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3 years ago

Five divided by the difference of a number and 8 equals the quotient of 10 and the sum of a number and 7. Find the number.

Mathematics

1 answer:

Sati [7]3 years ago

5 0

Answer:

Step-by-step explanation:

Let the number be x

Five divided by the difference of the number and 8 means

5 / (x-8) and this is

equals the quotient of 10 and the sum of a number and 7.This means

10 / (7+x)

Therefore,

5 / (x-8) = 10 / (7+x)

Cross multiplying,

5(7+x) = 10(x-8)

35 + 5x = 10x - 80

5x - 10x = -80- 35

-5x = - 115

x = -115/5 = 23

If Jon can paint the fence in 3 hours

This means Jon can paint the fence in 1/3 per hour

If Karen can paint it in 5 hours

This means Karen can paint the fence in 1/5 hours

Their combined rate is additive since they work simultaneously. Jon doesn't stop for Karen to work and Karen doesn't stop for Jon to work.

Their combined rate is

1/3 + 1/5 = 8/15

Let's assume the combined time is t hours.

The combined time per hour is 1/t per hour. Therefore 1/t = 8/15

t = 15/8 = 1.875 hours

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Find the equation of the circle if one of the endpoints of the diameter is (-2,-3) and the midpoint of the circle's diameter is

tankabanditka [31]

Answer:

The answer to your question is (x - 4)² + (y - 5)² = 100

Step-by-step explanation:

Data

Point = (-2, -3)

Midpoint = (4, 5)

Process

1.- Find the length of the radius using the formula of the distance between two points.

dPM = $\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}$

x1 = -2 y1 = -3 x2 = 4 y2 = 5

dPM = $\sqrt{(4 + 2)^{2} + (5 + 3)^{2}}$

dPM = $\sqrt{(6)^{2} + (8)^{2}}$

dPM = $\sqrt{36 + 64}$

dPM = $\sqrt{100}$

dPM = 10

2.- Find the equation of the line

(x - h)² + (y - k)² = r²

h = 4

k = 5

r = 10

(x - 4)² + (y - 5)² = 10²

(x - 4)² + (y - 5)² = 100

8 0

2 years ago

2(x+2)-5=3(x+1)

Eva8 [605]

Answer:

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$2(x + 2) - 5 = 3(x + 1) \\ 2x + 4 - 5 = 3x + 3 \\ 2x - 1 = 3x + 3 \\ - 1 - 3 = 3x - 2x \\ - 4 = x$

5 0

2 years ago

Read 2 more answers

16x² -9 = 4×² + (4x²+9)

lesya [120]

For this case we must solve the following equation:

$16x ^ 2-9 = 4x ^ 2 + (4x ^ 2 + 9)$

We remove the parentheses on the right side:

$16x ^ 2-9 = 4x ^ 2 + 4x ^ 2 + 9$

We add similar terms on the right side:

$16x ^ 2-9 = 8x ^ 2 + 9$

We subtract $8x ^ 2$ from both sides of the equation:

$16x ^ 2-8x ^ 2-9 = 9\\8x ^ 2-9 = 9$

We add 9 to both sides of the equation:

$8x ^ 2 = 9 + 9\\8x ^ 2 = 18$

We divide by 8 on both sides of the equation:

$x ^ 2 = \frac {18} {8}\\x ^ 2 = \frac {9} {4}$

We apply square root to both sides of the equation:

$x = \pm \sqrt {\frac {9} {4}}$

We have two roots:

$x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}$

Answer:

$x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}$

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2 years ago

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