SOLUTION: I'm still trying to finish this packet I have... So here's another few questions I'm having a hard time with. I really appreciate the help, and I reallyyy need it! 1. r to the th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm still trying to finish this packet I have... So here's another few questions I'm having a hard time with. I really appreciate the help, and I reallyyy need it! 1. r to the th      Log On


   



Question 362021: I'm still trying to finish this packet I have... So here's another few questions I'm having a hard time with.
I really appreciate the help, and I reallyyy need it!
1. r to the third + r^ - 6r
2. x^ - 14x + 49
x^ + 1 over 2x + 1 over 16
(as fractions)
3. 81m to the fourth - 16
4. 4- 2q - 6p + 3pq
5. 3n to the third + 12n^ - 36n
6. r^ + r + 3
7. 16x^ - 14x + 3
8. 7b^ - 42b + 56
9. y^ + 4y - 45
10. 8a^ + 23a - 3
Thank you againnn! I just really need to get this class out of my way. It's holding me back from continuing other work and classes that I don't even struggle with. I'm sure you can imagaine my frustration with this! But thank you for the help...

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
these are mostly quadratic equations(1,2,5,6,7,8,9,10) which are solved the same way you just need to do the calculations i will do one equation for u below:
#1
r%5E3%2Br%5E2-6r
r%28r%5E2%2Br-6%29
r%28r%5E2%2Br-6%29 +3 and -2 are two numbers that multiply to get -6 and add to get +1, if you cant do it this way use the quadratic formula to solve.
r%28%28r-2%29%28r%2B3%29%29
r-2=0=2
r%2B3=0=-3
#3
81m%5E4-16
%289m%5E2-4%29%289m%5E2-4%29
%28%283m-2%29%283m%2B2%29%29%28%283m-2%29%283m%2B2%29%29
3m=2=2%2F3
3m=-2=-2%2F3
#4 Im not sure what the question is asking for you to do, cause u cant find what either equals with 2 variables makes near unlimited possible solutions
#10
8a%5E2%2B23a-3
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 8a%5E2%2B23a%2B-3+=+0) has the following solutons:

a%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2823%29%5E2-4%2A8%2A-3=625.

Discriminant d=625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-23%2B-sqrt%28+625+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%2823%29%2Bsqrt%28+625+%29%29%2F2%5C8+=+0.125
a%5B2%5D+=+%28-%2823%29-sqrt%28+625+%29%29%2F2%5C8+=+-3

Quadratic expression 8a%5E2%2B23a%2B-3 can be factored:
8a%5E2%2B23a%2B-3+=+8%28a-0.125%29%2A%28a--3%29
Again, the answer is: 0.125, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B23%2Ax%2B-3+%29