23. evaluate: 2^4 - 3^2+7(0.5) a. 3.5 b. 5.5 c. 10.5 d. 14.5 24. rectangle pqrs has vertices at p(-2,5)…

Explanation:

Step1: Calculate powers

$2^4 = 16$, $3^2=9$

Step2: Calculate multiplication

$7(0.5)=3.5$

Step3: Calculate the expression

$16 - 9+3.5=10.5$

Answer:

C. 10.5

Explanation:

Step1: Find length of base

The length of the base of the rectangle can be found by calculating the distance between two points on the same horizontal - line. For points $P(-2,5)$ and $Q(4,5)$, the distance formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Since $y_1 = y_2 = 5$, the length of $PQ$ is $|4-(-2)|=6$.

Step2: Find length of height

For points $Q(4,5)$ and $R(4, - 1)$, since $x_1=x_2 = 4$, the length of $QR$ is $|5-(-1)|=6$.

Step3: Calculate area of rectangle

The area of a rectangle is $A = l\times w$. Here, $l = 6$ and $w = 6$, so $A=6\times6 = 36$.

Answer:

C. 36