Answer:
Step-by-step explanation:
Both angles are supplementary (they add up to 180°)
This means that (10x) + (6x - 12°) = 180°
(10x) + (6x - 12°) = 180°
10x + 6x - 12° = 180°
16x - 12° = 180°
16x = 192°
x = 12°
Hope this helps!
Answer:
The diagonal is 6.7082 ≈ 6.71
Step-by-step explanation:
Let the diagonal be x :
<em>To find the diagonal of a 3 by 6 rectangle</em>
<em>We can use the Pythagorean Theorem:</em>
![x^{2} = 3^{2} + 6^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%203%5E%7B2%7D%20%2B%206%5E%7B2%7D)
⇒ ![x^{2} = 9 +36](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%209%20%2B36)
⇒ ![x^{2} = 45](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%2045)
⇒ ![x=\sqrt{45}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B45%7D)
∴
≈
(corrected to 2 d.p.)
Answer:
Answer is x = -24/13, y = 3/13
Step-by-step explanation:
The vector equation of line is;
(x,y) = (
) + t (v) ............... 1
we know that;
(
) = (2,1)
and
v = 5i + 1j
put in equation 1
![(x,y) = (2,1) + t (5i + 1j)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%282%2C1%29%20%2B%20t%20%285i%20%2B%201j%29)
The parametric equation becomes;
![(x,y) = 2i + 1j + 5ti + 1tj](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%202i%20%2B%201j%20%2B%205ti%20%2B%201tj)
by comparison we get;
![x = 5t + 2.................... 2\\y = t + 1................... 3](https://tex.z-dn.net/?f=x%20%3D%205t%20%2B%202....................%202%5C%5Cy%20%3D%20t%20%2B%201...................%203)
multiply equation 3 by -5 and add it to equation 2
![-5y = -5t - 5\\x = 5t + 2\\\\x - 5y = -3](https://tex.z-dn.net/?f=-5y%20%3D%20-5t%20-%205%5C%5Cx%20%3D%205t%20%2B%202%5C%5C%5C%5Cx%20-%205y%20%3D%20-3)
we know that;
![m =(y_2 - y_1)/(x_2 -x_1)](https://tex.z-dn.net/?f=m%20%3D%28y_2%20-%20y_1%29%2F%28x_2%20-x_1%29)
so, m = 5
we can find the family of lines that are perpendicular to the above line by swapping the coefficients and change the sign of one of them:
![5x + y = c\\\\where \\x = 3 \\y = 6\\so,\\5(3) + 6 = c\\15 +6 =c\\21=c](https://tex.z-dn.net/?f=5x%20%2B%20y%20%3D%20c%5C%5C%5C%5Cwhere%20%5C%5Cx%20%3D%203%20%5C%5Cy%20%3D%206%5C%5Cso%2C%5C%5C5%283%29%20%2B%206%20%3D%20c%5C%5C15%20%2B6%20%3Dc%5C%5C21%3Dc)
So, the equation of other line is
![5x+y=21.......4\\x-5y = -3......5\\](https://tex.z-dn.net/?f=5x%2By%3D21.......4%5C%5Cx-5y%20%3D%20-3......5%5C%5C)
multiply equation 5 by -5
![-5x+25y=-15\\5x+y=21\\\\26y=6\\y=6/26\\y=3/13](https://tex.z-dn.net/?f=-5x%2B25y%3D-15%5C%5C5x%2By%3D21%5C%5C%5C%5C26y%3D6%5C%5Cy%3D6%2F26%5C%5Cy%3D3%2F13)
put this value of y in equation 5.
![x-5(3/13) =-3\\x-15/13=-3\\x=-3+\frac{15}{13}\\ x=\frac{-24}{13}](https://tex.z-dn.net/?f=x-5%283%2F13%29%20%3D-3%5C%5Cx-15%2F13%3D-3%5C%5Cx%3D-3%2B%5Cfrac%7B15%7D%7B13%7D%5C%5C%20x%3D%5Cfrac%7B-24%7D%7B13%7D)
please rate 5 stars
This is a test so I will not give you the answer. You need to be able to do this on your own. But I will give you a hint.
FA/BF=GA/CG