Answer:
Step-by-step explanation:
<u>Our expression given: 3(x-6) + 2y</u>
A. Substitute x = -7 and y = 10 into the equation.
![3( - 7 - 6) + 2(10)](https://tex.z-dn.net/?f=3%28%20-%207%20-%206%29%20%2B%202%2810%29)
<u>Use the Distributive Property:</u>
![- 21 - 18 + 20](https://tex.z-dn.net/?f=%20-%2021%20-%2018%20%2B%2020)
<u>Solve:</u>
![- 19](https://tex.z-dn.net/?f=%20-%2019)
B. Substitute x = 5 and y = -2 into the equation.
![3(5 - 6) + 2( - 2)](https://tex.z-dn.net/?f=3%285%20-%206%29%20%2B%202%28%20-%202%29)
<u>Use the Distributive Property:</u>
![15 - 18 + -4](https://tex.z-dn.net/?f=15%20-%2018%20%2B%20-4)
<u>Solve:</u>
![-7](https://tex.z-dn.net/?f=-7)
C. Substitute x = 0 and y = 6 into the equation.
![3(0 - 6) + 2(6)](https://tex.z-dn.net/?f=3%280%20-%206%29%20%2B%202%286%29)
<u>Use the Distributive Property:</u>
![- 18 + 12](https://tex.z-dn.net/?f=%20-%2018%20%2B%2012)
<u>Solve:</u>
![-6](https://tex.z-dn.net/?f=-6)
D. Substitute x = 3 and y = 3 into the equation.
![3(3 - 6) + 2(3)](https://tex.z-dn.net/?f=3%283%20-%206%29%20%2B%202%283%29)
<u>Use the Distributive Property:</u>
![9 - 18 + 6](https://tex.z-dn.net/?f=9%20-%2018%20%2B%206)
<u>Solve:</u>
![-3](https://tex.z-dn.net/?f=-3)
The general form is ax+by=c, let's first what we have to create the line in point-slope form, which is:
y-y1=m(x-x1), m=slope and (x1,y1) is any point on the line.
We are given m=-1/5 and (xy)=(0,5) so
y-5=(-1/5)(x-0)
y-5=-x/5 mutiply both sides by 5
5y-25=-x add x to both sides
x+5y-25=0 add 25 to both sides
x+5y=25
Answer:
![\displaystyle s=\frac{3\pi}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20s%3D%5Cfrac%7B3%5Cpi%7D%7B4%7D)
Step-by-step explanation:
<u>Trigonometric Values</u>
We need to find the angle s in the interval [π/2,π] where:
![\displaystyle \sin s=\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%20s%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
There are two possible angles that have the same sine value in the first rotation of s. Any angle on the first quadrant has the same sine as its supplementary angle in the second quadrant.
The first angle s whose sine is
is:
![\displaystyle s=\frac{\pi }{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20s%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D)
The other angle is its supplementary angle:
![\displaystyle s=\pi-\frac{\pi }{4}=\frac{3\pi}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20s%3D%5Cpi-%5Cfrac%7B%5Cpi%20%7D%7B4%7D%3D%5Cfrac%7B3%5Cpi%7D%7B4%7D)
Only this last angle lies on the required interval, thus:
![\boxed{\displaystyle s=\frac{3\pi}{4}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdisplaystyle%20s%3D%5Cfrac%7B3%5Cpi%7D%7B4%7D%7D)
Answer:
28/64
Step-by-step explanation:
7/16 = 14/32 = 28/64