Answer:
m(∠AOF) = 148°
Step-by-step explanation:
From the figure attached,
CD intersects line EF at a point O.
Line CD is perpendicular to the line EF.
m(∠AOE) = 32°
m(∠COE) = 90°
Since m(∠COE) = m(∠AOE) + m(∠AOC) = 90°
32° + m(∠AOC) = 90°
m(∠AOC) = 90° - 32° = 58°
m(∠AOF) = m(∠AOC) + m(∠COF)
= 58° + 90°
= 148°
Therefore, m(∠AOF) = 148° will be the answer.
Answer:
see explanation
Step-by-step explanation:
We require to find the slope m of the line joining the 2 given points
To find m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2,3) and (x₂, y₂ ) = (1, - 2)
m =
=
= 5
Given a line with slope m then the slope of a line perpendicular to it is
= -
= - ![\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ), thus
y = -
x + c ← is the partial equation of the perpendicular line
To find c substitute (- 3, 2) into the partial equation
2 =
+ c ⇒ c = ![\frac{7}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B5%7D)
y = -
x +
← perpendicular equation
Answer:
we have that√(87*x)we know that87 is equal to------> 3*29In order for the square root to go further, the number for "x" has to have a factor of 3 or 29the number 21-------> 3*7so√(87*x)------> √(3*29*3*7)------> √(3²*29*7)----> 3√203the answer isx=21
Step-by-step explanation:
Answer:
43.2
Step-by-step explanation:
40/100 * 108
4/100*108
43.2
Answer:
![x=-3\pm i \sqrt{5}](https://tex.z-dn.net/?f=x%3D-3%5Cpm%20i%20%5Csqrt%7B5%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Standard Form: ax² + bx + c = 0
- Quadratic Formula:
![x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
<u>Algebra II</u>
Step-by-step explanation:
<u>Step 1: Define function</u>
f(x) = -x² - 6x - 14
<u>Step 2: Set up</u>
- Set equation equal to 0: -x² - 6x - 14 = 0
- Factor out -1: -(x² + 6x + 14) = 0
- Divide both sides by -1: x² + 6x + 14 = 0
<u>Step 3: Define variables</u>
a = 1
b = 6
c = 14
<u>Step 4: Find roots</u>
- Substitute:
![x=\frac{-6\pm\sqrt{6^2-4(1)(14)} }{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B6%5E2-4%281%29%2814%29%7D%20%7D%7B2%281%29%7D)
- Exponents:
![x=\frac{-6\pm\sqrt{36-4(1)(14)} }{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B36-4%281%29%2814%29%7D%20%7D%7B2%281%29%7D)
- Multiply:
![x=\frac{-6\pm\sqrt{36-56} }{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B36-56%7D%20%7D%7B2%7D)
- Subtract:
![x=\frac{-6\pm\sqrt{-20} }{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B-20%7D%20%7D%7B2%7D)
- Factor:
![x=\frac{-6\pm\sqrt{-1} \sqrt{20} }{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B-1%7D%20%5Csqrt%7B20%7D%20%7D%7B2%7D)
- Simplify:
![x=\frac{-6\pm2i \sqrt{5} }{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm2i%20%5Csqrt%7B5%7D%20%7D%7B2%7D)
- Factor:
![x=\frac{2(-3\pm i \sqrt{5} )}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%28-3%5Cpm%20i%20%5Csqrt%7B5%7D%20%29%7D%7B2%7D)
- Divide:
![x=-3\pm i \sqrt{5}](https://tex.z-dn.net/?f=x%3D-3%5Cpm%20i%20%5Csqrt%7B5%7D)