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3 years ago

Expand and simplify 5(2x-1) + 2(3x-6)

Mathematics

1 answer:

aleksklad [387]3 years ago

8 0

5 (2x-1) + 2(3x-6)

I could only expand it :)

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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

3 0

3 years ago

Read 2 more answers

Solve the linear system by using Substitution. Enter your answer as an ordered pair.

MAXImum [283]

Answer: {y,x} = {4,2} ) ) ) )4

Step-by-step explanation: y

[2] y = -2x + 8

// Plug this in for variable y in equation [1]

[1] (-2x+8) - x = 2

[1] - 3x = -6

// Solve equation [1] for the variable x

[1] 3x = 6

[1] x = 2

// By now we know this much :

y = -2x+8

x = 2

// Use the x value to solve for y

y = -2(2)+8 = 4

Solution :

{y,x} = {4,2}

7 0

3 years ago

Read 2 more answers

A rectangular prism has a length of 412 millimeters, a width of 412 millimeters, and a height of 6 millimeters. Sally has a stor

Dominik [7]

Multiply the length*width*height to get the volume of the prism then, take out the difference between the volumes
Volume of the prism= 1018464
Then just subtract

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3 years ago

Simplify a+a+a= 4b-b 3x2+x2

Reika [66]

<h2>Good morning,</h2>

__________________

Answer:

a+a+a = 3a.

4b-b = 3b.

3x²+x² = 4x².

explanation

a+a+a = 3a.

4b-b = b(4 - 1) = b × 3 = 3b.

3x²+x² = x²(3 + 1) = x² × 4 = 4x².

_______________________________

7 0

3 years ago

If start fraction 1 over 3 end fraction is equivalent to 33start fraction 1 over 3 end fraction%, what percent is equivalent to

kotegsom [21]

Answer:

The answer is C 66%

Step-by-step explanation:

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3 years ago