Answer:
The measures of angles of triangle MNP are
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
step 1
Find the measure of arcs AB, BC and AC
we know that
The inscribed angle is half that of the arc it comprises.
so
![\gamma=\frac{1}{2}[arc\ AB] ----> arc\ AB=2\gamma\\\alpha=\frac{1}{2}[arc\ BC] ----> arc\ BC=2\alpha\\\beta=\frac{1}{2}[arc\ AC] ----> arc\ AC=2\beta](https://tex.z-dn.net/?f=%5Cgamma%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AB%5D%20----%3E%20arc%5C%20AB%3D2%5Cgamma%5C%5C%5Calpha%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20BC%5D%20----%3E%20arc%5C%20BC%3D2%5Calpha%5C%5C%5Cbeta%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%5D%20----%3E%20arc%5C%20AC%3D2%5Cbeta)
step 2
Find the measure of angle M
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![M=\frac{1}{2}[arc\ AB+arc\ BC-arc\ AC]](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AB%2Barc%5C%20BC-arc%5C%20AC%5D)
substitute
![M=\frac{1}{2}[2\gamma+2\alpha-2\beta]\\M=[\gamma+\alpha-\beta]](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cgamma%2B2%5Calpha-2%5Cbeta%5D%5C%5CM%3D%5B%5Cgamma%2B%5Calpha-%5Cbeta%5D)
step 3
Find the measure of angle N
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![N=\frac{1}{2}[arc\ AC+arc\ BC-arc\ AB]](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%2Barc%5C%20BC-arc%5C%20AB%5D)
substitute
![N=\frac{1}{2}[2\beta+2\alpha-2\gamma]\\N=[\beta+\alpha-\gamma]](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Calpha-2%5Cgamma%5D%5C%5CN%3D%5B%5Cbeta%2B%5Calpha-%5Cgamma%5D)
step 4
Find the measure of angle P
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![P=\frac{1}{2}[arc\ AC+arc\ AB-arc\ BC]](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%2Barc%5C%20AB-arc%5C%20BC%5D)
substitute
![P=\frac{1}{2}[2\beta+2\gamma-2\alpha]\\P=[\beta+\gamma-\alpha]](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Cgamma-2%5Calpha%5D%5C%5CP%3D%5B%5Cbeta%2B%5Cgamma-%5Calpha%5D)
Answer:
x= -12 and y=8
Step-by-step explanation:
Let's solve your system by substitution.
−x−y=4;x+2y=4
Step: Solve−x−y=4for x:
−x−y=4
−x−y+y=4+y(Add y to both sides)
−x=y+4
−x
−1
=
y+4
−1
(Divide both sides by -1)
x=−y−4
Step: Substitute−y−4forxinx+2y=4:
x+2y=4
−y−4+2y=4
y−4=4(Simplify both sides of the equation)
y−4+4=4+4(Add 4 to both sides)
y=8
Step: Substitute8foryinx=−y−4:
x=−y−4
x=−8−4
x=−12(Simplify both sides of the equation)
Answer:
x=−12 and y=8
I just took the test. The answer is y=250(4^x)
Answer:
-160 is the answer
Step-by-step explanation:
- × - = +
+ × + = +
so,-32-128
=-160
Answer:
No, it is not a function.
Step-by-step explanation:
Vertical line test. A function can only have one output, y, for each unique input, x.
