Answer:
Amount of material for chain link = 30 feet
Amount of material for rope = 50 feet
Step-by-step explanation:
Let the amount of chain link = X
The amount of rope be represented by Y
He bought a total of 80 feet of materials
Hence we have:
X + Y = 80 ....... Equation 1
Y = 80 - X
The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135
X × $2 + Y × $1.50 = $135
2X + 1.5Y = 135 ......Equation 2
Substitute 80 - X for Y in Equation 2
2X + 1.5(80 - X) = 135
2X + 120 - 1.5X = 135
Collect like terms
2X - 1.5X = 135 - 120
0.5X = 15
X = 15/0.5
X = 30 feet
Substitute 30 feet for X in Equation 1
X + Y = 80 ....... Equation 1
30 + Y = 80
Y = 80 - 30
Y = 50 feet
Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet
The answer to this question is false
There are 8! Eight sides on the shape, and all sides are the same shape.
So since c= 30 u do 2 times 30 which is 60 then since d=8 u do 4 times 8 which equals 32 then add 60 and 32 which is 92 so the answer is
ANSWER: D.92
Answer:
There are two choices for angle Y:
for
,
for
.
Step-by-step explanation:
There are mistakes in the statement, correct form is now described:
<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>
The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:
(1)
If we know that
,
and
, then we have the following second order polynomial:
![14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}](https://tex.z-dn.net/?f=14%5E%7B2%7D%20%3D%20XZ%5E%7B2%7D%20%2B%2018%5E%7B2%7D%20-%202%5Ccdot%20%2818%29%5Ccdot%20XZ%5Ccdot%20%5Ccos%2049%5E%7B%5Ccirc%7D)
(2)
By the Quadratic Formula we have the following result:
![XZ \approx 15.193\,\lor\,XZ \approx 8.424](https://tex.z-dn.net/?f=XZ%20%5Capprox%2015.193%5C%2C%5Clor%5C%2CXZ%20%5Capprox%208.424)
There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:
![XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y](https://tex.z-dn.net/?f=XZ%5E%7B2%7D%20%3D%20XY%5E%7B2%7D%20%2B%20YZ%5E%7B2%7D%20-%202%5Ccdot%20XY%20%5Ccdot%20YZ%20%5Ccdot%20%5Ccos%20Y)
![\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}](https://tex.z-dn.net/?f=%5Ccos%20Y%20%3D%20%5Cfrac%7BXY%5E%7B2%7D%2BYZ%5E%7B2%7D-XZ%5E%7B2%7D%7D%7B2%5Ccdot%20XY%5Ccdot%20YZ%7D)
![Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%20%5E%7B-1%7D%5Cleft%28%5Cfrac%7BXY%5E%7B2%7D%2BYZ%5E%7B2%7D-XZ%5E%7B2%7D%7D%7B2%5Ccdot%20XY%5Ccdot%20YZ%7D%20%5Cright%29)
1) ![XZ \approx 15.193](https://tex.z-dn.net/?f=XZ%20%5Capprox%2015.193)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-15.193%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
![Y \approx 54.987^{\circ}](https://tex.z-dn.net/?f=Y%20%5Capprox%2054.987%5E%7B%5Ccirc%7D)
2) ![XZ \approx 8.424](https://tex.z-dn.net/?f=XZ%20%5Capprox%208.424)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-8.424%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
![Y \approx 27.008^{\circ}](https://tex.z-dn.net/?f=Y%20%5Capprox%2027.008%5E%7B%5Ccirc%7D)
There are two choices for angle Y:
for
,
for
.