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3 years ago

Consider the relation y = 4|x + 2| + 7. What are the coordinates of the vertex?

1 answer:

5 0

To answer, we set the expression inside the absolute value symbol (II) equal to 0. That is,
x + 2 = 0
Then, we solve for the value of x.
x + 2 - 2 = 0 - 2
Hence, the value of x from the equation above is equal to -2.

Then, substitute the value of x to the equation and drop the absolute value symbol.
y = 4(x + 2) + 7
Substituting,
y = 4(-2 + 2) + 7
y = 4(0) + 7
y = 7

Thus, the vertex of the absolute value equation is equal to (-2,7). The answer is the last choice.

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What the answer question

kobusy [5.1K]

Answer:

$\bold{A_{_{\Delta XYZ}}=927.5\ cm^2}$

Step-by-step explanation:

m∠Z = 180° - 118° - 28° = 34°

$\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\$

$\dfrac{\overline{XY}}{\sin Z}=\dfrac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\dfrac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=\dfrac{42}{0.4695}\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_{\Delta XYZ}}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_{\Delta XYZ}}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5$

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3 years ago

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He simplified expression C because that is the only one that has only multiplications.

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It takes the hot water faucet 4 times as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and

Debora [2.8K]

If it takes the cold water faucet x minutes to fill 1 tub, then its flow rate is (1 tub)/(x min).

The hot water faucet takes 4 times as long, so its flow rate is (1 tub)/(4x min).

Together, the total flow rate is (1 tub)/(3 min), so we have

$\dfrac1x+\dfrac1{4x}=\dfrac13$

$\implies\dfrac5{4x}=\dfrac13$

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Step-by-step explanation:

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Write a system of equations with a solution (4,–3)

Gennadij [26K]

<span>1. </span><span>So we have the system of equation. (4, -3)
let’s create another system of equation.
Let a = 4
and Let b = -3
First equation
=> Let’s pick any numbers to be used. Let’s have number 5
=> 5a + 5b
=> 5 (4) + 5 (-3)
=> 20 + (-15)
negative and positive is equals to negative
=> 20 – 15
=> 5 (this the first value of our equation, let this be the value of X)

Second
=> Pick another number, Let’s have 6
=> 6a + 6b
=> 6 (4) + 6 (-3)
=> 24 + (-18)
=> 24 – 18
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Now, we have (A, B) = (4, -3) and (X, Y) = (5,6)</span>

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