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Answer: 
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Given: 
Find: 
Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.
<u>Plug in the values</u>
<u>Simplify and solve for y</u>
Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.
Answer:
f(g(x)) = 4x² + 16x + 13
Step-by-step explanation:
Given the composition of functions f(g(x)), for which f(x) = 4x + 5, and g(x) = x² + 4x + 2.
<h3><u>Definitions:</u></h3>
- The <u>polynomial in standard form</u> has terms that are arranged by <em>descending</em> order of degree.
- In the <u>composition of function</u><em> f </em>with function <em>g</em><em>, </em>which is alternatively expressed as <em>f </em>° <em>g,</em> is defined as (<em>f </em> ° <em>g</em>)(x) = f(g(x)).
In evaluating composition of functions, the first step is to evaluate the inner function, g(x). Then, we must use the derived value from g(x) as an input into f(x).
<h3><u>Solution:</u></h3>
Since we are not provided with any input values to evaluate the given composition of functions, we can express the given functions as follows:
f(x) = 4x + 5
g(x) = x² + 4x + 2
f(g(x)) = 4(x² + 4x + 2) + 5
Next, distribute 4 into the parenthesis:
f(g(x)) = 4x² + 16x + 8 + 5
Combine constants:
f(g(x)) = 4x² + 16x + 13
Therefore, f(g(x)) as a polynomial in <em>x</em> that is written in standard form is: 4x² + 16x + 13.
Answer:
- as written, -57
- as perhaps intended, C. -11
Step-by-step explanation:
The expression shown evaluates as ...
7 + 32(-5 +1)/2 = 7 +32(-4)/2 = 7 -128/2 = 7 -64 = -57
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If we assume your "32" is supposed to be 3², or 3^2, then the expression evaluates differently:
7 +3²(-5 +1)/2 = 7 + 9(-4)/2 = 7 -36/2 = 7 -18 = -11 . . . . matches choice C
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When in doubt, you can have the Google calculator evaluate your expression. However, you do have to write it properly and with all the required parentheses.