Answer:
y =
x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 2x + 2 ← is in slope- intercept form
with slope m = - 2
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
The line crosses the y- axis at (0, 1) ⇒ c = 1
y =
x + 1 ← equation of line
Tan =perpendicular/ base
= 4/7
Answer:
That would be 56. :D
Nice drawing sir/ma'am/person. :D
Step-by-step explanation:
1) If we let the lengths of the legs be x and 2x, then by the Pythagorean theorem,
![x+2x+\sqrt{x^{2}+(2x)^{2}}=28\\3x+x\sqrt{5}=28\\x(3+\sqrt{5})=28\\x=\frac{28}{3+\sqrt{5}} \cdot \frac{3-\sqrt{5}}{3-\sqrt{5}}=21-7\sqrt{5}](https://tex.z-dn.net/?f=x%2B2x%2B%5Csqrt%7Bx%5E%7B2%7D%2B%282x%29%5E%7B2%7D%7D%3D28%5C%5C3x%2Bx%5Csqrt%7B5%7D%3D28%5C%5Cx%283%2B%5Csqrt%7B5%7D%29%3D28%5C%5Cx%3D%5Cfrac%7B28%7D%7B3%2B%5Csqrt%7B5%7D%7D%20%5Ccdot%20%5Cfrac%7B3-%5Csqrt%7B5%7D%7D%7B3-%5Csqrt%7B5%7D%7D%3D21-7%5Csqrt%7B5%7D)
This means that the length of the hypotenuse is:
![\sqrt{5}(21-7\sqrt{5})=\boxed{21\sqrt{5}-35}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%2821-7%5Csqrt%7B5%7D%29%3D%5Cboxed%7B21%5Csqrt%7B5%7D-35%7D)
2) (Diagram attached) We know that
(in cm)
3) From the Pythagorean identity,
![\sin^{2}\left (\arccos \frac{5}{13} \right)+\cos^{2} \left (\arccos \frac{5}{13} \right)=1\\\left(\frac{5}{13} \right)^{2}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\frac{25}{169}+\sin^{2} \left (\arccos \frac{5}{13} \right)=1\\\sin^{2} \left (\arccos \frac{5}{13} \right)=\frac{144}{169}\\\sin \left (\arccos \frac{5}{13} \right)=\boxed{\frac{12}{13}}](https://tex.z-dn.net/?f=%5Csin%5E%7B2%7D%5Cleft%20%28%5Carccos%20%5Cfrac%7B5%7D%7B13%7D%20%5Cright%29%2B%5Ccos%5E%7B2%7D%20%5Cleft%20%28%5Carccos%20%5Cfrac%7B5%7D%7B13%7D%20%5Cright%29%3D1%5C%5C%5Cleft%28%5Cfrac%7B5%7D%7B13%7D%20%5Cright%29%5E%7B2%7D%2B%5Csin%5E%7B2%7D%20%5Cleft%20%28%5Carccos%20%5Cfrac%7B5%7D%7B13%7D%20%5Cright%29%3D1%5C%5C%5Cfrac%7B25%7D%7B169%7D%2B%5Csin%5E%7B2%7D%20%5Cleft%20%28%5Carccos%20%5Cfrac%7B5%7D%7B13%7D%20%5Cright%29%3D1%5C%5C%5Csin%5E%7B2%7D%20%5Cleft%20%28%5Carccos%20%5Cfrac%7B5%7D%7B13%7D%20%5Cright%29%3D%5Cfrac%7B144%7D%7B169%7D%5C%5C%5Csin%20%5Cleft%20%28%5Carccos%20%5Cfrac%7B5%7D%7B13%7D%20%5Cright%29%3D%5Cboxed%7B%5Cfrac%7B12%7D%7B13%7D%7D)
4) ![\frac{\pi}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B6%7D)
Its true because 4/3 = 16/12
correspond ing sides are in the same ratio