Question

1. what is the slope of the line that goes through the points (2,6) and (4, - 1)?

a) -\frac{7}{2}
b) - 2
c) \frac{1}{2}
d) \frac{7}{2}

1. a circle with a radius of 4 centimeters is inscribed inside a square. what is the perimeter of the square?

a) 8 centimeters
b) 16 centimeters
c) 24 centimeters
d) 32 centimeters

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(2,6)$ and $(x_2,y_2)=(4, - 1)$.

Step2: Substitute values

$m=\frac{-1 - 6}{4 - 2}=\frac{-7}{2}=-\frac{7}{2}$.

Step3: Recall relationship for inscribed - circle

If a circle of radius $r$ is inscribed in a square, the side - length $s$ of the square is equal to the diameter $d$ of the circle. Since $d = 2r$ and $r = 4$ cm, then $s=8$ cm.

Step4: Calculate perimeter of square

The perimeter $P$ of a square is given by $P = 4s$. Substituting $s = 8$ cm, we get $P=4\times8=32$ cm.

Answer:

A. $-\frac{7}{2}$
D. 32 centimeters