Page 450 - Algebra 1

20. Error Analysis Two students are using the product rule below to find the missing (64) value. Which student is correct? Explain the error.
If y varies inversely as x and y = 0.2 when x = 100, find y when x = 4.
21. Write a direct-variation equation relating x and y when x = 5 and y = 30. (56)
22. Write an inverse-variation equation relating x and y when x = 4 and y = 20. (64)
Multiply.
Student A
x1y2 = x2y1 100·y2 =4·0.2
100y2 = 0.8 y2 = 0.008
Student B
x1y1 = x2y2 100 · 0.2 = 4 · y2
20 = 4y2 5 = y2
23.
(60)
26.
(58)
27.
(64)
(2x-3)(2x-3) 24. (t-12)(t+12) 25. (y3 -4)2 (60) (60)
Justify Find the product of (2y + 4)(3y + 5) using the Distributive Property. Then find the product using the FOIL method. Show that the answers are the same using either method.
Life Expectancy For most mammals, there is an inverse relationship between life span and heart rate. Use the table below to write an inverse-variation equation to represent this relationship. Then find the life span in years, rounded to the nearest tenth, of a hamster with an average heart rate of 450 beats per minute.
Animal
Heart Rate (beats per minute)
Life Span (in minutes)
Guinea Pig
280
3,571,429
Rabbit
205
4,878,049
Dog
115
8,695,952
Rat
328
3,048,780
*28.
(65)
*29.
(65)
*30.
(66)
Coordinate Geometry Show that PQR is a right triangle.
Justify True or False: The lines represented by y = _x - 1 and -4 = 12x + 4y
are parallel. Explain. 3
2
x
-4
2
4
Q
-4
Running John plans to run at least 5 miles more this week than he ran last week. He ran 25 miles last week. Write and solve an inequality describing the number of miles John plans to run this week.
y
R
4
P
Lesson 66 435