![4x^5y^3+8x^4y^4+4x^3y^2](https://tex.z-dn.net/?f=4x%5E5y%5E3%2B8x%5E4y%5E4%2B4x%5E3y%5E2)
GCF is the greatest common factor
We take GCF of numbers first and then we take GCF for variables
GCF of 4, 8, 4 is 4 because all the numbers are divisible by 4
For variable, lowest exponent is our GCF
GCF of
is x^3
GCF of
is y^2
So GCF is 4x^3y^2
Answer:
172.27 in
Step-by-step explanation:
Apply the Sine Rule
Sine Rule is given as:
![\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20%3D%20%5Cfrac%7Bc%7D%7Bsin%28C%29%7D%20)
c = x = ?
C = 180 - (52 + 48) = 80° (sum of triangle)
b = 130 in.
B = 48°
Plug in the values
![\frac{130}{sin(48)} = \frac{x}{sin(80)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B130%7D%7Bsin%2848%29%7D%20%3D%20%5Cfrac%7Bx%7D%7Bsin%2880%29%7D%20)
Multiply both sides by sin(80)
![\frac{130*sin(80)}{sin(48)} = x](https://tex.z-dn.net/?f=%20%5Cfrac%7B130%2Asin%2880%29%7D%7Bsin%2848%29%7D%20%3D%20x%20)
172.274641 = x
x = 172.27 in. (to 2 decimal places)
Answer:
d = 1/4
Step-by-step explanation:
Multiply the equation by the inverse of the coefficient of the variable.
![\dfrac{2}{3}d=\dfrac{1}{6}\\\\\dfrac{3}{2}\cdot\dfrac{2}{3}d=\dfrac{3}{2}\cdot\dfrac{1}{6}\\\\d=\dfrac{3\cdot 1}{2\cdot 6}=\dfrac{3}{12}=\dfrac{3\cdot 1}{3\cdot 4}\\\\d=\dfrac{1}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B3%7Dd%3D%5Cdfrac%7B1%7D%7B6%7D%5C%5C%5C%5C%5Cdfrac%7B3%7D%7B2%7D%5Ccdot%5Cdfrac%7B2%7D%7B3%7Dd%3D%5Cdfrac%7B3%7D%7B2%7D%5Ccdot%5Cdfrac%7B1%7D%7B6%7D%5C%5C%5C%5Cd%3D%5Cdfrac%7B3%5Ccdot%201%7D%7B2%5Ccdot%206%7D%3D%5Cdfrac%7B3%7D%7B12%7D%3D%5Cdfrac%7B3%5Ccdot%201%7D%7B3%5Ccdot%204%7D%5C%5C%5C%5Cd%3D%5Cdfrac%7B1%7D%7B4%7D)
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For each of the problems, twice the angle formed by the chords is equal to half the sum of the angles of the arcs.
So, for the first problem, we have
![94 \cdot 2 = x+103](https://tex.z-dn.net/?f=94%20%5Ccdot%202%20%3D%20x%2B103)
, so
![x = 188 - 103 = 85](https://tex.z-dn.net/?f=x%20%3D%20188%20-%20103%20%3D%2085)
.
For the second,
![102 \cdot 2 = x + 118](https://tex.z-dn.net/?f=102%20%5Ccdot%202%20%3D%20x%20%2B%20118)
, so
![x = 204 - 118 = 86](https://tex.z-dn.net/?f=x%20%3D%20204%20-%20118%20%3D%2086)
.
For the last problem,
![106 \cdot 2 = x + 88](https://tex.z-dn.net/?f=106%20%5Ccdot%202%20%3D%20x%20%2B%2088)
, so
![x = 212 - 88 = 124](https://tex.z-dn.net/?f=x%20%3D%20212%20-%2088%20%3D%20124)
.
Feel free to comment below if you have any questions!