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3 years ago

QRST is a parallelogram. Find x and y.

Mathematics

1 answer:

Wewaii [24]3 years ago

5 0

In parallelograms, opposite sides are congruent, meaning that they are the same lengths. So, we have:

y - 4x = 9

-x + 4 = y

Add x to both sides of the second equation:

y + x = 4

y - 4x = 9

This is a system of linear equations. Solve by eliminating the y and subtracting the two equations:

5x = -5

x = -1

Use x to solve for y:

y + (-1) = 4

y = 5

So, x = -1 and y = 5.

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Answer:

$(x+3)^2+(y-2)^2=9$

Step-by-step explanation:

Equation of a circle

$(x-a)^2+(y-b)^2=r^2$

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(a, b) is the center
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From inspection of the diagram, the center of the circle appears to be at point (-3, 2), although this is not very clear. Therefore, a = -3 and b = 2.

Substitute these values into the general form of the equation of a circle:

$\implies (x-(-3))^2+(y-2)^2=r^2$

$\implies (x+3)^2+(y-2)^2=r^2$

Again, from inspection of the diagram, the maximum vertical point of the circle appears to be at y = 5. Therefore, to calculate the radius, subtract the y-value of the center point from the y-value of the maximum vertical point:

⇒ radius (r) = 5 - 2 = 3

Substitute the found value of r into the equation:

$\implies (x+3)^2+(y-2)^2=3^2$