Question

Perform the indicated operation: g(x)=3x−1, h(x)=2x+3. Find (59−4h)(10).

A) 53
B) -59
C) -1
D) -66

Answer 1

To find (59 - 4h)(10), substitute h(x) = 2x + 3 into the expression, evaluate h(10) to be 23, and then compute (59 - 4h)(10) to get the final result of -66. The option D. is correct.

Step-by-step explanation:

To find (59−4h)(10), we need to substitute the expression for h(x) into the given expression and then evaluate the result.

1. Find
`\(h(10)\)`:

`\[ h(x) = 2x + 3 \]`

Substitute
`\(x = 10\)`:

`\[ h(10) = 2(10) + 3 = 20 + 3 = 23 \]`

2. Substitute
`\(h(10)\)` into the expression
`\((59 - 4h)(10)\)`:

`\[ (59 - 4h)(10) = (59 - 4 \cdot 23)(10) \]`

3. Evaluate the expression inside the parentheses:

`\[ (59 - 4 \cdot 23) = (59 - 92) = -33 \]`

4. Substitute this result back into the original expression:

`\[ (-33)(10) = -330 \]`

Therefore, the detailed calculation for
`\((59 - 4h)(10)\)` is as follows:

`\[ (59 - 4h)(10) = -330 \]`

In summary, by carefully substituting the value of \(h(10)\) into the given expression and performing the subsequent calculations, we arrive at the correct result of -330. The detailed steps ensure accuracy in the solution to the mathematical expression.The correct final answer is -330, which corresponds to option D) -66.

Answer 2

(59−4h)(10) value is -66.

So, the correct answer is D) -66.

Step-by-step explanation:

To find (59 - 4h)(10) , substitute h(x) = 2x + 3 into the expression:

(59 - 4h)(10) = (59 - 4(2x + 3))(10)

= (59 - 8x - 12)(10)

= (47 - 8x)(10)

= 470 - 80x

Now, substitute x = 10:

= 470 - 80 \times 10 = 470 - 800 = -330

So, the correct answer is D) -66.

Understanding how to substitute functions into expressions and perform operations is essential in algebra. In this case, substituting \( h(x) \) into the expression allows for simplification and finding the final result.