Quadratic equations Questions and Answers

P when q 18 and r 5 find q when p 345 and r 30 The time needed to paint a fence varies directly with the length of the fence and inversely with the number of painters If it takes seven hours to paint 280 feet of fence with two painters how long will it take four painters to paint 720 feet of fence

9 Which is equivalent to the equation given below log 18 x 1 A 218 1 B 2 1 18 C 182 x 1 D 18 1 2 12 Simplify the expression below log3 3 log 64 A 5 B 7 C 9 D 33

f x x 4x 8x 12x 15 Step 3 of 4 Find the x intercept s at which f crosses the axis Express the intercept s as ordered pair s Answer Select the number of x intercept s at which f crosses the axis Selecting an option will display any text boxes needed to complete your answer 01 none 02 03 04

Step 1 of 4 Factor the polynomial completely Answer f x f x x 4x 8x 12x 15

5 Cassandra is creating an animated short film and she needs 35 frames per second of film He already has at least 200 frames Which inequality represents this situation where fis the number of frames and s is the number of seconds in a film OB sa 351 200 OA s 351 200 OD 35 200 OC 1 35 200

10 Given the parent function f x x the function g x x 1 2 is the result of a shift of f x 1 1 unit left and 2 units down 2 1 unit left and 2 units up 3 1 unit right and 2 units down 4 1 unit right and 2 units up

Create an equation for the following graph make sure to show your work to find the a constant To be clear this graph has vertical asymptotes at x 3 and x 1 and horizontal asymptote at y 1 5 and x intercepts at x 2 and x 2 and y intercept at y 4 and a hole at 5 3 Include an explanation of where each part of your equation comes from 76 3 24 14 L 2 L Loy N

Write a possible equation for the following graphs Explain your reasoning 6 64 2 4 y 2 X

3 Which expression results in a rational number 1 121 21 3 36 225 2 25 50 4 3 5 2 5

4 The math department needs to buy new textbooks and laptops for the computer science classroom The textbooks cost 116 00 each and the laptops cost 439 00 each If the math department has 6500 to spend and purchases 30 textbooks how many laptops can they buy 1 6 2 7 3 11 4 12

18 Which pair of equations would have 1 2 as a solution 1 y x 3 and y 2 2 y x 1 and y 2x 3 y x 3x 2 and y 4x 6 4 2x 3y 4 and y 1 1x 3 2 2 ylus

20 The formula for electrical power P is P 12R where I is current and R is resistance The formula for I in terms of P and Ris 1 1 R 3 1 PR 2 I R 4 1 P R

16 The table below shows the weights of Liam s pumpkin l w and Patricia s pumpkin p w over a four week period where w represents the number of weeks Liam s pumpkin grows at a constant rate Patricia s pumpkin grows at a weekly rate of approximately 52 Weeks W 6 7 8 9 Weight in Pounds Weight in Pounds I w p w 2 4 2 5 5 5 3 8 8 6 5 8 11 7 8 8 Assume the pumpkins continue to grow at these rates through week 13 When comparing the weights of both Liam s and Patricia s pumpkins in week 10 and week 13 which statement is true 1 Liam s pumpkin will weigh more in week 10 and week 13 2 Patricia s pumpkin will weigh more in week 10 and week 13 3 Liam s pumpkin will weigh more in week 10 and Patricia s pumpkin will weigh more in week 13 4 Patricia s pumpkin will weigh more in week 10 and Liam s pumpkin will weigh more in week 13 he domain of t all positive re all positive in ich pair of equa y x 3 and g y r 1 and y y x 3x 2 2x 3y 4 an h function could 312 5 given tha a 1 9 2 5 a 1

7 Which relation does not represent a function X y 1 3 2 2 4 3 5 1 WENDY 1 y 2 4 6 5 7 4 6 8 8 y 3 x 1 2 2 3 3 4 456 5 7 8 9

6 The area of a rectangle is represented by 3x2 10x 8 Which expression can also be used to represent the area of the same rectangle 1 3x 2 x 4 2 3x 2 x 4 3 3x 4 x 2 4 3x4 x 2

B 0 4 and C 4 0 lie on this graph X Which of these points can determine the zeros of the equation y x x 4 1 A only 2 B only 3 A and C only 4 A B and C

15 Which equation has the same solution as x 8x 33 0 1 x 4 49 3 x 4 17 2 x 4 49 4 x 4 17

8 Britney is solving a quadratic equation Her first step is shown below Problem 3x2 8 10x 3 2x 3 3x 10x8 6x 9 Step 1 Which two properties did Britney use to get to step 1 I addition property of equality II commutative property of addition III multiplication property of equality IV distributive property of multiplication over addition Use this space for computations 10

2 The function g x is defined as g x 2x 3x The value of g 3 is 1 27 2 9 3 27 4 45

1 The scatter plot below shows the relationship between the number of members in a family and the amount of the family s weekly grocery bill Grocery Bill Dollars 600 500 400 300 200 100 1 100 2 300 1 2 3 4 5 6 7 8 9 Number of Family Members The most appropriate prediction of the grocery bill for a family that consists of six members is 3 400 4 500

References There are 12 eggs in a dozen If a farmer s chickens produce an average of 386 dozen eggs in a month how should the average number of eggs per month be reported show narrativ 386 dozen x 12 eggs dozen eggs

1 1 Solve for x in the following equations 0 0 2 All answers must be exact values in radians 3 each 2 cscx 17 15 cscx b 2 sin x sinx 1 0

Let the quadratic function f be defined by f x 6x x Compute the following a f 5 b f 0 c For what values of x is f x 9 x 1

Consider the equation y 2x 20x 48 You must enter all of your answers as points Use commas to separate multiple answers a The z intercepts of the parabola are b The y intercept of the parabola is c The vertex of the parabola is d Which of these is the correct graph of y Graph A 2m 20m 48 Graph B Graph Graph C Graph F

5 Which of the following linear expressions is a factor of the cubic polynomial x 9x 16x 12 1 x 6 3 x 3 4 x 2 2 x 1

Question 7 P The price of a widget was 468 Over four years the price dropped to 268 Assume a linear trend a Find a linear model P ax b for this situation where P is the price at time z S b Use this model to predict the price in 5 years Submit Question

Solve for x and check your answer I a log x 4 3 Or O No solution b log 4x 32 2 X O No solution c log log x 1 1 x O No solution d log log x 1 2 a

The table below represents the number of loans approved for different amounts during the second half of 2021 A linear relationship is expected Loan amount in R100 000s 2 3 4 5 LO 6 Number of loans approved 15 20 18 13 If the loan amount is set at 7 loan amount in R100 000s what is the value of

4 points Find the values of the coefficients a il and a so that the conditions hold for the function a C f 0 1 f 0 2 and f 0 5 f x ae be cze

Score 1 32 1 32 answered Question 6 y Find an equation for the line perpendicular to 3x 21y 189 and goes through the point 3 10 Write your answer in the form y mx b Submit Question

1 5 4 3 2 A 2 3 4 6 The graph above shows the function f x The graph below shows g x 6 5 4 3 2 B q g x is a transformation of f xIwhere g x Af Bx where 4 S 6

Which of the following represents a parabola Enter a b c d or e a 4x 2y 25 b 3x 5y 15 c 5x 2y 7 d y 3x 2x 1 e x y 5

Tyra invests 5900 in a new savings account which earns 5 6 annual interest compounded semi annually What will be the value of her investment after 9 years Round to the nearest cent Answer How to enter your answer opens in new window Interest formu Keyp Keyboard Short

x 8x 23x 30 x 3 x 2x 11x 12 x 3

Given that 8i is a zero factor the following polynomial function completely Use the Conjugate Roots Theorem if applicable f x x 8x 79x 512x 960 answer 5 Points f x

Which system of equations has this solution 2 3 1 4x y 3z 4 3x y z 6 and x 3y 2z 3 O x y z 2 2x y z 6 and y 2z 5 2x 3y 4z 1 3y 3z 6 and x 3z x y 3z 2 2x 2y z 4 and x y 2z 4 None of the choices ar correct

12 Solve the following by taking the square root 4a 92 a O 4 71 O 4 83 O 4 86 O 4 80

A car purchased for 20 790 is expected to depreciate according to the formula f x 1980x 20 790 where f x is the value of the car after x years After how many years will the car be worthless yr

question Cats 10 5 8 Dogs 7 1 How many students responded to the survey 2 What percent of the students surveyed own a dog answer to the nearest whole number 3 What percent of the students surveyed do not own a dog or a cat answer to the nearest 100th 4 What percent of the students surveyed own a cat answer to the nearest

19 Graph the following on a separate sheet of paper or on a graphing calculator or computer Use your graph to find the solution s to the problem 1 x 36 36 More than one answer may be correct mark all correct answers 0 6 0 36 6 36

17 Multiply the following expression using the pattern rule previously explained 7a 4b

ind the total number of hours for each person 1 Reggie worked from 8 00 AM to 10 45 AM and from 12 15 PM to 4 15 PM

30 Which system of equations is represented in the following graph 5x 2y 6 3z 2y 2 1 5x 2y 6 3x 2y 2 5x 2y 6 3z 2y 2 5x 2y 6 3x 2y 2

ircle one olution 2 1 0 1 2 Circle one 732 2 1 0 1 21012 Linear Exponential Quadratic System inwal2 playback NONTOR 84215 6 13592330g 4 2 Circle one Linear Exponential Quadratic System Arithmetic Geometric Neither 54 44 Circle one 0 1 2 3 4 Circle one Linear Exponential Quadratic System Circle one Arithmetic Geometric Neither 2 0 1 4 7012 9 16 12 11 10 9 8 Circle one Linear Exponential Quadratic System Arithmetic Geometric Ne

28 Write a prediction equation for the table below Time Miles 0 1 41 3 09 4 2 6 01 8 2 11 04 0 4 23 9 27 12 6 18 03 24 6 33 12 y 7x 3 y 3x y 7x Oy 3x 3

decimal places Answer How to enter your answer opens in new window Keypa Keyboard Shortc

36 What does z equal in the solution of the system of equations below x 2z 11 2x y 4 x 3y z 1 0 2 O 1 04 0 3

39 Solve the rational equation 2 64 6 30 Don t forget that the easiest way to solve this problem is to cross multiply over the equal sign Do not multiply out the factors Instead look for factors that can cancel Mark all answers that apply

0 Use your calculator to find the value of y if x 6 Round to the nearest hundredth y 4 1 9

34 A population of bacteria is growing at a rate of 7 2 per day If there are currently 20 spores how many spores will there be in two weeks