Question

2 fill in the blank 1 point if uw = 6x - 35, find uw. 19 4x - 20 u v w uw = type your answer.. 3 fill in the blank 1 point a circle on the coordinate plane has a diameter with endpoints at (6, 8) and (15, 8). a. what are the coordinates of the center of the circle? type your answer.. type your answer.. b. what is the diameter of the circle? (hint: use distance formula) diameter = type your answer.. c. what is the radius of the circle? radius = type your answer..

Explanation:

Step1: Set up equation for segment lengths

Since $UW = UV+VW$, we have $6x - 35=19+(4x - 20)$.

Step2: Simplify the right - hand side

$19+(4x - 20)=4x - 1$. So the equation becomes $6x - 35 = 4x-1$.

Step3: Solve for x

Subtract $4x$ from both sides: $6x-4x - 35=4x - 4x-1$, which simplifies to $2x-35=-1$. Then add 35 to both sides: $2x-35 + 35=-1 + 35$, so $2x = 34$. Divide both sides by 2: $x = 17$.

Step4: Find UW

Substitute $x = 17$ into the expression for $UW$: $UW=6x - 35=6\times17-35=102 - 35=67$.

Step5: For circle problem part A

The center of a circle is the mid - point of the diameter. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For points $(6,8)$ and $(15,8)$, the x - coordinate of the center is $\frac{6 + 15}{2}=\frac{21}{2}=10.5$ and the y - coordinate is $\frac{8 + 8}{2}=8$.

Step6: For circle problem part B

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 6,y_1 = 8,x_2 = 15,y_2 = 8$. So $d=\sqrt{(15 - 6)^2+(8 - 8)^2}=\sqrt{9^2+0^2}=9$.

Step7: For circle problem part C

The radius $r$ of a circle is half of the diameter. Since the diameter $d = 9$, the radius $r=\frac{d}{2}=\frac{9}{2}=4.5$.

Answer:

1. UW = 67
2. A. 10.5, 8

B. 9
C. 4.5