Given:
Consider the below figure attached with this question.
and
.
To find:
The measure of angle 3.
Solution:
From the below figure it is clear that, angle 3 and angle 4 are vertically opposite angles.
We know that, vertically opposite angles are always equal. So,
![m\angle 3=m\angle 4](https://tex.z-dn.net/?f=m%5Cangle%203%3Dm%5Cangle%204)
![(x+30)^\circ=(2x-80)^\circ](https://tex.z-dn.net/?f=%28x%2B30%29%5E%5Ccirc%3D%282x-80%29%5E%5Ccirc)
![x+30=2x-80](https://tex.z-dn.net/?f=x%2B30%3D2x-80)
![x-2x=-30-80](https://tex.z-dn.net/?f=x-2x%3D-30-80)
![-x=-110](https://tex.z-dn.net/?f=-x%3D-110)
![x=110](https://tex.z-dn.net/?f=x%3D110)
Now,
![m\angle 3=(110+30)^\circ](https://tex.z-dn.net/?f=m%5Cangle%203%3D%28110%2B30%29%5E%5Ccirc)
![m\angle 3=140^\circ](https://tex.z-dn.net/?f=m%5Cangle%203%3D140%5E%5Ccirc)
Therefore, the measure of angle 3 is 140 degrees.
If it is not intersect they are not parallel
Answer:
Step-by-step explanation:
If given tables in the picture show the proportional relationship,
Number of wheels (w) ∝ Number of buses (b)
w ∝ b
w = kb
Here, k = proportionality constant
k = ![\frac{w}{b}](https://tex.z-dn.net/?f=%5Cfrac%7Bw%7D%7Bb%7D)
Number of buses (b) Number wheels (w) Wheels per bus ![(\frac{w}{b})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bw%7D%7Bb%7D%29)
5 30
8 48 ![\frac{48}{8}=6](https://tex.z-dn.net/?f=%5Cfrac%7B48%7D%7B8%7D%3D6)
10 60 ![\frac{60}{10}=6](https://tex.z-dn.net/?f=%5Cfrac%7B60%7D%7B10%7D%3D6)
15 90 ![\frac{90}{15}=6](https://tex.z-dn.net/?f=%5Cfrac%7B90%7D%7B15%7D%3D6)
Here, proportionality constant is 6.
Similarly, If number of wheels (w) ∝ Number of train cars (t)
w = kt
Here, k = proportionality constant
k = ![\frac{w}{t}](https://tex.z-dn.net/?f=%5Cfrac%7Bw%7D%7Bt%7D)
Number of train cars(t) Number of wheels(w) Wheels per train car (
)
20 184 ![\frac{184}{20}=9.2](https://tex.z-dn.net/?f=%5Cfrac%7B184%7D%7B20%7D%3D9.2)
30 264 ![\frac{264}{30}=8.8](https://tex.z-dn.net/?f=%5Cfrac%7B264%7D%7B30%7D%3D8.8)
40 344 ![\frac{344}{40}=8.6](https://tex.z-dn.net/?f=%5Cfrac%7B344%7D%7B40%7D%3D8.6)
50 424 ![\frac{424}{50}=8.48](https://tex.z-dn.net/?f=%5Cfrac%7B424%7D%7B50%7D%3D8.48)
Since, ratio of w and t is not constant, relation between number of wheels and number of train cars is not proportional.
Answer:
10d - 3x
Step-by-step explanation:
Distribute the 4: 12d - 8x
Distribute the -1: -2d + 5x
Add like terms: 10d - 3x