{~m}= $ $ \qquad $ mm $ \square $ 4. $ 143000 \mathrm{mg}= $ $ \qquad $ g $ \square $ 5. $ 15.49 \mathrm{~km}= $ $ \qquad $ dm $ \square $ 6.…

6. In a circle with centre $ \mathrm{O}, \mathrm{A} 13 $ is a chord and $ \mathrm{OM} \perp \mathrm{AB} $ meets the circle in C . If $ \angle \mathrm{AOC}=80^{\circ} $, find $ \triangle \mathrm{MCB} $.

149. A and B enter into a partnership for a year. A contributes Rs. 1500 and B Rs. 2000. After 4 months they admit C, who contributes Rs. 2250. If B withdraws his contribution after 9 months, how would they share the profit of Rs. 900 at the end of the year? a) Rs. 100 b) Rs. 150 c) Rs. 225 d)…

Maxwell has 1023 one-dollar coins. He puts them in 10 bags so he can make any amount from \$1 to $ \$ 1000 $ by choosing the right bags. How many coins go in each bag?

149. $ A $ and $ B $ enter into a partnership for a year. A contributes Rs. 1500 and B Rs. 2000. After 4 months they admit C, who contributes Rs. 2250. If B withdraws his contribution after 9 months, how would they share the profit of Rs. 900 at the end of the year? a) Rs. 100 b) Rs. 150 c)…

Pre-Assessment Page 1: Question 6 (1 point) The formula $ F=\frac{9}{5} C+32 $ can be used to find a temperature in degrees Fahrenheit, $ F $, when given a temperature in degrees Celsius, $ C $. If $ C=115 $, find the value of $ F $. 239 144 28 9 Question 7 (1 point) Evaluate the…

6. Name a line that is not contained in plane $ \boldsymbol{\mathcal { N }} $. $ \qquad $ 7. Name a plane that contains point $ B $. $ \qquad $ 8. Name three collinear points. $ \qquad $

tudent Profile D2L 8/26/25-25FA MA 110: COLLEG D2L Quizzes - 25FA MA 110: COLLE /d2//lms/quizzing/user/attempt/quiz_start_frame_auto.d2lใou=2023511\&isprv=\&qi=4728325\&cfql=18 e-Assessment ge 1: Question 1 (1 point) \begin{tabular}{c|c} 2 & 3 \\ -- & - \\ -…

(a) Mr Pretorius starts an investment with a deposit of R60 000. Three years later he deposits another R40 000. Exactly 4 years after he started the investment, he withdraws R15 000. For the first 3 years, interest is calculated at $ 5,5 \% \mathrm{p}, \mathrm{a} $. compounded semi-annually…

Question 10 Mary is a second year college student and wants to earn some extra pocket money. She is good with making hamburgers, so she is considering opening up a hamburger stall on weekends at the local flea market near the campus. After investigating, she found the following: She can rent…

b) Let $ f(x)=\frac{2 x}{x-1}-\frac{1}{2} $ and $ g(x)=\sqrt{x} $. Find $ (g \circ f)(x) $ and determine the domain.

Q15. Given: $ 4-2 x<16 $ where $ x \in R $. Solve the inequality.

A man equally between his two offsprings A and B for agriculture to produce radish and carrot the man found at ratio between dash land and carrot land on whole part of land 7:5 if a produces a radish only at 60% part of his land then find at what percent part of these land be produces carrot

b) Let $ f(x)=\frac{2 x}{x-1}-\frac{1}{2} $ and $ g(x)=\sqrt{x} $. Find $ (g \circ f)(x) $ and determine the domain.

QUESTION 10 $ \square $ Which of these three points lie on the same line? Use the determinant below. \[ \left|\begin{array}{lll} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & x_{3} & 1 \end{array}\right|=0 \] A. $ (4,2),(3,2),(2,2) $ B. $ (0,0),(2,1),(3,1)) $ C. \( (1,0),(2,-1),(5,2)…

148. A mixture contain milk and water in the ratio of $ 8: 3 $. On adding 3 litres of water, the ratio of milk to water becomes $ 2: 1 $. The quantity of milk and water in the mixture are: a) 16 litres and 6 litres respectively b) 32 litres and 12 litres respectively c) 40 litres and 15…

wich the matrix $ A I-A $ is a singular mat $ \times $ given that $ A=\left(\begin{array}{lll}3 & 2 & 4 \\ 2 & 0 & 2 \\ 4 & 2 & 3\end{array}\right) $

QUESTION9 $ \square $ Which of these determinant results in the equation of a straight line, $ 2 x-7 y+11 $ ? A. $ \left|\begin{array}{rrr}x & y & 1 \\ 2 & 4 & 1 \\ -1 & 3 & 1\end{array}\right|=0 $ B. \( \left|\begin{array}{rrr}x & y & 1 \\ 1 & -2 & 1 \\ 3 & 2 & 1\end{array}\right|=0…

Performance Task Directions: Draw a representation of a garden showing positive energy brought by plants which length is 8 more than 2 times the width. The polynomial function to model the area of the garden would be $ f(x)=2 x^{2}+8 x $ where $ f(x) $ is the area and $ x $ is the measure…

147. If 30 men do a piece of work in 27 days, in what time can 18 men do another piece of work 3 times as great? a) 135 days b) 140 days .c) 160 days d) 185 days

146. Rs, 425 is divided among 4 men, 5 women and 6 boys such that the share of a man, a woman and a boy may be in the ratio of $ 9: 8: 4 $. What is the share of a woman? a) $ R_{s} 34 $ b) Rs. 54 c) Rs. 64 d) Rs .70

144. How many quadrilaterals can be formed by joining the vertices of an octagon? a) 40 b) 50 c) 60 d) 70

Solve $ \sin x+\cos x=\sqrt{2} $ if $ 0 \leqslant x \leqslant 2 \pi $

a) Using the distributive and associative properties of sets, simplify \[ \left[X^{\prime} \cup(Y \cap Z)\right]^{\prime} \]

14:06 information. An instrument shows the number of revolutions per minute made by each tire of a car. In each revolution, the car travels a distance equal to the circumference of one of its tires. The circumference of each tire is equal to $ 2 \pi r $, where $ r $ is the radius of the…

14:06 Q26 1 балл \begin{table} \captionsetup{labelformat=empty} \caption{Ticket Prices by Row Number} \begin{tabular}{|c|c|} \hline Row number & Ticket price \\ \hline $ 1-2 $ & $ \$ 25 $ \\ \hline $ 3-10 $ & $ \$ 20 $ \\ \hline $ 11-20 $ & $ \$ 15 $…

140. If $ \mathrm{x}+\frac{1}{x}=3 $ then the value of $ x^{8}+\frac{1}{x^{8}} $ is: a) 2207 b) 2127 c) 2397 d) 2947

14:06 Q24 1 балл Century and Region of United States Presidents' Births as of 2014 \begin{tabular}{|l|c|c|c|} \hline \multirow{2}{*}{} & \multicolumn{3}{|c|}{ Century } \\ \cline { 2 - 4 } & 18 th & 19 th & 20 th \\ \hline Northeast & 5 & 6 & 3 \\ \hline South & 9 & 4 & 3 \\ \hline Midwest &…

2marks each Q11. Determine the equation of the line through $ (4 ; 3) $ with gradient -1 . Q12. Sketch the function $ y(x)=|x|-3 $ for the domain $ 2 \leq x<2 $. Q13. Solve simultaneously for $ y $ and $ x $ : \[ 5 x+4 y=21 \text { and } 2 x=3-y \] Q14. Sketch the inequality $ x $…

140. If $ \mathrm{x}+\frac{1}{x}=3 $ then the value of $ x^{8}+\frac{1}{x^{8}} $ is: a) 2207 . b) 2127 c) 2397 d) 2947

s-) By what number should we multiply $ (-8)^{-1} $ to obtain a product $ 10^{2} $ ?

136. In a school $ 45 \% $ of the students play cricket, $ 30 \% $ play hockey and $ 15 \% $ play both. Then the percentage of students who play neither cricket nor hockey is: a) 50 b) 30 c) 60 d) 40

135. Two poles 15 metres and 30 metres Thigh stand upright in a playground. If their feet be 36 meters apart, the distance between their tops is: a) 39 m b) 54 m c) 66 m d) 89 m

Q17 1 балл \[ |5-x|=4 \] The value of one solution to the equation above is 1 . What is the value of the other solution? Мой ответ

Use the following data to make a segmented bar graph of getting rich by gender. \begin{tabular}{|l|l|l|l|l|l|l|} \hline \multicolumn{5}{|c|}{} & & $ \frac{F M}{x}=\frac{T}{1001} $ \\ \hline & & Female & Male & Total & Reforme $ { }^{4} $ & Relative Froa \\ \hline & Almost no chance & 96 &…

1. Write the rate for each problem and simplify your answers. a. Write the rate as a proper or improper fraction in lowest terms. 10 feet in 40 seconds. b. If Maya rides for 3 hours on a bicycle, what is her rate if she rides 33 miles? c. If Juan checks his pulse for 5 minutes what is his rate…

QUESTION 21 Use the Gassion elimination method with back subactitution solve the following system of equations. ง man drafget utt cuse ard lawer side of that ix all 240 . \[ \begin{array}{r} 3 x-1 y=2 \\ 7 x-10 y=8 \end{array} \] (5 marks)

QUESTION 20 What is the solution to this system of linear equations? \[ \left[\begin{array}{rrr} 2 & -3 & 7 \\ 0 & 1 & -5 \end{array}\right] \]

13:46 c. d. Q14 1 балл The figure above shows that the shaded triangular region with a hypotenuse of 5 centimeters (cm) has been removed from a rectangular tile with dimensions $ x \mathrm{~cm} $ by $ y \mathrm{~cm} $. Of the following, which best approximates the area, in square…

13:46 A researcher is investigating the relationship between the price of a four-pack of AA batteries at a convenience store and the number of competitors the store has. She defines a store's competitor as another similar store within a 1 -mile radius of the store she selects. She selects 32…

Solve: 1. If rice cost 22.00 per kilo, how many kilograms can Mother's $ \$ 88.00 $ buy? 2. Grapes are sold at $ \$ 120.00 $ per kilo. How much will you pay if you want to buy $ 1 / 4 $ kilo? 3. Mother bought 200 grams of iodized salt and 500 grams of brown sugar. How many grams of salt…

QUESTION 18 Calculate the determinant of matrix. $ \left[\begin{array}{rrr}2 & 3 & -2 \\ -2 & -1 & 4 \\ 1 & 0 & 5\end{array}\right] $. \[ =2[-5-0]-3[-10-4]-2[6+1] \]

134. A hall whose length is 16 metres and breadth twice its height, takes 168 metrers of paper 2 metres wide for its four walls. The area of the floor is: a) 144 sq. Metres b) 192 sq. Metres c) 220 sq. Metres d) 260 sq. Metres

QUESTION 16 Find $ x $ such that $ \left[\begin{array}{cr}2+x & 5 \\ -4 & -1\end{array}\right]=\left[\begin{array}{cr}3 x-4 & 5 \\ -4 & -1\end{array}\right] $.

(a) Mr Pretorius starts an investment with a deposit of R60 000. Three years later he deposits another R40 000. Exactly 4 years after he started the investment, he withdraws R15 000. For the first 3 years, interest is calculated at $ 5,5 \% \mathrm{p}, \mathrm{a} $. compounded semi-annually…

solve for $ x $ \[ (5+2 \sqrt{6})^{x^{2}-3}+(5-2 \sqrt{6})^{x^{2}-3}=10 \]

13:35 Telegram I Uवग Arrangement I A project coordinator at a banquet hall is given the task of arranging seating for an awards ceremony. The figure above shows the first three possible arrangements of tables and the maximum number of seats in each arrangement. If the number of seats in each…

solve for $ x $ \[ (5+2 \sqrt{6})^{x^{2}-3}+(5-2 \sqrt{6})^{x^{2}-3}=10 \]

Exercise 2: 1. The figure below shows a rectangular grass lawn JKLM in which JK = 24 m and $ / M=30 \mathrm{~m} $. What is the area covered by grass in $ \mathrm{m}^{2} $ ? 2 What is the area in hectares of the figure shown below? Where $ P R= S Q $ and $ M N $ is parallel to \( P Q…

solve for $ x $ \[ (5+2 \sqrt{6})^{x^{2}-3}+(5-2 \sqrt{6})^{x^{2}-3}=10 \]

13:25 A cable company recorded the percentage of households in the United States that had cable television from 1987 to 1997. In the scatterplot below, $ x $ represents the number of years since 1987 and $ y $ represents the percentage of households with cable television. The line of best…

f) Find all solutions for $ 2 \sin ^{2} x-\cos x-1=0 $ such that $ 0 \leq x \leq 2 \pi $. (5ma

13:17 Questions 20-21 refer to the following information. \begin{table} \captionsetup{labelformat=empty} \caption{Nutritional Information for 1-Ounce Servings of Seeds and Nuts} \begin{tabular}{|l|c|c|c|} \hline Seed or nut & Calories & \begin{tabular}{c} Total fat \\ (grams) \end{tabular} &…

13:17 d. Q17 1 балл The temperature, in degrees Celsius ( $ { }^{\circ} \mathrm{C} $ ), of a hot object placed in a room is recorded every five minutes. The temperature of the object decreases rapidly at first, then decreases more slowly as the object's temperature approaches the…

Find the value or $ n $. If (i) sum of the roots of the equation $ 2 k x^{2}-3 x+4 k=0 $ is twice the pre roots. (ii) sam of the roots of the equation $ x^{2}+(3 k-7) x+5 k=0 $ i product of the roots. Find $ k $, if (i) sum of the squares of the roots of the equation \[ 4 / r^{2}+3 k…

solve for $ x $ \[ (5+2 \sqrt{6})^{x^{2}-3}+(5-2 \sqrt{6})^{x^{2}-3}=10 \]

$ \sqrt{5^{2}+2^{2}} $ ก. $ \sqrt{5^{2} \cdot 2^{2}} $ o. $ \sqrt{3} \cdot \sqrt{21} $ p. $ (\sqrt{5}-2 \sqrt{5})^{2} $

$ \frac{3+2^{-2}}{3-3^{-1}} $

Multiplying simple monomials how do I do it?

133. A man can row $ 7 \mathrm{~km} / \mathrm{hr} $ in still water. In a stream which is flowing at $ 3 \mathrm{~km} / \mathrm{hr} $, it takes him 7 hours to row to a place and back. How far is the place? a) 6 km b) 10 km c) 12 km d) 20 km

132. Two runners cover the same distance at the rate of 15 km and 16 km per hour respectively. The distance they travelled when one takes 16 minutes longer than the other is: a) 48 km b) 56 km c) 64 km d) 72 km

Which categories in the real number system can the number -9 be placed into? rational numbers irrational numbers whole numbers natural numbers integers

$ \frac{2 \cdot 2^{3}-2^{2}(4)}{3-5} $

131. The distance between two stations, Delhi and Amritsar is 450 km . A train starts at 4 p.m. from Delhi and moves towards Amritsar at an average speed of $ 60 \mathrm{~km} / \mathrm{hr} $. Another train starts from Amritsar at 3.20 p.m. and moves towards Delhi at an average speed of \( 80…

Use number proparties to simplify the following expression. \[ -5+(5+3) \] In the box below, show each step in simplifying the expression and explain which property you used in each step.

with 16 litres of water is worth Rs. 0.90 per litre. If pure milk be worth Rs. 1.08 per litre, how 3CO-21 130. A boy walking at a speed of $ 10 \mathrm{~km} / \mathrm{hr} $ reaches his school 15 minutes late. Next time 9 IV he increases his speed by $ 2 \mathrm{~km} / \mathrm{hr} $, but…

If $ n=4 $, all of the following expressions are equivalent except $ \qquad $ . 16 $ \frac{1}{16} $ $ n^{-2} $ $ \frac{1}{n^{2}} $

Damon does the following math problem: $ 4 \cdot 7 \cdot \frac{1}{4} $ $ 4 \cdot \frac{1}{4} \cdot 7 $ $ 1 \cdot 7 $ 7 Damon has used all of the following number properties except $ \qquad $ commutative property of multiplication multiplicative identity multiplicative…

At the market, Joey buys 3 avocados for $ \$ .40 $ each and 5 lemons for $ \$ 0.40 $ each. The cashier in training rings up $ 3 \times $ 0.40 and then $ 5 \times 0.40 $ to get the total. The experienced cashier says to add the 3 plus 5 in his head and then ring up 8 \( \times 0.40…

$ \frac{1}{18}+\frac{5}{12} $

Charlie does the following problem: \[ 3^{3} \cdot 3^{2}=3^{6}=3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3=729 . \] Which of the following is a true statement? He is incorrect because he should have 6 factors of 9 . He is incorrect because he should have 3 factors of 6 . He is incorrect because…

Gina gets money from her grandfather every day for the entire week of her birthday, starting on Monday. She gets $ \$ 2 $ on Monday, $ \$ 4 $ on Tuesday, and the previous day's amount gets multiplied by 2 each day. Which of the following would represent how much money Gina would receive on…

126. A certain number of men can do a work in 60 days. If there were 8 men more, it could be finished in 10 days less. How many men are there? a) 20 men b) 25 men c) 30 men d) 40 men

$ \frac{1}{18}+\frac{5}{12} $

$ 15^{7} \div 15^{4} $ is equal to $ \qquad $ 1 $ 15^{3} $ $ 15^{11} $ $ 15^{\frac{7}{4}} $

Which property would allow you to use mental computation to simplify the problem $ 27+15+3+5 $ ? cistributive property additive inverse additive identity commutative property of adidition

11:41 16 Q25 1 балл Todetermine whether to buy a plot of land, a farmer is having the soil tested for lead. The lable above shows the amount of lead, in parts per million (ppm), in six of the seven samples of soil selected at random. If the average (arithmetic mean) amount of lead in the…

If $ b=3 $, then $ b^{-2} $ is equivalent to $ \qquad $ 9 $ -6 $ $ \frac{1}{9} $ $ -9 $

Q21 1 балл \[ a n+2=a(n+2)+0.8 \] If $ n=-3 $ in the equation above, what is the value of $ a^{\prime} $ ? Мой ответ

Give the value of the underlined digit. 1. $ 987 \underline{206} $ $ \qquad $ 2. 302005 $ \qquad $ 3. 40075 $ \qquad $ 4. 145097 $ \qquad $

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