70 times .9 is 63 so 90 minus 63 is27 so it was $27
15.
I had x before the movie.
x - 13.50 = 26.50
Add 13.50 to both sides of the equation:
x = 40
I had $40 before the movie.
16.
The original balance was x.
x - 161.15 = 423.28
Add 161.15 to both sides:
x = 584.43
The previous balance was $584.43
Answer:
See below
Step-by-step explanation:
Here we need to prove that ,
![\sf\longrightarrow sin^2\theta + cos^2\theta = 1](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20sin%5E2%5Ctheta%20%2B%20cos%5E2%5Ctheta%20%3D%201%20)
Imagine a right angled triangle with one of its acute angle as
.
- The side opposite to this angle will be perpendicular .
- Also we know that ,
![\sf\longrightarrow sin\theta =\dfrac{p}{h} \\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20sin%5Ctheta%20%3D%5Cdfrac%7Bp%7D%7Bh%7D%20%5C%5C)
![\sf\longrightarrow cos\theta =\dfrac{b}{h}](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20cos%5Ctheta%20%3D%5Cdfrac%7Bb%7D%7Bh%7D%20)
And by Pythagoras theorem ,
![\sf\longrightarrow h^2 = p^2+b^2 \dots (i)](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20h%5E2%20%3D%20p%5E2%2Bb%5E2%20%5Cdots%20%28i%29%20)
Where the symbols have their usual meaning.
Now , taking LHS ,
![\sf\longrightarrow sin^2\theta +cos^2\theta](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20sin%5E2%5Ctheta%20%2Bcos%5E2%5Ctheta%20)
- Substituting the respective values,
![\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%5Cbigg%28%5Cdfrac%7Bp%7D%7Bh%7D%5Cbigg%29%5E2%2B%5Cbigg%28%5Cdfrac%7Bb%7D%7Bh%7D%5Cbigg%29%5E2%5C%5C)
![\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%5Cdfrac%7Bp%5E2%7D%7Bh%5E2%7D%2B%5Cdfrac%7Bb%5E2%7D%7Bh%5E2%7D%5C%5C%20)
![\sf\longrightarrow \dfrac{p^2+b^2}{h^2}](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%5Cdfrac%7Bp%5E2%2Bb%5E2%7D%7Bh%5E2%7D%20)
![\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%5Ccancel%7B%20%5Cdfrac%7Bh%5E2%7D%7Bh%5E2%7D%7D%5C%5C%20)
![\sf\longrightarrow \bf 1 = RHS](https://tex.z-dn.net/?f=%5Csf%5Clongrightarrow%20%5Cbf%201%20%3D%20RHS%20)
Since LHS = RHS ,
Hence Proved !
I hope this helps.
Answer
8 %( When we round off to the neaerest tenths we get 10%)
Step-by-step explanation
4/50*100
=4*2
=8%
The formula for finding the length is
![{a}^{2} + {b}^{2} = {c}^{2}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%3D%20%7Bc%7D%5E%7B2%7D%20)
All we have to do is plug in the numbers.
![{6}^{2} + {8}^{2} = {c}^{2}](https://tex.z-dn.net/?f=%20%7B6%7D%5E%7B2%7D%20%20%2B%20%20%7B8%7D%5E%7B2%7D%20%20%3D%20%20%7Bc%7D%5E%7B2%7D%20)
36 + 64 = 100
Since 100 =
![{c}^{2}](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20)
we have to find the square root.
![\sqrt{100} = 10](https://tex.z-dn.net/?f=%20%5Csqrt%7B100%7D%20%20%3D%2010)
The length of the slide is 10 feet.