There are an infinite number of solutions to this linear equation in two variables. It will graph as a straight line.
In standard form, the equation would be written
.. 105x +56y = 30
Answer:
y-4=4(x+2)/7
Step-by-step explanation:
slope(m) = (8-4)/(5-(-2)) =4/7
b = 4-(4/7)×(-2) = 36/7
y = mx+b
y = 4x/7+36/7
in point-slope form,
y-4=4(x+2)/7
Answer:
It costs 19 cents or 0.19 dollars per fluid ounce.
Step-by-step explanation:
4.75 divided by 25 is 0.19. 0.19 is 19 cents.
Answer:
![z=\frac{15\sqrt{3}}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B15%5Csqrt%7B3%7D%7D%7B2%7D)
Step-by-step explanation:
In leftmost triangle:
opposite side =y
adjacent=a
now, we can use trig formula
![tan(60)=\frac{y}{a}](https://tex.z-dn.net/?f=tan%2860%29%3D%5Cfrac%7By%7D%7Ba%7D)
now, we can solve for y
![y=atan(60)](https://tex.z-dn.net/?f=y%3Datan%2860%29)
In rightmost triangle:
adjacent=b
opposite=y
a+b=15
b=15-a
now, we can use trig formula
![tan(30)=\frac{y}{15-a}](https://tex.z-dn.net/?f=tan%2830%29%3D%5Cfrac%7By%7D%7B15-a%7D)
now, we can solve for y
![y=(15-a)tan(30)](https://tex.z-dn.net/?f=y%3D%2815-a%29tan%2830%29)
now, we can set them equal
and then we can solve for a
![atan(60)=(15-a)tan(30)](https://tex.z-dn.net/?f=atan%2860%29%3D%2815-a%29tan%2830%29)
![\sqrt{3}a\cdot \:3=\frac{\sqrt{3}\left(15-a\right)}{3}\cdot \:3](https://tex.z-dn.net/?f=%5Csqrt%7B3%7Da%5Ccdot%20%5C%3A3%3D%5Cfrac%7B%5Csqrt%7B3%7D%5Cleft%2815-a%5Cright%29%7D%7B3%7D%5Ccdot%20%5C%3A3)
![4\sqrt{3}a=15\sqrt{3}](https://tex.z-dn.net/?f=4%5Csqrt%7B3%7Da%3D15%5Csqrt%7B3%7D)
![a=\frac{15}{4}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B15%7D%7B4%7D)
now, we can find b
![b=15-\frac{15}{4}](https://tex.z-dn.net/?f=b%3D15-%5Cfrac%7B15%7D%7B4%7D)
![b=\frac{45}{4}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B45%7D%7B4%7D)
now, we can use trig formula
![cos(30)=\frac{b}{z}](https://tex.z-dn.net/?f=cos%2830%29%3D%5Cfrac%7Bb%7D%7Bz%7D)
now, we can find z
![z=\frac{\frac{45}{4}}{cos(30)}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Cfrac%7B45%7D%7B4%7D%7D%7Bcos%2830%29%7D)
we can simplify it
and we get
![z=\frac{15\sqrt{3}}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B15%5Csqrt%7B3%7D%7D%7B2%7D)