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
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:
4
Step-by-step explanation:
All you need to do is replace the variables with the numbers given.
t=9 & u=11
3+ 11t - 9u
3+ 11(9)-9(11)
3+ 99 - 99
The 99's cancel each other out, so you are left with 3.
The answer is 3.
<span>(x−5)^ 2 = (x-5)(x-5) = x^2 - 10x + 25 (answer)</span>
Answer:
4x-2y =42 is the required equation
Step-by-step explanation:
given equation is,
4x-2y -7=0---------eqn1
parallel equation of given equation is
4x -2y+k =0-------eqn 2
now passing it through (9,-3), we get,
4×9 + 2×3 +k = 0
or,36+6+k =0
or,42+k =0
or, k= -42
putting the value of k in eqn2
4x-2y - 42=0
4x-2y = 42