Suppose that y varies directly with x and y=12 when x=-2. What is x when y=-6
Please help me!!

9514 1404 393

  x = 1

Step-by-step explanation:

You can work this several ways.

1) Consider the factor that gets you from the y-value of the known pair to the y-value of the unknown pair. Here, that factor is -6/12 = -1/2.

Then the unknown value of x is the known value multiplied by that same factor:

  x = (-1/2)(-2)

  x = 1

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2) You can write the equation for a "varies directly" relationship and solve for the constant of proportionality. Then you can use that equation to find the unknown value of x.

  y = kx . . . . . . . . . . . . . . y varies directly with x

  k = y/x = 12/-2 = -6

Now we know ...

  y = -6x

Filling in the new value for y, we have ...

  -6 = -6x

  1 = x . . . . . . divide by -6

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3) You can write a proportion. Since we want to find a value for x, it is convenient to put that in the numerator.

  -2/12 = x/-6

Multiplying by -6, we get ...

  (-6)(-2)/12 = x = 1

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734