Answer:
-1/3
Step-by-step explanation:
at x=0 y= 5
at x=3 y= 4
y=ax+b
b= 5
4=3x+5
3x= -1
x= -1/3
![y = - \frac{x}{3} + 5](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7Bx%7D%7B3%7D%20%20%2B%205)
Change the sign of the y component.
(6,-14)
Answer: 64 years old
Step-by-step explanation:You subtract 2082 by 2018 to get the sum of 64
Answer:
18.11 miles per gallon
Step-by-step explanation:
Get the miles traveled from the trip odometer, or subtract the original odometer reading from the new one.
Divide the miles traveled by the amount of gallons it took to refill the tank. The result will be your car’s average miles per gallon yield for that driving period.
44,895-44,587 = 308 miles
308/17 = 18.11
Step-by-step explanation:
Let x represent theta.
![\sin( \frac{\pi}{4} - x )](https://tex.z-dn.net/?f=%20%5Csin%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20-%20x%20%29%20)
Using the angle addition trig formula,
![\sin(x - y) = \sin(x) \cos(y) - \cos(x) \sin(y)](https://tex.z-dn.net/?f=%20%5Csin%28x%20-%20y%29%20%20%3D%20%20%5Csin%28x%29%20%20%5Ccos%28y%29%20%20-%20%20%5Ccos%28x%29%20%20%5Csin%28y%29%20)
![\sin( \frac{\pi}{4} ) \cos(x) - \cos( \frac{\pi}{4} ) \sin(x)](https://tex.z-dn.net/?f=%20%5Csin%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%20%20%5Ccos%28x%29%20%20-%20%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%20%20%5Csin%28x%29%20)
![( \frac{ \sqrt{2} }{2}) \cos(x) - (\frac{ \sqrt{2} }{2} )\sin(x)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B2%7D%29%20%20%5Ccos%28x%29%20%20-%20%20%28%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20%20%29%5Csin%28x%29%20)
Multiply one side at a time
Replace theta with x , the answer is
![\frac{ \sqrt{2} \cos(x) }{2} - \frac{ \sin(x) \sqrt{2} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%5Ccos%28x%29%20%20%7D%7B2%7D%20%20-%20%20%5Cfrac%7B%20%5Csin%28x%29%20%5Csqrt%7B2%7D%20%20%7D%7B2%7D%20)
2. Convert 30 degrees into radian
![\frac{30}{1} \times \frac{\pi}{180} = \frac{\pi}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%7D%7B1%7D%20%20%5Ctimes%20%20%5Cfrac%7B%5Cpi%7D%7B180%7D%20%20%3D%20%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20)
Using tangent formula,
![\tan(x + y) = \frac{ \tan(x) + \tan(y) }{1 - \tan(x) \tan(y) }](https://tex.z-dn.net/?f=%20%5Ctan%28x%20%2B%20y%29%20%20%3D%20%20%5Cfrac%7B%20%5Ctan%28x%29%20%20%2B%20%20%5Ctan%28y%29%20%7D%7B1%20-%20%20%5Ctan%28x%29%20%5Ctan%28y%29%20%20%7D%20)
![\frac{ \tan(x) + \tan( \frac{\pi}{6} ) }{1 - \tan(x) \tan( \frac{\pi}{6} ) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Ctan%28x%29%20%2B%20%20%5Ctan%28%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%29%20%20%7D%7B1%20-%20%20%5Ctan%28x%29%20%5Ctan%28%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%29%20%20%7D%20)
Tan if pi/6 is sqr root of 3/3
![\frac{ \tan(x) + ( \frac{ \sqrt{3} }{3} ) }{1 - \tan(x) (\frac{ \sqrt{3} }{3} ) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Ctan%28x%29%20%2B%20%20%28%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B3%7D%20%29%20%20%7D%7B1%20-%20%20%5Ctan%28x%29%20%20%28%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B3%7D%20%29%20%20%7D%20)
Since my phone about to die if you later simplify that,
you'll get
![\frac{(3 \tan(x) + \sqrt{3} )(3 + \sqrt{3} \tan(x) }{3(3 - \tan {}^{2} (x) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%283%20%5Ctan%28x%29%20%2B%20%20%5Csqrt%7B3%7D%20%29%283%20%2B%20%20%5Csqrt%7B3%7D%20%20%5Ctan%28x%29%20%20%7D%7B3%283%20-%20%20%5Ctan%20%7B%7D%5E%7B2%7D%20%28x%29%20%7D%20)
Replace theta with X.