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3 years ago

The answer to the problem. I don't know how to solve the exponents

Mathematics

1 answer:

Margaret [11]3 years ago

7 0

When muliplying these terms you ADD the exponents so

7^0 * 7^4 * 7^16 = 7^(0+4+16) = 7^20 (NOTE you can any multiply when the base number, in this case 7, is the same)

so we simplify to

3^4 * 7^20

---------------

3^2 * 7^12

When dividing we SUBTRACT the exponents so 3^4 / 3^2 = 3^(4-2) = 3^2 and

7^20 / 7^12 = 7^8

so the answer is 3^2 * 7^8 <------- Option J

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Answer:

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Step-by-step explanation:

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3 years ago

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What is the scale factor in the dilation if the coordinates of A prime are (–7, 6) and the coordinates of C prime are (–4, 3)?

olchik [2.2K]

Option A: $\frac{1}{3}$ is the dilation factor

Explanation:

The Coordinates of the square ABCD are A(-21,18), B(-12,18), C(-12,9), D(-21,9)

Also, the coordinates of the square A'B'C'D' are A'(–7, 6), B'(-4,6), C'(-4,3), D'(-8,3)

Now, we shall determine the scale factor in the dilation if the coordinates A' and C'.

Since, the dilation is the enlargement of the image in the same shape but different size.

To determine the scale factor, let us divide A'C' by AC

Thus, we have,

$\begin{aligned}A^{\prime} C^{\prime} &=\sqrt{(-4+7)^{2}+(3-6)^{2}} \\&=\sqrt{3^{2}+(-3)^{2}} \\&=\sqrt{9+9} \\&=\sqrt{18}\\&=3\sqrt{2} \end{aligned}$

Also,

$\begin{aligned}A C &=\sqrt{(-12+21)^{2}+(9-18)^{2}} \\&=\sqrt{9^{2}+(-9)^{2}} \\&=\sqrt{81+81} \\&=\sqrt{162}\\&=9\sqrt{2} \end{aligned}$

Dividing A'C' by AC, we have,

$\frac{A'C'}{AC} =\frac{3\sqrt{2} }{9\sqrt{2}} =\frac{1}{3}$

Thus, $\frac{1}{3}$ is the dilation factor

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3 years ago

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X + y = –4<br> y = 3x + 16

babymother [125]

If
x+y=-4
y-3x=16 or we cn write as
x+y=-4
-3x+y=16
i multiply the first equation by 3
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4y=4
y=1
x+1=-4
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3 years ago

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3 years ago

Evaluate the function f (x)= x squared -4x+1 at the given values of the independent variable and simplify.

Ivan

<h3>Given</h3>

... f(x) = x² -4x +1

... a) f(-8)

... b) f(x+9)

... c) f(-x)

<h3>Solution</h3>

In each case, put the function argument where x is, then simplify.

a) f(-8) = (-8)² -4(-8) +1 = 64 +32 + 1 = 97

b) f(x+9) = (x+9)² -4(x+9) +1

... = x² +18x +81 -4x -36 +1

... f(x+9) = x² +14x +46

c) f(-x) = (-x)² -4(-x) +1

... f(-x) = x² +4x +1

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3 years ago