Stephanie earned 8 points for every book she read over the summer. The equation y = 8x represents Stephanie's points based on th
e number of books she read.
Use the table and equation to complete the statements and find the number of books Stephanie read.
1. Stephanie earned 72 points. Did she read fewer than 2 books, between 2 and 5 books, between 5 and 6 books, or more than 7 books? Explain how you know.
2. The equation y = 8x gives the points, y, earned by reading x books.
Use this equation to find the number of books Stephanie read to earn 72 points. Show your work.
(here are the tables)(plz answer both and dont be greedy as * and say i d k and get pts!)
Use the table and equation to complete the statements and find the number of books Stephanie read.
1. Stephanie earned 72 points. Did she read fewer than 2 books, between 2 and 5 books, between 5 and 6 books, or more than 7 books? Explain how you know.
2. The equation y = 8x gives the points, y, earned by reading x books.
Use this equation to find the number of books Stephanie read to earn 72 points. Show your work.
(here are the tables)(plz answer both and dont be greedy as * and say i d k and get pts!)
1 answer:
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Answer:
x = 30 and x = 3 both solve the equation correctly. See work below.
Step-by-step explanation:
The very first step is to realize that p(x) is in hundreds of dollars and that the given number is not. 60000 is not in hundreds of dollars. It is in dollars. 60000 dollars = 60000/100 = 600 hundreds of dollars.
Make the polynomial = 600
-x^3+3x^2+900x-2100 = 600 Subtract 600 from both sides
-x^3+3x^2+900x-2100 - 600 = 0 Combine
-x^3+3x^2+900x- 2700 = 0 Group the first and second term and the Thrid and fourth terms.
(-x^2 + 3x^2) + (900x - 2700) = 0 Bring out the common factors from both groups.
-x^2(x - 3) + 900(x - 3) = 0 Factor out x - 3 on both sides of the plus sign
(- x^2 + 900)(x - 3) = 0 Reverse -x^2 + 900 to 900 - x^2
(900 - x^2)(x - 3) = 0 factor (900 - x^2) using the difference of squares
(30 - x)(30 + x) (x - 3) = 0
The two answers that work are
30 - x = 0 Solve
- x = - 30 Divide by - 1
-x/-1 = -30/-1 Combine
x = 30
============
x - 3 = 0
x = 3
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There are two values that will work to give p(x) = 600. There is no way to account for why both values work.
The graph below confirms both answers.
