<h3>
Answer: 180 inches</h3>
Work Shown:
L = 54 = length
W = 36 = width
P = 2(L+W) ... perimeter of the rectangle
P = 2(54+36)
P = 2(90)
P = 180
She needs 180 inches of ribbon.
To convert to feet, divide by 12. So 180 inches = 180/12 = 15 feet.
Answer:
1/10
Step-by-step explanation:
490 x 2/5 = 980/5 = 196 girls at Garland
945 x 5/7 = 4725/7 = 675 girls at Bowood
Bowood has more girls:
675-196 = 479 more
Y = x + 5....so we sub in x + 5 for y in the other equation
4x + y = 20
4x + x + 5 = 20
5x + 5 = 20
5x = 20 - 5
5x = 15
x = 15/5
x = 3
y = x + 5
y = 3 + 5
y = 8
solution is (3,8)
Step ![1](https://tex.z-dn.net/?f=%201%20)
<u>Find the length of the side MN</u>
we know that
Applying the Pythagorean Theorem
![ML^{2} =NL^{2} +MN^{2}](https://tex.z-dn.net/?f=%20ML%5E%7B2%7D%20%3DNL%5E%7B2%7D%20%2BMN%5E%7B2%7D%20%20)
Solve for MN
![MN^{2}=ML^{2} -NL^{2}](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3DML%5E%7B2%7D%20-NL%5E%7B2%7D%20%20)
in this problem
![ML=25\ units\\ NL=15\ units](https://tex.z-dn.net/?f=%20ML%3D25%5C%20units%5C%5C%20NL%3D15%5C%20units%20)
Substitute in the formula above
![MN^{2}=25^{2} -15^{2}](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3D25%5E%7B2%7D%20-15%5E%7B2%7D%20%20)
![MN^{2}=400](https://tex.z-dn.net/?f=%20MN%5E%7B2%7D%3D400%20%20)
![MN=20\ units](https://tex.z-dn.net/?f=%20MN%3D20%5C%20units%20%20)
Step ![2](https://tex.z-dn.net/?f=%202%20)
<u>Find the value of cos (M)</u>
we know that
in the right triangle MNL
![cos (M)=\frac{adjacent\ side\ angle\ M}{hypotenuse}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7Badjacent%5C%20side%5C%20angle%5C%20M%7D%7Bhypotenuse%7D%20%20%20)
![adjacent\ side\ angle\ M=MN=20\ units\\ hypotenuse=ML=25\ units](https://tex.z-dn.net/?f=%20adjacent%5C%20side%5C%20angle%5C%20M%3DMN%3D20%5C%20units%5C%5C%20hypotenuse%3DML%3D25%5C%20units%20)
Substitute
![cos (M)=\frac{20}{25}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7B20%7D%7B25%7D%20%20%20)
![cos (M)=\frac{4}{5}](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D%5Cfrac%7B4%7D%7B5%7D%20%20%20)
![cos (M)=0.8](https://tex.z-dn.net/?f=%20cos%20%28M%29%3D0.8%20%20%20)
therefore
The answer is
The value of cos(M) is equal to ![0.8](https://tex.z-dn.net/?f=%200.8%20)