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harina [27]
3 years ago
9

Solve 3(2x - 5) = 9(10 - x)

Mathematics
2 answers:
alisha [4.7K]3 years ago
4 0

Answer:

x=7

Step-by-step explanation:

3(2x - 5) = 9(10 - x)

6x-15=90-9x

6x+9x=90+15

15x=105

x=7

Helen [10]3 years ago
3 0

Answer:

x = 7

Step-by-step explanation:

First, we need to expand the brackets:

3(2x-5)=9(10-x) (equation given)

6x-15=90-9x

15x -15 = 90 (add 9x on both sides)

15x = 105 (add 15 on both sides)

x = 7 (divide by 15 on both sides)

Hope this helps :)

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What is the area of the piece of red paper after the hole for
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Answer:

     \large\boxed{\large\boxed{47unit^2}}

Explanation:

The complete question is:

<em>A hole the size of a photograph is cut from a red piece of paper to use in a picture frame.</em>

<em />

<em>On a coordinate plane, 2 squares are shown. The photograph has points (-3, -2), (- 2, 2), (2, 1), and (1, -3). The red paper has points (- 4, 4), (4, 4), (4, -4), and (-4, -4).</em>

<em />

<em>What is the area of the piece of red paper after the hole for the photograph has been cut?</em>

<em />

<h2><em>Solution</em></h2>

<em />

The area of the piece of redpaper after the hole has been cut is equal to the area of the big square less the area of the small rectangle.

<u>1. Area of the big rectangle</u>

Vertices:

  • <em>(- 4, 4) </em>
  • <em>(4, 4)</em>
  • <em>(4, -4)</em>
  • <em>(-4, -4)</em>

<em />

The side length is the distance between two consecutive vertices:

The two points (-4,4) and (4,4) has the same y-coordinate, thus the length is just the absolute value of the difference of the x-coordinates:

  • 4-(-4)=4+4=8

The area of this square is    (8unit)^2=64unit^2

<u>2. Area of the small square</u>

Vertices:

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  • <em>(- 2, 2) </em>
  • <em>(2, 1)</em>
  • <em>(1, -3)</em>

<em />

To find the side length use the distance formula for two consecutive points, for instance (2,1) and (-2,2):

      d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\ \\d=\sqrt{(2-(-2))^2+(2-1)^2}=\sqrt{4^2+1^2}=\sqrt{17}

The area is:

          (\sqrt{17}unit)^2}=17unit^2

<u>3. Area of the piece of red paper after the holw for the photograph has been cut:</u>

<u />

Find the difference:

<u />

         64unit^2-17unit^2=47unit^2

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Answer:

Step-by-step explanation:

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