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2 years ago

Three vertices of parallelogram PRTV are P(-4,-4), R(-10,0), and V(5,-1). Find the coordinates of vertex T.

1 answer:

7 0

Slope of TV = Slope of PR
(y + 1)/(x - 5) = (0 + 4)/(-10 + 4)
(y + 1)/(x - 5) = -4/6
6(y + 1) = -4(x - 5)
6y + 6= -4x + 20
equation #1: 6y + 4x = 14

Slope of RT = Slope of PV
(y - 0)/(x + 10) = (-1 + 4)/(5 + 4)
(y - 0)/(x + 10) = 3/9
3(y - 0) = 9(x + 10)
3y = 9x +90
equation #2: 3y = 9x +90

<span>We now we have 2 equations with 2 variables, and we can use any method (substitution, linear combination, matrix) to solve for the x and y coordinates.
</span>
equation #1: 6y + 4x = 14
equation #2: 3y - 9x = 90

Multiply equation 2 by -2

equation #1: 6y + 4x = 14
equation #2: -6y + 18x = -180

Add together Eq. 1 & 2

22x = -166
x = -7.5

6y +4(-7.5) = 14
6y = 44
y = 7 1/3

(-7 1/2, 7 1/3)

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Solve the rational equation x+3/3x-2-x-3/3x+2=44/9x^2-4

Drupady [299]

Answer:

$x=2$

Step-by-step explanation:

When given the following equation;

$\frac{x+3}{3x-2}-\frac{x-3}{3x+2}=\frac{44}{9x^2-4}$

One has to solve for the variable (x). Remember, when working with fractions, one must have a common denominator in order to perform operations. Since the denominators on the left side of the equation are unlike, one must change them so that they are like denominators. Multiply each fraction by the other fraction's denominator on the respective side. Remember to multiply both the numerator and denominator by the value to ensure that the equation remains true.

$=\frac{x+3}{3x-2}*(\frac{3x+2}{3x+2})-\frac{x-3}{3x+2}*(\frac{3x-2}{3x-2})=\frac{44}{9x^2-4}$

Simplify,

$=\frac{(x+3)(3x+2)}{(3x-2)(3x+2)}-\frac{(x-3)(3x-2)}{(3x+2)(3x-2)}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}$

Distribute the negative sign to simplify the left side of the equation;

$=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-(3x^2-11x+6)}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-3x^2+11x-6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{22x}{9x^2-4}{=\frac{44}{9x^2-4}$

Since the denominators on opposite sides of the equation are like, one can now ignore the denominators,

$=22x=44$

Inverse operations,

$=22x=44$

÷ $2$ ÷ $2$

$x=2$

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2 years ago

ian is trying to estimate the distance across the lake d. he knows the measures shown in the diagram. which estimate is closest

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Step-by-step explanation:

In the given image, we can see that there is a right triangle, in which d is the side opposite to the right angle (largest angle in the triangle) which means its the longest side of the triangle.

[Since side opposite to the larger angle is larger]

Therefore, by Pythagoras Theorem we have

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The estimate is closest to the distance d is 4.2 miles.

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