Answer:
x = 7
Step-by-step explanation:
Given
4x - 2(x - 2) = - 4 + 5x - 13 ← distribute left side and simplify
4x - 2x + 4 = 5x - 17
2x + 4 = 5x - 17 ( subtract 5x from both sides )
- 3x + 4 = - 17 ( subtract 4 from both sides )
- 3x = - 21 ( divide both sides by - 3 )
x = 7
Answer:
The answer is A.
Step-by-step explanation:
A polyhedron is a three-dimensional solid made up of polygons. It has flat faces, straight edges, and vertices. For example, a cube, prism, or pyramid are polyhedrons.
Using the cosine double angle formula,
![\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}](https://tex.z-dn.net/?f=%5Ccos%202%5Ctheta%3D2%5Ccos%5E2%20%5Ctheta-1%3D%5Cfrac%7B12%7D%7B13%7D%5C%5C%5C%5C2%5Ccos%5E%7B2%7D%20%5Ctheta%3D%5Cfrac%7B25%7D%7B13%7D%5C%5C%5C%5C%5Ccos%5E%7B2%7D%20%5Ctheta%3D%5Cfrac%7B25%7D%7B26%7D%5C%5C%5C%5C%5Cboxed%7B%5Ccos%20%5Ctheta%3D%5Cfrac%7B5%7D%7B%5Csqrt%7B26%7D%7D%7D)
(Note I took the positive case since
terminates in the first quadrant)
Using the Pythagorean identity,
![\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}](https://tex.z-dn.net/?f=%5Csin%5E2%20%5Ctheta%2B%5Ccos%5E2%20%5Ctheta%3D1%5C%5C%5C%5C%5Csin%5E2%20%5Ctheta%2B%5Cfrac%7B25%7D%7B26%7D%3D1%5C%5C%5C%5Csin%5E2%20%5Ctheta%3D%5Cfrac%7B1%7D%7B26%7D%5C%5C%5C%5C%5Cboxed%7B%5Csin%20%5Ctheta%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B26%7D%7D%7D)
(Note I took the positive case since
terminates in the first quadrant)
The number 21/5 is a rational number because it can be simplified down to 4.2, or 21/5