If f(x)=2x+1 and g(x)=x-3, find f(g(f(x)))
2 answers:
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Answer:
<u>24 meters</u> is the width of the original rectangle.
Step-by-step explanation:
Given:
Bobby knows that the perimeter of the original rectangle is 120 meters. He also knows that the perimeter of the reduced rectangle is 30 meters and the reduced rectangle has a length of 9 meters.
Now, to get the width of original rectangle.
The reduced rectangle's perimeter = 30 meters.
The reduced rectangle's length = 9 meters.
Now, we find the width of reduced rectangle by using formula:
Let the width of reduced rectangle be
<em>Subtracting both sides by 18 we get:</em>
<em /><em />
<em>Dividing both sides by 2 we get:</em>
The width of reduced rectangle = 6 meters.
Now, to get the width of original rectangle:
Let the width of original rectangle be
<em>As given, the perimeter of the original rectangle = 120 meters.</em>
<em>And, the perimeter of reduced rectangle is 30 meters and its width is 6 meters.</em>
<em>So, 30 is equivalent to 6.</em>
<em>Thus, 120 is equivalent to </em><em />
Now, to get the width using cross multiplication method:
<em>By cross multiplying we get:</em>
<em /><em />
<em>Dividing both sides by 30 we get:</em>
<em /><em />
<em>The width of original rectangle = 24 meters.</em>
Therefore, 24 meters is the width of the original rectangle.
Answer:
B. No, the remainder is -50.
General Formulas and Concepts:
<u>Algebra I</u>
- Roots are when the polynomial are equal to 0
<u>Algebra II</u>
- Synthetic Division
Step-by-step explanation:
<u>Step 1: Define</u>
Function f(x) = x³ - 10x² + 27x - 12
Divisor/Root (x + 1)
<u>Step 2: Synthetic Division</u>
<em>See Attachment.</em>
To determine whether a given root is an actual root, the remainder must equal 0. Since we have a remainder of -50, the given root is not a factor of the polynomial.
<em>Please excuse the bad handwriting. Hope this helped!</em>
