Answer:
When raised to the power of 4, the binomial (4 + y) expands to:
![y^4 + 16y^3 + 96y^2 + 256y + 256](https://tex.z-dn.net/?f=y%5E4%20%2B%2016y%5E3%20%2B%2096y%5E2%20%2B%20256y%20%2B%20256)
Step-by-step explanation:
![(4 + y)^4 \\= (y^2 + 8y + 16)^2\\= y^4 + 8y^3 + 16y^2 + 8y^3 + 64y^2 + 128y + 16y^2 + 128y + 256\\= y^4 + 16y^3 + 96y^2 + 256y + 256](https://tex.z-dn.net/?f=%284%20%2B%20y%29%5E4%20%5C%5C%3D%20%28y%5E2%20%2B%208y%20%2B%2016%29%5E2%5C%5C%3D%20y%5E4%20%2B%208y%5E3%20%2B%2016y%5E2%20%2B%208y%5E3%20%2B%2064y%5E2%20%2B%20128y%20%2B%2016y%5E2%20%2B%20128y%20%2B%20256%5C%5C%3D%20y%5E4%20%2B%2016y%5E3%20%2B%2096y%5E2%20%2B%20256y%20%2B%20256)
Answer:
x = 45
Step-by-step explanation:
The 3 angles of a triangle add up to 180
<a + <b + <c = 180
substitute what you know
55+ 80 + <c = 180
combine like terms
135 + <c = 180
subtract 135 from each side
<c = 180 -135
<c = 45
x = 45
![x = 4 \cos(a)](https://tex.z-dn.net/?f=x%20%3D%204%20%5Ccos%28a%29%20)
![\frac{x}{4} = \cos(a) \\](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B4%7D%20%20%3D%20%20%5Ccos%28a%29%20%20%5C%5C%20)
![( { \frac{x}{4} })^{2} = ({ \cos(a) })^{2} \\](https://tex.z-dn.net/?f=%28%20%7B%20%5Cfrac%7Bx%7D%7B4%7D%20%7D%29%5E%7B2%7D%20%20%3D%20%20%28%7B%20%5Ccos%28a%29%20%7D%29%5E%7B2%7D%20%20%5C%5C%20)
![\frac{ {x}^{2} }{16} = {cos}^{2} (a) \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B16%7D%20%20%3D%20%20%7Bcos%7D%5E%7B2%7D%20%28a%29%20%5C%5C%20)
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![y = 5 \tan(a)](https://tex.z-dn.net/?f=y%20%3D%205%20%5Ctan%28a%29%20%20)
![\frac{y}{5} = \tan(a) \\](https://tex.z-dn.net/?f=%20%5Cfrac%7By%7D%7B5%7D%20%20%3D%20%20%5Ctan%28a%29%20%20%5C%5C%20)
![( { \frac{y}{5} })^{2} = ( { \tan(a) })^{2} \\](https://tex.z-dn.net/?f=%28%20%7B%20%5Cfrac%7By%7D%7B5%7D%20%7D%29%5E%7B2%7D%20%20%3D%20%28%20%7B%20%5Ctan%28a%29%20%7D%29%5E%7B2%7D%20%20%5C%5C%20)
![\frac{ {y}^{2} }{25} = {tan}^{2} (a) \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7By%7D%5E%7B2%7D%20%7D%7B25%7D%20%20%3D%20%20%7Btan%7D%5E%7B2%7D%20%28a%29%20%5C%5C%20)
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Thus ;
![\frac{ {x}^{2} }{16} - \frac{ {y}^{2} }{25} = \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B16%7D%20%20-%20%20%5Cfrac%7B%20%7By%7D%5E%7B2%7D%20%7D%7B25%7D%20%20%3D%20%20%5C%5C%20)
![{cos}^{2} (a) - {tan}^{2} (a)](https://tex.z-dn.net/?f=%20%7Bcos%7D%5E%7B2%7D%20%28a%29%20-%20%20%7Btan%7D%5E%7B2%7D%20%28a%29)
That answer for that would be D
These angles are adjacent angels.
adjacent angels- have a common side and the same vertex.
(pictured below)
To solve this we set the sum of both angles equal to 180°. We do this because they are two adjacent angles on a straight line. The measure of a straight lines angle is 180°.
180= 5x + (x+96)
180=6x+96
84= 6x
x=14
any questions?