Answer:
See answers below.
Step-by-step explanation:
<u>Large Rectangle:</u><u> </u> length x width = (x + 3)(x - 4) =
x² - 4x + 3x - 12
x² - x - 12
<u>Smaller Rectangle:</u> length x width = (x)(3) = 3x
<u>Shaded Region: </u>shaded area = lg. rectangle minus small rectangle
A = (x² - x - 12) - 3x
A = x² - 4x - 12
<u>Solve for x, if shaded reion's area is 48 square units: </u>
48 = x² - 4x - 12
x² - 4x - 12 -48 = 0
x² - 4x - 60 = 0
(x - 10)(x + 6) = 0
x - 10 = 0 or x + 6 = 0
x = 10 or x = -6
But x represents a length, so x cannot be -6.
x = 10
Answers:
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Explanation:
The piecewise function f(x) changes based on what the input is.
We have two cases:
- Case A) if x > 4, then f(x) = 3x-1
- Case B) If , then f(x) = 2x
The input x = -3 satisfies the inequality , so we go with case B for this input
f(x) = 2x
f(-3) = 2(-3)
f(-3) = -6
In contrast, the input x = 7 satisfies the inequality x > 4. So we go for case A this time.
f(x) = 3x-1
f(7) = 3(7)-1
f(7) = 21-1
f(7) = 20
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Side note: It might be better to let g(x) = 3x-1 and h(x) = 2x. Then we could further say "If x > 4, then f(x) = g(x) OR if , then f(x) = h(x)". Though this might be a more wordy definition.
Answer:
R (6x + 120) = 108x^2 + 4608x +48960
Step-by-step explanation:
Set Up Composite function and evaluate
Answer:
5^2 * 5^9
5^3 * 5^8
5^4 * 5^7
Step-by-step explanation:
The easiest way to approach this problem is to first express 5^(11) in its simplest form:
5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
Then you can regroup them as you want, to still express the same value, but shown as a product of different numbers, including:
(5) * (5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5) = 5 * 5^(10)
(5 * 5) * (5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5) = 5^2 * 5^9
(5 * 5 * 5) * (5 * 5 * 5 * 5 * 5 * 5 * 5 * 5) = 5^3 * 5^8
(5 * 5 * 5 * 5) * (5 * 5 * 5 * 5 * 5 * 5 * 5) = 5^4 * 5^7
And so on....