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2 years ago

5( x + 7) - 3 ( x - 4) = 7x + 2 what is x?

Mathematics

2 answers:

S_A_V [24]2 years ago

8 0

Answer:

x=9

Step-by-step explanation:

5( x + 7) - 3 ( x - 4) = 7x + 2

Distribute

5x+35 - 3x +12 = 7x +2

2x +47 = 7x+2

Subtract 2x from each side

2x+47-2x =7x -2x+2

47 = 5x+2

Subtract 2 from each side

47-2= 5x+2-2

45= 5x

Divide by 5

45/5 =5x/5

9 =x

brilliants [131]2 years ago

3 0

Answer:

x = 9

Step-by-step explanation:

→Distribute the 5 to (x + 7), Distribute the -3 to (x - 4):

5(x + 7) - 3(x - 4) = 7x + 2

5x + 35 - 3x + 12 = 7x + 2

→Add like terms:

2x + 47 = 7x + 2

→Subtract 2x from both sides:

47 = 5x + 2

→Subtract 2 from both sides:

45 = 5x

→Divide both sides by 5:

9 = x

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Step-by-step explanation:

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3 years ago

Choose all that give the correct effect on the linear graph of the parent function ƒ(x).

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2 years ago

Lee wants to cut this piece of canvas into two rectangles that are 3×2 and 3×5. He wants the sum of the areas of the two small r

scoray [572]

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2 years ago

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

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2 years ago