Answer:
Step-by-step explanation:
point-slope equation looks like y-y1 = m(x-x1)
plug in the given point for x and y.... and the slope for m
y-9 = 3/2(x-6)
y-9 = 3/2x - 9
y = 3/2x
Answer:
a) The possible solutions are:
x=7 and x=-3
b)The extraneous solution
is x=
Step-by-step explanation:
The last step gives us the possible solutions.
![(x + 3)(x - 7) = 0](https://tex.z-dn.net/?f=%28x%20%2B%203%29%28x%20-%207%29%20%3D%200)
By the zero product property,
![x + 3 = 0 \: or \: x - 7 = 0](https://tex.z-dn.net/?f=x%20%2B%203%20%3D%200%20%5C%3A%20or%20%5C%3A%20x%20-%207%20%3D%200)
This implies that:
![x = - 3 \: or \: x = 7](https://tex.z-dn.net/?f=x%20%20%3D%20%20-%203%20%5C%3A%20or%20%5C%3A%20x%20%3D%207)
The original equation is
![\sqrt{30 - 2x} = x - 3](https://tex.z-dn.net/?f=%20%5Csqrt%7B30%20-%202x%7D%20%20%3D%20x%20-%203)
We substitute x=-3 to get;
![\sqrt{30 - 2 \times - 3} = - 3 - 3 \\ \sqrt{30 + 6} = - 6 \\ \sqrt{36} = - 6 \\ 6 = - 6](https://tex.z-dn.net/?f=%5Csqrt%7B30%20-%202%20%5Ctimes%20%20-%203%7D%20%20%3D%20%20-%203%20-%203%20%5C%5C%20%20%5Csqrt%7B30%20%2B%206%7D%20%20%3D%20%20-%206%20%5C%5C%20%20%5Csqrt%7B36%7D%20%3D%20%20-%206%20%5C%5C%20%206%20%3D%20%20-%206%20)
This not true, therefore x=-3 is an extraneous solution.
We substitute x=7
![\sqrt{30 - 2 \times 7} = 7- 3 \\ \sqrt{30 - 14} = 4 \\ \sqrt{16} = 4 \\ 4 = 4](https://tex.z-dn.net/?f=%5Csqrt%7B30%20-%202%20%5Ctimes%207%7D%20%20%3D%207-%203%20%5C%5C%20%20%5Csqrt%7B30%20-%2014%7D%20%20%3D%204%20%5C%5C%20%20%5Csqrt%7B16%7D%20%20%3D%204%20%5C%5C%204%20%3D%204)
Therefore x=7 is the only solution.
First we distribute
![\frac{1}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7D%20)
into
![n](https://tex.z-dn.net/?f=n)
and
![-\frac{1}{7}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%7D%7B7%7D)
.
![\frac{1}{5} * n = \frac{1}{5} n](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7D%20%2A%20n%20%3D%20%20%5Cfrac%7B1%7D%7B5%7D%20n%20)
![\frac{1}{5} * -\frac{1}{7} = - \frac{1}{35}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7D%20%20%2A%20%20-%5Cfrac%7B1%7D%7B7%7D%20%20%3D%20-%20%5Cfrac%7B1%7D%7B35%7D%20)
That makes the left side of the equation
![\frac{1}{5} n - \frac{1}{35} = \frac{1}{6} n](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7D%20n%20-%20%20%5Cfrac%7B1%7D%7B35%7D%20%3D%20%20%5Cfrac%7B1%7D%7B6%7D%20n)
Now we subtract
![\frac{1}{5}n](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7Dn)
from
![\frac{1}{6} n](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B6%7D%20n)
, which makes
![\frac{1}{30}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B30%7D%20)
Now the equation is
![-\frac{1}{35} = -\frac{1}{30n}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B1%7D%7B35%7D%20%3D%20%20-%5Cfrac%7B1%7D%7B30n%7D%20)
Our goal is to isolate
![n](https://tex.z-dn.net/?f=n)
, so we both sides by 30
That will make the equation
![- \frac{30}{35} = -n](https://tex.z-dn.net/?f=-%20%5Cfrac%7B30%7D%7B35%7D%20%3D%20-n)
We multiply -1 on both sides of the equation:
![\frac{30}{35} = n](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%7D%7B35%7D%20%3D%20n)
Finally we simplify
![\frac{30}{35}](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%7D%7B35%7D%20)
, which makes
So the answer is
Answer:
It would definitely show a more realistic picture of the wealth of our nation because our economy would be measured in real dollars
Answer:
I think the answer is 124 though I'm in 8th grade . I have completed algebra 1.
Step-by-step explanation:
The other side of the circle has four minor arcs since they each measure less than 180
.