Y= ax+b
when x=3, y=11 and when x= -2, y=11
3a+b=11
-2a+b=11 | * -1
3a+b=11
2a-b=-11
------------
5a=0, a=0:5, a=0
⇒ b=11
y=11 for every x
So ( 1,11) or (2,11) are also points on the graph
Answer:
2x+100
Step-by-step explanation:
9 divided by 3 = 3 3divided by 3 = 1 1 divided by 3 = 1/3 so 1/3 divided by 3=1/9
It would be .43, rounded. You get this answer by taking all of the 10th graders (14) and looking at how many prefer sporting events (6). Then, you simply form a decimal from 6/14, and that comes out to .428, and .43 rounded up. I hope this helps! :)
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.