For this case we have that, by definition, the equation of a line in the slope-intersection form is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where:
m: It's the slope
b: It is the cutting point with the y axis
We have, according to the statement data that:
![m = - \frac {2} {3}](https://tex.z-dn.net/?f=m%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D)
So, the equation is of the form:
![y = - \frac {2} {3} x + b](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D%20x%20%2B%20b)
We also have that the line intersects the "x" axis at -3, that is, the line passes through the point ![(x, y): (- 3,0)](https://tex.z-dn.net/?f=%28x%2C%20y%29%3A%20%28-%203%2C0%29)
We substitute to find "b":
![0 = -\frac {2} {3} (- 3) + b\\0 = -2 + b\\b = 2](https://tex.z-dn.net/?f=0%20%3D%20-%5Cfrac%20%7B2%7D%20%7B3%7D%20%28-%203%29%20%2B%20b%5C%5C0%20%3D%20-2%20%2B%20b%5C%5Cb%20%3D%202)
Finally, the equation is of the form:
![y = - \frac {2} {3} x + 2](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D%20x%20%2B%202)
Answer:
![y = - \frac {2} {3} x + 2](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B3%7D%20x%20%2B%202)
Answer:
38 cents
Step-by-step explanation:
quarter= 25
nickles= 5
pennies= 1
5+5+25+3= 38
Answer:
I got 12,148. Is that an option?
Step-by-step explanation:
98.00 checking account
car (value - outstanding balance) 12,500
plus jewelry $1750
Answer: ![9\pi\ in.](https://tex.z-dn.net/?f=9%5Cpi%5C%20in.)
Step-by-step explanation:
Given
The diameter of a circle is ![d=9\ in.](https://tex.z-dn.net/?f=d%3D9%5C%20in.)
So, the radius is ![r=\frac{d}{2}=4.5\ in.](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bd%7D%7B2%7D%3D4.5%5C%20in.)
The circumference is given by ![2\pi r](https://tex.z-dn.net/?f=2%5Cpi%20r)
Insert the values
![\Rightarrow 2\pi \cdot 4.5\\\Rightarrow 9\pi \ in.](https://tex.z-dn.net/?f=%5CRightarrow%202%5Cpi%20%5Ccdot%204.5%5C%5C%5CRightarrow%209%5Cpi%20%5C%20in.)
Thus, the circumference of the circle is
Answer:
x = 4 or x = -3
Step-by-step explanation:
![\sqrt{x+12}=x](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B12%7D%3Dx)
Take square both the sides,
![(\sqrt{x+12})^{2}=x^{2}\\\\x+12=x^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx%2B12%7D%29%5E%7B2%7D%3Dx%5E%7B2%7D%5C%5C%5C%5Cx%2B12%3Dx%5E%7B2%7D)
x² - x - 12 = 0
x² - 4x + 3x - 3*4 =0
x*(x - 4) + 3*(x - 4)= 0
(x- 4 )(x+3) =0
x -4 =0 or x + 3 = 0
x = 4 or x = -3