Question

evaluate each algebraic expression for
a. $34 - y^2$ for $y = 5$

b. $m^3 - 18$ for $m = 2$

c. $\frac{d}{5} + 42$ for $d = -70$

Explanation:

Part A

Step1: Substitute \( y = 5 \) into the expression

We have the expression \( 34 - y^2 \). Substitute \( y = 5 \), so we get \( 34 - 5^2 \).

Step2: Calculate the exponent

First, calculate \( 5^2 = 25 \). Then the expression becomes \( 34 - 25 \).

Step3: Subtract the numbers

\( 34 - 25 = 9 \).

Part B

Step1: Substitute \( m = 2 \) into the expression

We have the expression \( m^3 - 18 \). Substitute \( m = 2 \), so we get \( 2^3 - 18 \).

Step2: Calculate the exponent

First, calculate \( 2^3 = 8 \). Then the expression becomes \( 8 - 18 \).

Step3: Subtract the numbers

\( 8 - 18 = -10 \).

Part C

Step1: Substitute \( d = -70 \) into the expression

We have the expression \( \frac{d}{5} + 42 \). Substitute \( d = -70 \), so we get \( \frac{-70}{5} + 42 \).

Step2: Calculate the fraction

First, calculate \( \frac{-70}{5} = -14 \). Then the expression becomes \( -14 + 42 \).

Step3: Add the numbers

\( -14 + 42 = 28 \).

Answer:

A. \( 9 \)
B. \( -10 \)
C. \( 28 \)