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3 years ago

12

A direct variation includes the points (21,7) and (27,Y. Findvalue of y.

1 answer:

rjkz [21]3 years ago

3 0

Answer:

13

Step-by-step explanation:

5 has been added by the 21 to make 27 to leave with adding 5 to old y and leaving the new variable y 13

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The equation of the line is 3y+2x=12 . what is the slope of the line perpendicular to this equation?

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The slope
$\frac{3}{2}$

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3 years ago

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River C is 400 miles longer than River D. If the sum of their lengths is 5,590 miles, what is the length of each river?

pychu [463]

Answer:

River C is: 2,965 miles long.

River D is: 2,565 miles long.

Step-by-step explanation:

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2 years ago

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Our current equation is:

inessss [21]

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C

Step-by-step explanation:

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3 years ago

Find the product of all real values of r for which 1/2x=r-x/7

Dahasolnce [82]

Answer:

$r = \±\sqrt{14$

$Product = -14$

Step-by-step explanation:

Given

$\frac{1}{2x} = \frac{r - x}{7}$

Required

Find all product of real values that satisfy the equation

$\frac{1}{2x} = \frac{r - x}{7}$

Cross multiply:

$2x(r - x) = 7 * 1$

$2xr - 2x^2 = 7$

Subtract 7 from both sides

$2xr - 2x^2 -7= 7 -7$

$2xr - 2x^2 -7= 0$

Reorder

$- 2x^2+ 2xr -7= 0$

Multiply through by -1

$2x^2 - 2xr +7= 0$

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

$b^2 - 4ac = 0$

For a quadratic equation

$ax^2 + bx + c = 0$

By comparison with $2x^2 - 2xr +7= 0$

$a = 2$

$b = -2r$

$c =7$

Substitute these values in $b^2 - 4ac = 0$

$(-2r)^2 - 4 * 2 * 7 = 0$

$4r^2 - 56 = 0$

Add 56 to both sides

$4r^2 - 56 + 56= 0 + 56$

$4r^2 = 56$

Divide through by 4

$r^2 = 14$

Take square roots

$\sqrt{r^2} = \±\sqrt{14$

$r = \±\sqrt{14$

Hence, the possible values of r are:

$\sqrt{14$ or $-\sqrt{14$

and the product is:

$Product = \sqrt{14} * -\sqrt{14}$

$Product = -14$

8 0

3 years ago