Page 583 - Algebra 1

3 4 17. Measurement One square has an area of 16 square units and another square has an (82) area of 36 square units. A third square has an area greater than that of the smaller square and less than that of the larger square. What are the possible lengths of the
sides of the third square?
18. Multiple Choice What is the factored form of 32x2 - 50y2?
(83) A 2(4x + 5y)2 B 2(4x - 5y)2
C 2(4x + 5y)(4x - 5y) D 2(16x + 25y)(16x - 25y)
*19. Verify Rewrite the expression y2 - x2 - 8x - 41 as a difference of two squares (83) minus a perfect-square polynomial to show that y2 - x2 - 8x - 41 =
(y + 5)(y - 5) - (x + 4)2.
20. Error Analysis Two students are asked if the equation 7x2 + 24 = y - 6x(2 - 3x2)
(84) is a quadratic function. Which student is correct? Explain the error.
21. Economics A company has developed a new product. To determine the selling
(84) price, the company uses the function y = -55x2 + 1500x to predict the profit for selling the product for x dollars. Does the graph of this function open upward or
downward? Explain why this might be given the context of the situation. 22. Use the Pythagorean Theorem to find the missing side length. Give the
(85) answer in simplest radical form.
√84 10
*23. Geometry A right isosceles triangle is a right triangle whose legs are equal in (85) length.
a. Find the length of the hypotenuse of a right isosceles triangle with leg lengths of 3.
b. Find the length of the hypotenuse of a right isosceles triangle with leg lengths of 5.
c. Formulate Use the results of parts a and b to suggest a formula for the hypotenuse of a right isosceles triangle with legs of length a.
*24. Error Analysis Two students use the Pythagorean Theorem to find length p. Which p
Student A
y = -18x3 + 7x2 + 12x + 24 no
Student B
y=10x2 +12x+24 yes
n
(85) student is correct? Explain the error.
2 7
Student A
22 +72 =p2 4 + 49 = p2 53 = p2
√ 53 = p
Student B
22 + p2 = 72 4+p2 =49 p2 = 45
p = √ 45 p = 3 √ 5
568 Saxon Algebra 1