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Simora [160]
3 years ago
14

Solve the equation and find what X is. 9x-7=10

Mathematics
1 answer:
Marysya12 [62]3 years ago
6 0

Answer:

x = 1 8/9 or 17/9

Step-by-step explanation:

Step 1: Add 7 to both sides.

  • 9x - 7 + 7 = 10 + 7
  • 9x = 17

Step 2: Divide both sides by 9.

  • \frac{9x}{9} = \frac{17}{9}  
  • x = \frac{17}{9} = 1 \frac{8}{9}

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The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2 : 3, what is the rati
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<h2>Answer:</h2>

The ratio of the area of region R to the area of region S is:

                    \dfrac{24}{25}

<h2>Step-by-step explanation:</h2>

The sides of R are in the ratio : 2:3

Let the length of R be: 2x

and the width of R be: 3x

i.e. The perimeter of R is given by:

Perimeter\ of\ R=2(2x+3x)

( Since, the perimeter of a rectangle with length L and breadth or width B is given by:

Perimeter=2(L+B) )

Hence, we get:

Perimeter\ of\ R=2(5x)

i.e.

Perimeter\ of\ R=10x

Also, let " s " denote the side of the square region.

We know that the perimeter of a square with side " s " is given by:

\text{Perimeter\ of\ square}=4s

Now, it is given that:

The perimeters of square region S and rectangular region R are equal.

i.e.

4s=10x\\\\i.e.\\\\s=\dfrac{10x}{4}\\\\s=\dfrac{5x}{2}

Now, we know that the area of a square is given by:

\text{Area\ of\ square}=s^2

and

\text{Area\ of\ Rectangle}=L\times B

Hence, we get:

\text{Area\ of\ square}=(\dfrac{5x}{2})^2=\dfrac{25x^2}{4}

and

\text{Area\ of\ Rectangle}=2x\times 3x

i.e.

\text{Area\ of\ Rectangle}=6x^2

Hence,

Ratio of the area of region R to the area of region S is:

=\dfrac{6x^2}{\dfrac{25x^2}{4}}\\\\=\dfrac{6x^2\times 4}{25x^2}\\\\=\dfrac{24}{25}

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