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masya89 [10]
4 years ago
8

Solve for x: 125^(3x+7)=25^(5x−11)

Mathematics
1 answer:
vodomira [7]4 years ago
6 0

Answer:

x = 43

Step-by-step explanation:

125^(3x+7)=25^(5x−11)

Rewriting the bases as powers of 5

125 = 5^3  and 25 = 5^2

5^3 ^ (3x+7) = 5^2^(5x-11)

We know a^b^c = a^ (b*c)

5^(3 * (3x+7)) = 5^(2*(5x-11))

Distribute

5^(9x+21) = 5^(10x-22)

The bases are the same so the exponents are the same

9x+21 = 10x-22

Subtract 9x from each side

9x+21 -9x = 10x-9x-22

21 = x-22

Add 22 to each side

21+22 = x-22+22

43 = x

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Write the equation of the line passing through (-3, 4) and normal to -2x + 7y = -3. (Note: normal means perpendicular)
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Answer:

The answer to your question is     y = -7/2x -13/2

Step-by-step explanation:

Point = (-3, 4)

Line   -2x + 7y = -3

Process

1.- Solve equation for y to find the slope of the perpendicular line

                  7y = 2x - 3

                    y = 2/7 x - 3/7

slope = 2/7

Slope of the perpendicular line = -7/2

2.- Find the equation of the new line

                   y - y1 = m(x - x1)

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                   y = -7/2x - 21/2 + 4

                   y = -7/2x -21/2 + 8/2

3.- Result

                   y = -7/2x -13/2

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