1.) 3:1
2.) i think this one is 40 degrees because a complementary angles equal 90 degrees
3.) 53/60 because it comes out to 88.3% whereas 34/40 is 85% and 20/25 is 80%
Answer:
2 5/12
Step-by-step explanation:
you can combine two fractions if they have the same denominator (bottom number) by adding the numerators (top numbers) and keeping the bottom number the same.
1/12+4/12 is the same as 1+4 you just put the sum over 12:
2 1/12+4/12= 2 5/12
it can also be written as 29/12
the ball thrown off course was
° .
<u>Step-by-step explanation:</u>
Here we have , A ball is dropped from the top of a 45 foot building. Once the ball is released, a gust of wind blows the ball off course and is dropped 4 feet from the base of the building. We need to find that How many degrees was the ball thrown off course? Let's find out:
Basically above given condition is a case of right angled triangle with following parameters
![Perpendicular = 4 ft](https://tex.z-dn.net/?f=Perpendicular%20%3D%204%20ft)
![Base = 45 ft](https://tex.z-dn.net/?f=Base%20%3D%2045%20ft)
x = angle between Perpendicular & base
Now , ![tanx = \frac{Perpendicular}{base}](https://tex.z-dn.net/?f=tanx%20%3D%20%5Cfrac%7BPerpendicular%7D%7Bbase%7D)
⇒ ![tanx = \frac{Perpendicular}{base}](https://tex.z-dn.net/?f=tanx%20%3D%20%5Cfrac%7BPerpendicular%7D%7Bbase%7D)
⇒ ![tanx = \frac{4}{45}](https://tex.z-dn.net/?f=tanx%20%3D%20%5Cfrac%7B4%7D%7B45%7D)
Taking tan inverse both sides , in order to obtain x :
⇒ ![tan^{-1}(tanx) = tan^{-1}(\frac{4}{45})](https://tex.z-dn.net/?f=tan%5E%7B-1%7D%28tanx%29%20%3D%20tan%5E%7B-1%7D%28%5Cfrac%7B4%7D%7B45%7D%29)
⇒ ![x = tan^{-1}(\frac{4}{45})](https://tex.z-dn.net/?f=x%20%3D%20tan%5E%7B-1%7D%28%5Cfrac%7B4%7D%7B45%7D%29)
⇒ ![x = tan^{-1}(0.08)](https://tex.z-dn.net/?f=x%20%3D%20tan%5E%7B-1%7D%280.08%29)
⇒
°
Therefore, the ball thrown off course was
° .
Answer:
These two equations are related to each other by identity
Step-by-step explanation:
We have given equations
![\frac{x^2-1}{x+1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-1%7D%7Bx%2B1%7D)
We know the algebraic identity
![a^2-b^2=(a+b)(a-b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a%2Bb%29%28a-b%29)
So ![a^2-1^2=(x+1)(x-1)](https://tex.z-dn.net/?f=a%5E2-1%5E2%3D%28x%2B1%29%28x-1%29)
So ![\frac{x^2-1}{x+1}=\frac{(x+1)(x-1)}{x+1}=(x-1)](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-1%7D%7Bx%2B1%7D%3D%5Cfrac%7B%28x%2B1%29%28x-1%29%7D%7Bx%2B1%7D%3D%28x-1%29)
So these two equations are related to each other by algebraic identity ![a^2-b^2=(a+b)(a-b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a%2Bb%29%28a-b%29)
The number
means: which exponent we have to give to 9 in order to get 81?
Since
, the answer is 2.