Quadratic equations Questions and Answers

2 37 The angle between the lines 2x 3y Z and 6x y 4z is theta Then value of os theta n 4 is

If f x 10 18x and g x 11 1 2 3 for what values of x is g x f x

on 3 of 13 Macmillan Learning Convert an angle of degree measure 20 to radian measure Give an exact answer Use symbolic notation and fractions where needed 20

4 1 Score 2 53 2 16 answered Question 12 Quectic Assuming the function f is one to one and f 6 8 find f 8 f 8

4 1 Score 2 53 2 16 answered Question 16 For the following exercise find f x for the function f x I x 5 f x Question Help R

Score 2 53 2 16 answered Question 9 For the following exercises use the graph of f shown below 103 78 43 Solve f x 5 40 0 5 J 6 16 6 7 2 8

Question 3 For the following exercise use each pair of functions to find f g x and g f x Simplify your answers 1 x 2 f g x 6 g x 2 x g f x Question Help VIDEO Written Example Post to forum

A peer reviewed medical journal publishes a report on the results of a clinical trial for a new drug It reports that the clinical trial had 1 042 participants who were given either the drug or a placebo Based on the data the journal reports tha there was no statistical significance in the difference between the effects of the drug and of the placebo Select the true statement regarding this report A No conclusions were made regarding the results of the clinical trial The results of the trial are still valid even though there was no statistical significance The clinical trials methodology was flawed which is why there was no statistical significance No statistical significance indicates that the results of the clinical trial were not medically important 00 B C D

A population characteristic is normally distributed Approximately what percentage of the population lies within two standard deviations of the mean A 48 B 68

Which answer is a value for x if 2 log 37 A 8 OOC B C O 9 32 64

Maggie claims that the function g x Which statement provides a correct analysis of Maggie s claim A B C D 4 is the inverse of the function of f x 3x 4 Maggie s claim is correct because if you add 4 to g x and then multiply it by 3 you get f x Maggie s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when f x is substituted into every occurrence of x in g x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 8 therefore g x is not the inverse of f x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

Which function is the inverse of f x x 3 g x x 3 A B Oc O D g x x 2 g x x 3 g x x 2

Which graph represents the function f x 2 3 A B 0 2 0 3 0 4

Tree height feet Tree Growth y 2 4 0 2 6 4 Age years X Use the graph to write an equation of the line

Solve 5x 4 3x 8 a Model b Perform the step to have variables circles on only one side c Write the resulting step

Note that this function does not have any vertical asymptotes because the denominator cannot equal zero In the graph below drag the green intercepts to the correct positions Drag the orange horizontal asymptote to the correct position Drag the blue y intercept to the correct position When finished click CHECK 10 5 0 10 6 0 1 0 5 0 10

x 4 In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the orange horizontal asymptote to the correct position hese Determine several points of the function and drag the blue point to one locations Choose a point that is not an x intercept and for which the y coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue poin to the exact location When finished click CHECK 10 6 2 5 10 5 5 5 10

confirm your work In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the orange horizontal asymptote to the correct position Determine several points of the function and drag the blue point to one of these locations Choose a point that is not an x intercept and for which the y 10 f x coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue point to the exact location When finished click CHECK 6 2 2x 12x 18 x 2x 8 5 10 5 0 5 10

Consider the rational function below x 3 x 1 x 4 x 4 x 5 x 4 Give the domain of f by listing all a values that are restricted domain restrictions List the x coordinates of the x intercept s Separate multiple answers with a commas x intercepts at List the locations of the vertical asymptote s Separate multiple answers with commas vertical asymptotes List the x value s for which f has a missing point removable discontinuity Separat multiple answers with commas missing points at

Graph the rational function below on paper by hand Then do the steps that follow to confirm your work In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the orange horizontal asymptote to the correct position Determine several points of the function and drag the blue point to one of these locations Choose a point that is not an x intercept and for which the y 10 f x coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue point to the exact location When finished click CHECK 6 2 5 x 5 x 4 10 5 5 10

5 The amount of money that a news Poper company cand is directly Proportional to the numbers OF Popara they sell Th News Paper Company earn s 150 For every God Pafer they Jell How much money would the Company ean on a day Ipere they sell 1500 Paperd

Jack has a huge Poper due for his literature Class at the end of the Semester If he con write a Pase every 2 of on hour how long will it take him to write his entire il Page Paper 2

A polynomial of degree 6 has the following characteristics a leading coefficient 1 a zero of multiplicity 3 at x 6 a zero of multiplicity 2 at x 8 a zero of multiplicity 1 at x 7 11 Determine a possible polynomial of degree 6 that satisfies the above conditions P x Par

Shelly is buying 13 4 pounds of chicken to use in several recipes The chicken is on sale for 1 70 per pound at the grocery store How much will it cost Shelly to purchase the chicken

2x6 y 4 2 x5 y 3

expressions Estimates are OK If you would like to enlarge the graph or make numbers and letters easier to read you may click on it to open it in a new window You may then enlarge that window with your mouse To further enlarge the image use your browser s zoom capabilities On a PC this is usually ctrl shift and zooming out is ctrl On an Apple computer this is usually apple shift and zooming out is apple 10 8 6 a H 4 7 2 104 Y 5 5 2 4 y H x 6 8 10

Find the least common denominator y 2 2y 5y 3 LCD and 3y 2 5 y 3y 4 Type your answer in factored form

Perform the indicated operations and simplify the result 36 x 19 x 19 2 x 324 x 18 x 18 36 x 19 x 19 11

Find the least common denominator for the following rational expressions 5 5 198pn and 8 2 143p n

Click here to watch the video Find the least common denominator of the following rational expressions 6s 5 s 3 and 2 s 2s 24 s 8s 16

Click here to watch the video Perform the indicated operation 3x 2 x 7 X 6 X 7 3x 2 x 6 x 7 X 7 11 Simplify your answer

4 At a bake sale they are selling pies brownies and cookies Over the course of the day they sell 200 total baked goods If 60 people buy a cookie 20 people buy a pie and the rest buy brownies what percentage of customers bought a brownie a 10 b 30 c 60 d 80

3 At a zoo there are 10 zebras 12 lions 6 giraffes and 12 monkeys Zebras make up what percentage of all animals a 10 b 20 c 25 d 33

Which binomial expressions are factors of 5x3 8x 7x 6 Select each correct answer O x 1 O x 2 0 x 1 O x 2

Which real numbers are zeros of the function f x 2x 9x 7x 6x Select each correct answer 0 3 0 2 0 1 2 0 H

Paula used synthetic division to divide the polynomial f x by x 1 as shown in the table What is the value of f 1 0 2 0 1 1 2 5 4 2 3 2 3 7

Describe and correct the error a student made in solving an equation x2 5x 5 0 a 1 b 5 c 5 X 5 5 4 1 5 2 1 5 25 20 2 X A The student used b instead of b in the first term in the numerator when substituting values into the formula OB The student tried to use parameters from the wrong form of the quadratic equation The student should have rewritten the equation as a x b c 0 and then substituted those values into the Quadratic Formula OC The student dropped the negative sign in simplifying the expression 5 D The student used a instead of 2a in the denominator when substituting values into the formula

Find the vertex of the graph of the quadratic function Determine whether the graph opens upward or downward find the y intercept and sketch the graph f x x 2x 8 The vertex is Simplify your answer Type an ordered pair

Find the vertex of the graph of the quadratic function by completing the square or using the vertex formula f x 3x 18x 20 The vertex is Type an ordered pair

Multiply and simplify the rational expression 2 X 2 x 2 X 4 2 X 64 4 2 X 2 2 x 6x 16 2 x 2x 8 6x 16

Divide the rational expression Simplify the quotient if possible 2 p 3p 18 2p 3p 2 2 p 3p 2 p 2p 8 p 3p 18 2p 3p 2 2 3P P 2 p 2p 8

Click here to watch the video Simplify the rational expression y y 12 2 y 5y 36 y y 12 Simplify your answer

Multiply and simplify the rational expressions 20x 60 2x x 15 2 2x 11x 15 12 4x 20x 60 2 2x x 15 com ur

Multiply and simplify the following rational expression 2 m 6m 9 2m 13m 7 7 m 2m 7m 3 2 2 m 6m 9 2m 13m 7 2 7 m 7 Simplify your answer

Click here to watch the video Divide the rational expressions 10b 11c 2 5b 4 4 10b 22c 2 11c 5 11 Simplify your answer

Which of the following describe the function g z log x 2 3 Choose ALL that apply There is no x intercept and the y intercept 0 10 The domain is the set of all real number greater than 2 A vertical asymptote at x 10 DA graph of 0 Avertical asymptote at x 2 DA graph of 0 10 15 O The graph of god is symmetric to its inverse exponential function over the line y x D The graph of gbd is symmetric to its inverse exponential function over the line y 0 The domain is the set of all real number less than 2

Which of the following functions has the same horizontal asymptote and range as the function graphed below 5 5 Of x 2 2 3 Of x 2 2 3 Of x 2 2 2 Of x 2 2 2 0 5 10 5

Marlee solved the equation below by graphing a system of equations log 5x logg x 5 Which system of equations could be used to approximate her solution What is the approximate solution for her system of equations O System y log2 5x and y logs x 5 O System y log2 5x and y logg x 5 System y log 5x and y log x 5 Solution x 0 35 O System y 5x and y x 5 Solution x 0 806 Solution x 0 806 Solution x 0 35

The combined area of New York and California is 204 188 square miles The area of California is 108 532 square miles more than that of New York Find the land of each state

logo 2x 4 2 O x 25 Ox 40 O x 2 O x 20