Worth 90 points

find each angle measure

a) UXW = 78 degrees

b) UWY = 48 degrees

c) WZX = 48 degrees

d) XYZ = 42 degrees

Step-by-step explanation:

Apply rules and theorems:

Angles in a triangle add up to 180 degrees.

Angles on a straight line add up to 180 degrees.

Right angles are 90 degrees.

Vertically opposite angles are equal.

With these we can solve for the angles.

1)
We have to find the slope of these lines;
Given two points (x₁,y₁) and (x₂,y₂) ; the slope would be:
m=(y₂-y₁)/(x₂-x₁)
Line 1: (2,3) and (-4,5) ⇒ m=(5-3)/(-4-2)=2/-6=-1/3.
Line 2: (-4,9) and (-3,12) ⇒ m=(12-9)/(-3+4)=3

m and m´are perpendicular if m=-1/m

In this case: 3=-1/(-1/3); therefore these lines are perpendicular.

the lines are perpendicular.

2)
We have two points: (3,25) and (8,115); the average rate of change of dollars per hour, would be the slope of the line passes through these points.
m=(y₂-y₁)/(x₂-x₁)
m=(115-25)/(8-3)=90/5=18

the average rate of  change would be 18 dollar/hour.

3)
We have two points: (1, 6.2) and (3 , 20); the  rate of change of miles per hour, would be the slope of the line passes through these points.
m=(y₂-y₁)/(x₂-x₁)
m=(20-6.2)/(3-1)=13.8/2=6.9

The rate of change would be 6.9 miles/ hour.

4)
1) We have to compute the slope of the line passes through these points.
m=(y₂-y₁)/(x₂-x₁)
m=(11-5)/(-2+2)=6/0; because the denominator is equal to zero, we have a perpendicula line.
 In this case  we  can look at one point  (x₀,y₀), then the equation  of the line would be: x=x₀;
We choose one point, for example : (-2,5), then the equation of the line will be x=-2

the equation of the line would be x=-2.

5)
slope-intercept form:
y=mx+b
m=slope

In this case:

y=money of Shelly
x=number of weeks

y=-30x+250

The slope would be m=-30.

the slope would be m=-30.

6)
We have the following equation:
y=0.3x+95
y=total money charged
x=number of miles.

We have the following information:
y=101.6

Then:
101.6=0.3x+95
0.3x+95=101.6
0.3x=101.6-95
0.3x=6.6
x=6.6/0.3
x=22

22 miles