The vertices of a parallelogram are shown below.

1 answer:

4 0

The vertices for the dilated image can be found by multiplying the coordinates of the original image by the scale factor. In this problem, the scale factor is 1/3.

(0,0) ⇒ 0 x 1/3 = 0 ; 0 x 1/3 = 0 ⇒ (0,0)
(27,0) ⇒ 27 x 1/3 = 9 ; 0 x 1/3 = 0 ⇒ (9,0)
(36,30) ⇒36 x 1/3 = 12 ; 30 x 1/3 = 10 ⇒ (12,10)
(9,30) ⇒ 9 x 1/3 = 3 ; 30 x 1/3 = 10 ⇒ (3,10)

Answer is choice D. (3,10)

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Write an equation of the line that passes through the given point and is parallel to the graph of the given equation.

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Question 1:

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Find Slope
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Equation: y = 5x - 2
Slope = 5
Slope of parallel line = 5

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Insert slope into the general equation y = mx + c
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y = 5x + c

--------------------------------------------------------------------
Find y-intercept
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At point (2, -1)
y = 5x + c
-1 = 5(2) + c
c = -1 - 10
c = -11

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Insert y-intercept into the equation
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y = 5x + c
y = 5x - 11

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Answer: y = 5x - 11
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Question 2:

--------------------------------------------------------------------
Find Slope
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y = 9x
Slope = 9
Slope of the parallel line = 9

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Insert slope into the equation y = mx + c
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y = 9x + c

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Find y-intercept
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y = 9x + c
At point (0, 5)
5 = 9(0) + c
c = 5

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Insert y-intercept into the equation
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y = 9x + c
y = 9x + 5

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Answer: y = 9x + 5
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3 years ago

Which of the following is the portion of a line that starts at one point and goes off in a particular direction to infinity?

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Answer: Vertex
Explanation:

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3 years ago

Read 2 more answers

(x+16)²=12 plz help me and show work

Readme [11.4K]

Answer:

The answer is $x=-16$ ± $2\sqrt{3}$ in exact form or $x=-12.535898$ , $x=-19.464102$ in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring $x+16$ , which will look like $x^{2} +32x+256-12=0$ . Next, simplify the equation again, which will look like $x^{2} +32x+244=0$ .

Then, use the quadratic formula to find the solutions. The quadratic formula looks like $\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}$ .

For this problem, the quadratic variables are as follows:

$a=1$

$b=32$

$c=244$

The next step is to substitute the values $a=1$ , $b=32$ , and $c=244$ into the quadratic formula and solve. The quadratic formula will look like $\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}$ . To simplify the equation, start by simplifying the numerator, which will look like $x=\frac{-32(+-)4\sqrt{3} }{2*1}$ . Then, multiply 2 by 1 and simplify the equation, which will look like $x=-16(+-)2\sqrt{3}$ . The final answer is $x=-16$ ± $2\sqrt{3}$ in exact form. In decimal form, the final answer is $x=-12.535898$ , $x=-19.464102$ .