Question

3 functions f and a are defined by these equations:
$f(x) = 80 - 15x$ $a(x) = 25 + 10x$
which function has a greater value when x is 2.5?

4 an equilateral triangle has three sides of equal length. function p gives the perimeter of an equilateral triangle of side length s.
a. find $p(2)$
b. find $p(10)$
c. find $p(s)$

5 from unit 5, lesson 1
imagine a situation in which a person is using a garden hose to fill a child’s pool. think of two quantities that are related in this situation and that can be seen as a function.
a. define the function using a statement of the form “____ is a function of ____.” be sure to consider the units of measurement.
b. sketch a possible graph of the function. be sure to label the axes.
then, identify the coordinates of one point on the graph, and explain its meaning.

Explanation:

Problem 3

Step1: Calculate \( f(2.5) \)

Substitute \( x = 2.5 \) into \( f(x)=80 - 15x \).
\( f(2.5)=80-15\times2.5 \)
\( =80 - 37.5 \)
\( = 42.5 \)

Step2: Calculate \( A(2.5) \)

Substitute \( x = 2.5 \) into \( A(x)=25 + 10x \).
\( A(2.5)=25+10\times2.5 \)
\( =25 + 25 \)
\( = 50 \)

Step3: Compare the two values

Since \( 42.5<50 \), \( A(x) \) has a greater value.

Step1: Recall the perimeter formula for equilateral triangle

The perimeter \( P \) of an equilateral triangle with side length \( s \) is \( P(s)=3s \) (because all three sides are equal, so perimeter = 3×side length).

Step2: Substitute \( s = 2 \) into \( P(s) \)

\( P(2)=3\times2=6 \)

Step1: Use the perimeter formula \( P(s)=3s \)

Step2: Substitute \( s = 10 \) into \( P(s) \)

\( P(10)=3\times10 = 30 \)

Answer:

\( A(x) \)

Problem 4

Part a