Answer: x = 50
Concept:
Here, we need to know the idea of alternative interior angles and the angle sum theorem.
<u>Alternative interior angles</u> are angles that are formed inside the two parallel lines, and the values are equal.
The <u>angle sum theorem</u> implies that the sum of interior angles of a triangle is 180°
If you are still confused, please refer to the attachment below or let me know.
Step-by-step explanation:
<u>Given information:</u>
AC ║ DE
∠ABC = 85°
∠A = 135°
<u>Find the value of ∠BAC</u>
∠A + ∠BAC = 180° (Supplementary angle)
(135°) + ∠BAC = 180°
∠BAC = 45°
<u>Find the value of ∠BCA</u>
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)
(85°) + (45°) + ∠BCA = 180°
∠BCA = 50°
<u>Find the value of x (∠EBC)</u>
∠EBC ≅ ∠BCA (Alternative interior angles)
Since, ∠BCA = 50°
Therefore, ∠EBC = 50°
Hope this helps!! :)
Please let me know if you have any questions
Answer:
The radius of the cylinder is 7 in
Step-by-step explanation:
To calculate the radius of a cylinder we have to use the following formula:
v = volume = 980π in³
h = height = 20in
π = pi
r = radius
v = (π * r²) * h
we replace with the known values
980π in³ = (π * (r)²) * 20in
980π in³ / 20in = π * (r)²
49 in² = (r)²
√(49 in²) = r
7 in = r
The radius of the cylinder is 7 in
Hello LovingAngel!
To find the slope, you can use the formulas
as well as
. I am using the latter to calculate and ensuring my answer with the former.
[Note: (x,y) is the format for ordered pairs]
First pair: value 1:(1,5) and value 2:(2,8)
->
->
or 3.
The slope for (1,5) and (2,8) is 3(/1). Second pair: value 1: (3,1) value 2 (3,-1)
->
->
Slope for the second pair is -2/0Checking work with
1. Slope: 3/1, meaning rise (y) +3 and run (x) +1. (1,5) -> (1+1,5 + 3) -> (2,8) ✔
2. Slope: -2/0, meaning rise (y) -2/drop (y) 2 and run 0. (3,1) -> (3 + 0, 1 + -2) -> (3,-1) <span>✔</span>
Step 1 ) Separate the 4 and x.
↓
Step 2 ) Simplify the square root of 4.
↓
Step 3 ) Simplify.
↓
This is now in its simplest form, so the final answer is...
or it could be...
Either one is correct. Only difference is one is in simplest form and one isn't.
•
•
- Marlon Nunez
