They ate 4 1/5 ounces of candy.
EF = 6
EG = 21
You would subtract EF from EG to find FG:
21 - 6 = 15.
The answer is B.) 15
Answer:
|x-3|-5
Step-by-step explanation:
f(x) = |x|
These lines are lines of absolute value equations. g(x) is shifted 3 units left so we subtract 3 from within the bars, and shifted down 5 units so we subtract 5 from the absolute value which leaves us with |x-3|-5
Answer:
z=-3 so 2y+3(-3)=-8, 2y-9=-8, add 9 to both sides 2y=1 divide both sides by 2, y=1/2, so 3x+4(1/2)+-3=-2, 3x+2-3=-2, 3x-1=-2, add 1 to both sides, 3x=-1, divide both sides by 3, x=-1/3
Answer:
![\cos{\theta} = \frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)
Step-by-step explanation:
For any angle
, we have that:
![(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Csin%7B%5Ctheta%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
Quadrant:
means that
is in the first quadrant. This means that both the sine and the cosine have positive values.
Find the cosine:
![(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Csin%7B%5Ctheta%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![(\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![\frac{1}{16} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![(\cos{\theta})^{2} = 1 - \frac{1}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201%20-%20%5Cfrac%7B1%7D%7B16%7D)
![(\cos{\theta})^{2} = \frac{16-1}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%20%5Cfrac%7B16-1%7D%7B16%7D)
![(\cos{\theta})^{2} = \frac{15}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%20%5Cfrac%7B15%7D%7B16%7D)
![\cos{\theta} = \pm \sqrt{\frac{15}{16}}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B15%7D%7B16%7D%7D)
Since the angle is in the first quadrant, the cosine is positive.
![\cos{\theta} = \frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)