The area of a rectangle is 18 square centimeters, and its perimeter is 22 centimeters. find the dimensions of the rectangle.

2, 9, 2, 9

Step-by-step explanation:

length = x

width = y

xy = 18

2x + 2y = 22

Substitute the second equation into the first. to do that, rewrite the equation

2x + 2y = 22 becomes y = -x + 11

Then use the new equation and substitute it with the y in the first equation.

x(-x + 11) = 18

-x^2 +11x - 18

Divide by -1

x^2 -11x + 18 = (x - 2) (x - 9)

x = 2, 9

when x = 2, y = 9 and when x = 9, y = 2 so they are interchangeable. the sides are 2, 9, 2, and 9.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.