Page 287 - Algebra 1

Example
3
Application: Moving Objects
The expression 3.5t + 0.7t2 represents the distance a moving object travels through time t. The expression 1.4t2 represents the distance the same object moves fro_m rest with twice the acceleration.
3.5t + 0.7t2 Simplify 1.4t2 .
SOLUTION
Math Reasoning
Analyze Determine
the undefin_ed value
for the rational
in the context of the problem?
3.5t + 0.7t expression 2 .
1.4t2 What is its meaning
1.4t2 t ≠ 0
Identify the denominator. Determine undefined values.
Factor the numerator.
Factor the denominator. Simplify.
0.7t(5 + t) _ _
3.5t + 0.7t2 1.4t2 =
1.4t2
= 0.7t(5 + t)
_0.7t (2t) = 5 + t
2t
The simplified expression is 5 + t , t ≠ 0.
_ 2t
Lesson Practice
Practice
272 Saxon Algebra 1
Determine the values for which each rational expression is undefined.
(Ex1) _ _ _
a. 16x-7 b. 1+3x c. 11-x
5x x + 8 6x - 42 Simplify each rational expression. Determine undefined values.
___
5x 9x2 +15x 3x2 +21x
(Ex 2)
d.7x-27 e. 3x2-3x f. 4x+28
A package is needed that uses the least amount of material to hold the greatest volume of product. A container in the shape of a right circular cylinder has a surface area of S = 2πrh + 2πr2 and a volume of V = πr2h.
πr2h
Distributed and Integrated
Evaluate each function for the given input value.
1. f(x) = -2x for x = -5 2. h(x) = 3x - 1 for x = 7
(30) (30)
Find the indicated term of each arithmetic sequence. 3. an = 16 + (n - 1)(-0.5), 15th term
(34)
4. -8, -6, -4, -2, ..., 100th term (34)
__2 g. Simplify 2πrh + 2πr .