X+3y=7
x-3y=1
add them together
x+3y=7
<u>x-3y=1 +
</u>2x+0y=8
2x=8
divide 2
x=4
subsitute
x+3y=7
4+3y=7
subtract 4
3y=3
divid 3
y=1
x=4
y=1
answer is A
<u />
36-40= -4
36 subtracted by 40 equals negative 4
-4
The point-slope form of a line is:
y-y1=m(x-x1), where m=slope and (x1,y1) is any point on the line
First we need to find the slope, which is (y2-y1)/(x2-x1)
m=(4--1)/(8-2)
m=5/6 and we can use either point, I'll use (8,4)
y-4=(5/6)(x-8)
That is your equation in point-slope form.
Now the standard equation of a line is ax+by=c
y-4=(5/6)(x-8) we can perform the indicated multiplication on the right side
y-4=(5x-40)/6 multiply both sides by 6
6y-24=5x-40 add 24 to both sides
6y=5x-16 subtract 5x from both sides
-5x+6y=-16 and by convention, the standard equation of a line should be expressed with a positive coefficient for x, so multiply both sides by -1
5x-6y=16
Answer:
See explanation
Step-by-step explanation:
1. Given the expression
![\dfrac{\sqrt[7]{x^5} }{\sqrt[4]{x^2} }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B7%5D%7Bx%5E5%7D%20%7D%7B%5Csqrt%5B4%5D%7Bx%5E2%7D%20%7D)
Note that
![\sqrt[7]{x^5}=x^{\frac{5}{7}} \\ \\\sqrt[4]{x^2}=x^{\frac{2}{4}}=x^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Bx%5E5%7D%3Dx%5E%7B%5Cfrac%7B5%7D%7B7%7D%7D%20%5C%5C%20%5C%5C%5Csqrt%5B4%5D%7Bx%5E2%7D%3Dx%5E%7B%5Cfrac%7B2%7D%7B4%7D%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
When dividing ![\sqrt[7]{x^5}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Bx%5E5%7D)
by ![\sqrt[4]{x^2},](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E2%7D%2C)
we have to subtract powers (we cannot subtract 4 from 7, because then we get another expression), so
and the result is ![x^{\frac{3}{14}}=\sqrt[14]{x^3}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B3%7D%7B14%7D%7D%3D%5Csqrt%5B14%5D%7Bx%5E3%7D)
2. Given equation ![3\sqrt[4]{(x-2)^3} -4=20](https://tex.z-dn.net/?f=3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20-4%3D20)
Add 4:
![3\sqrt[4]{(x-2)^3} -4+4=20+4\\ \\3\sqrt[4]{(x-2)^3}=24](https://tex.z-dn.net/?f=3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20-4%2B4%3D20%2B4%5C%5C%20%5C%5C3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%3D24)
Divide by 3:
![\sqrt[4]{(x-2)^3} =8](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20%3D8)
Rewrite the equation as:
Hence,
