Answer:
So, 35 degrees is your answer.
Step-by-step explanation:
180 - 100 - 45 = 35 degrees
Hope my answer has helped you!
Answer:
![y =\dfrac{12}{5}x + 22](https://tex.z-dn.net/?f=y%20%3D%5Cdfrac%7B12%7D%7B5%7Dx%20%2B%2022)
Step-by-step explanation:
Slope-intercept form of line:
First find the slope of the line AB. ie, m
Slope of the perpendicular line = -1/m
(2 , 3) ⇒ x₁ = 2 & y₁ = 3
(-10, 8) ⇒ x₂ = -10 & y₂ = 8
![\boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}](https://tex.z-dn.net/?f=%5Cboxed%7BSlope%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%7D)
![= \dfrac{8-3}{-10-2}\\\\=\dfrac{5}{-12}\\\\=\dfrac{-5}{12}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B8-3%7D%7B-10-2%7D%5C%5C%5C%5C%3D%5Cdfrac%7B5%7D%7B-12%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-5%7D%7B12%7D)
![\sf slope \ of \ the \ perpendicular \ line \ m_1 = \dfrac{-1}{m}= -1 \ \div \dfrac{-5}{12}](https://tex.z-dn.net/?f=%5Csf%20slope%20%5C%20of%20%5C%20the%20%5C%20perpendicular%20%5C%20line%20%5C%20m_1%20%3D%20%5Cdfrac%7B-1%7D%7Bm%7D%3D%20-1%20%5C%20%5Cdiv%20%5Cdfrac%7B-5%7D%7B12%7D)
![\sf = -1 * \dfrac{12}{-5}=\dfrac{12}{5}](https://tex.z-dn.net/?f=%5Csf%20%3D%20-1%20%2A%20%5Cdfrac%7B12%7D%7B-5%7D%3D%5Cdfrac%7B12%7D%7B5%7D)
Equation of the required line: y = mx + b
![y =\dfrac{12}{5}x+b](https://tex.z-dn.net/?f=y%20%3D%5Cdfrac%7B12%7D%7B5%7Dx%2Bb)
The line passes through (-5 , 10). Substitute in the above equaiton,
![10 =\dfrac{12}{5}*(-5) + b\\\\ 10 = (-12) + b\\\\](https://tex.z-dn.net/?f=10%20%3D%5Cdfrac%7B12%7D%7B5%7D%2A%28-5%29%20%2B%20b%5C%5C%5C%5C%2010%20%3D%20%28-12%29%20%2B%20b%5C%5C%5C%5C)
10 + 12 = b
b = 22
Equation of the line:
![y =\dfrac{12}{5}x + 22](https://tex.z-dn.net/?f=y%20%3D%5Cdfrac%7B12%7D%7B5%7Dx%20%2B%2022)
Answer:
$135
Step-by-step explanation:
We need to find the profit first.
1.75 x 500 = 875.
$875 is how much money they have. We need to find the total cost it took to make the pencils and then subtract that from the money they have, to find the profit.
0.40 x 500 = 200
so subtract.
875 x 200 = 675.
So they mad $675. To find twenty percent of that, we need 20% as a decimal and multiply it by 675.
0.20 x 675 = 135
$135
Hope this helps! Please mark as brainliest! Thanks!
Answer:
x=28
Step-by-step explanation: