Answer:
One of the angles in the triangle might be 50.
AND
The length of the third side must be 11cm or smaller.
Step-by-step explanation:
-The triangle might be an equilateral triangle (having all the same sides and angles). False, since the triangle sum theorem states that all angles inside of a triangle must add up to 180, so an equilateral triangle would need to have all three angles at 60 degrees.
-One of the angles in the triangle must be 120 (false; it can be anything above 90, which is not only 120)
-The length of the third side must be 11cm or smaller. (True, Triangle Inequality Theorem)
-One of the angles in the triangle might be 50 (possibly, so very much true)
We have that
<span>4x -2y =22------> clear variable y
2y=4x-22--------> y=4x/2-22/2---------> y=2x-11-----> equation 1
2x + 4y = 6------> equation 2
substitute equation 1 in equation 2
2x+4*[2x-11]=6-----> 2x+8x-44=6----> 10x=50------> x=5
then
y=2x-11----> y=2*5-11----> y=-1
</span>
Answer:
<em>The ladder touches the wall at 24 feet from the ground.</em>
Step-by-step explanation:
The wall of the building, the ground, and the ladder form a right triangle, whose longer side is the length of the ladder.
In any right triangle, we can apply Pythagora's theorem to find any missing side length.
The ladder is 26 feet in length, the distance from the bottom of the ladder and the building is 10 feet. Calling H to the distance above the ground where the ladder touches the wall, then:

Calculating:

Solving:



H=24 feet
The ladder touches the wall at 24 feet from the ground.
Answer:
![12-[20-2(6^2\div3\times2^2)]=88](https://tex.z-dn.net/?f=12-%5B20-2%286%5E2%5Cdiv3%5Ctimes2%5E2%29%5D%3D88)
Step-by-step explanation:
So we have the expression:
![12-[20-2(6^2\div3\times2^2)]](https://tex.z-dn.net/?f=12-%5B20-2%286%5E2%5Cdiv3%5Ctimes2%5E2%29%5D)
Recall the order of operations or PEMDAS:
P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.
E: Within the parentheses, if exponents are present, do them before all other operations.
M/D: Multiplication and division next, whichever comes first.
A/S: Addition and subtraction next, whichever comes first.
(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)
Thus, we should do the operations inside the parentheses first. Therefore:
![12-[20-2(6^2\div3\times2^2)]](https://tex.z-dn.net/?f=12-%5B20-2%286%5E2%5Cdiv3%5Ctimes2%5E2%29%5D)
The parentheses is:

Square the 6 and the 4:

Do the operations from left to right. 36 divided by 3 is 12. 12 times 4 is 48:

Therefore, the original equation is now:
![12-[20-2(6^2\div3\times2^2)]\\=12- [20-2(48)]](https://tex.z-dn.net/?f=12-%5B20-2%286%5E2%5Cdiv3%5Ctimes2%5E2%29%5D%5C%5C%3D12-%20%5B20-2%2848%29%5D)
Multiply with the brackets:
![=12-[20-96]](https://tex.z-dn.net/?f=%3D12-%5B20-96%5D)
Subtract with the brackets:
![=12-[-76]](https://tex.z-dn.net/?f=%3D12-%5B-76%5D)
Two negatives make a positive. Add:

Therefore:
![12-[20-2(6^2\div3\times2^2)]=88](https://tex.z-dn.net/?f=12-%5B20-2%286%5E2%5Cdiv3%5Ctimes2%5E2%29%5D%3D88)