The two angles shown are vertical angles. They form when you cross two lines. They are opposite one another. Note: They don't have to be vertically up and down in relation to each other. It's possible to have them horizontally side by side like this.
So because they are vertical angles, they are congruent. This means they are equal in measure
x+90 = 4x
x+90-x = 4x-x
90 = 3x
3x = 90
3x/3 = 90/3
x = 30
Therefore the answer is choice C) The value of x is x = 30
We can check it by plugging this into the original equation above
x+90 = 4x
30+90 = 4*30
120 = 120
our answer checks out
You get 1 9/10. You can change 0.38 to 38/100 which simplifies to 19/50. Then u can change 15 1/3 to an improper fraction. You get 46/3. Then multiply 19/50 by 46/3 and you get 19/10 which simplifies to 1 9/10.
Answer:
-4 + 2 = -2
Step-by-step explanation:
-4 -(-2) uses the process of cancellation. -(-2) is equal to positive 2, since the negatives cancel out. -4 + 2 is left, which equals -2.
Subtracting a negative from a negative is like subtracting a positive from a positive. It is even like 1-1. Once you subtract one from another, nothing is left.
Given:
Point P is the incenter of triangle HKM.
To find:
The measure of JP.
Solution:
In triangle MNP, using Pythagoras theorem, we get
![Hypotenuse^2=base^2+Perpendicular^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3Dbase%5E2%2BPerpendicular%5E2)
![(MP)^2=(MN)^2+(NP)^2](https://tex.z-dn.net/?f=%28MP%29%5E2%3D%28MN%29%5E2%2B%28NP%29%5E2)
![(25)^2=(24)^2+(NP)^2](https://tex.z-dn.net/?f=%2825%29%5E2%3D%2824%29%5E2%2B%28NP%29%5E2)
![625=576+(NP)^2](https://tex.z-dn.net/?f=625%3D576%2B%28NP%29%5E2)
![625-576=(NP)^2](https://tex.z-dn.net/?f=625-576%3D%28NP%29%5E2)
![49=(NP)^2](https://tex.z-dn.net/?f=49%3D%28NP%29%5E2)
Taking square root on both sides, we get
![\pm \sqrt{49}=NP](https://tex.z-dn.net/?f=%5Cpm%20%5Csqrt%7B49%7D%3DNP)
![\pm 7=NP](https://tex.z-dn.net/?f=%5Cpm%207%3DNP)
Side cannot be negative. So,
![NP=7](https://tex.z-dn.net/?f=NP%3D7)
Point P is the incenter of triangle HKM.
[Incenter is equidistant from each side of triangle]
![JP=7](https://tex.z-dn.net/?f=JP%3D7)
Therefore, the value of JP is 7 units.
Answer:
152cm²
Step-by-step explanation:
math and stuff and things