Y = -x + 4.....so sub in -x + 4 in for y in the other equation
x + 2y = -8
x + 2(-x + 4) = -8
x - 2x + 8 = -8
x - 2x = -8 - 8
-x = -16
x = 16
y = -x + 4
y = -16 + 4
y = - 12
one solution (16,-12)
I got 18. i did this by using the SOH CAH TOA method. In this case you have the the angle and the hypotenuse, and you’re looking for the adjacent side, therefore you need to use CAH
Let the two numbers be x and y.
We have x+y=45
⇒ y= 45-x.
The two numbers multiply and get 121, so we have another equation:
x*y = 121 (1)
Plug y= 45-x in (1), we have:
x* (45-x)=121
⇒ 45x - x^2 = 121 (distributive property)
⇒ x^2 - 45x = -121 (multiply -1 on both sides)
⇒ x^2- 45x + 121= 0
⇒ x= 42.128 or x= 2.872
y= 45- 42.128= 2.872
or y= 45- 2.872= 42.128.
Because it does not matter what number, x or y, is larger, the two numbers are 2.872 and 42.128.
Hope this helps~
<span>cos 2x + sqrt(2) sinx=1
</span><span>
Note that: cos 2x = cos^2x - sin^2x = (1-sin^2x) - sin^2x = 1 - 2sin^2x.
So, when alternatively written, you have the following equation:
</span>- 2sin^2x + sqrt(2)sinx + 1 = 1
- 2sin^2x + sqrt(2)sinx = 0
Then, let z=sin(x). So you get,
- 2z^2 + sqrt(2)z = 0
z(- 2z + sqrt(2)) = 0
Either z=0, or - 2z + sqrt(2) = 0 ---> z=sqrt(2)/2.
Then, since z=0 or z=sqrt(2)/2, therefore sin(x)=0, or sin(x)=sqrt(2)/2.
Then, for you remains just to list the angles. (Let me know if this is not fair or if you got questions.)
