Factor the following:
12 x^4 - 42 x^3 - 90 x^2
Factor 6 x^2 out of 12 x^4 - 42 x^3 - 90 x^2:
6 x^2 (2 x^2 - 7 x - 15)
Factor the quadratic 2 x^2 - 7 x - 15. The coefficient of x^2 is 2 and the constant term is -15. The product of 2 and -15 is -30. The factors of -30 which sum to -7 are 3 and -10. So 2 x^2 - 7 x - 15 = 2 x^2 - 10 x + 3 x - 15 = x (2 x + 3) - 5 (2 x + 3):
6 x^2 x (2 x + 3) - 5 (2 x + 3)
Factor 2 x + 3 from x (2 x + 3) - 5 (2 x + 3):
Answer: 6 x^2 (2 x + 3) (x - 5)
Would you mind taking a picture of your problem so you may receive help?
Answer:
a=13
b=5
c=16.25
d=26.25
Step-by-step explanation:
Answer: ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Step-by-step explanation:
total sides = 6
p (rolling a 1) = ![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
p (rolling a 2) = ![\frac{1}{6\\}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%5C%5C%7D)
Note:
or - add
and - multiply
∴ ![\frac{1}{6} +\frac{1}{6} = \frac{2}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D%20%2B%5Cfrac%7B1%7D%7B6%7D%20%3D%20%5Cfrac%7B2%7D%7B6%7D)
∴ ![\frac{2}{6} = \frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B6%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
hence, p (rolling a 1 or 2) = ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Call the number of hours babysitting
![B](https://tex.z-dn.net/?f=B)
and the number of hours walking dogs
![D](https://tex.z-dn.net/?f=D)
.
We know that she earns $6/hr for babysitting or
![6B](https://tex.z-dn.net/?f=6B)
, and $5/hr walking dogs or
![5D](https://tex.z-dn.net/?f=5D)
. We also know the total money is $43 and the total time is 8hours. Therefore:
![B+D=8](https://tex.z-dn.net/?f=B%2BD%3D8)
![6B+5D=43](https://tex.z-dn.net/?f=6B%2B5D%3D43)
To solve: First rearrange equation 1 to solve for either
![B](https://tex.z-dn.net/?f=B)
or
![D](https://tex.z-dn.net/?f=D)
(doesn't matter which, I'll use
![B](https://tex.z-dn.net/?f=B)
):
![B=8-D](https://tex.z-dn.net/?f=B%3D8-D)
Now substitute into equation 2:
![6(8-D)+5D=43](https://tex.z-dn.net/?f=6%288-D%29%2B5D%3D43)
and solve for
![D](https://tex.z-dn.net/?f=D)
![48-6D+5D=43](https://tex.z-dn.net/?f=48-6D%2B5D%3D43)
![-D=-5](https://tex.z-dn.net/?f=-D%3D-5)
![D=5](https://tex.z-dn.net/?f=D%3D5)
Now backsubstitute to solve for
![B](https://tex.z-dn.net/?f=B)
:
![B=8-D](https://tex.z-dn.net/?f=B%3D8-D)
![B=8-5](https://tex.z-dn.net/?f=B%3D8-5)
![B=3](https://tex.z-dn.net/?f=B%3D3)
She babysat for 3 hours and walked dogs for 5.
To check our work:
![6B+5D=43](https://tex.z-dn.net/?f=6B%2B5D%3D43)
![6(3)+5(5)=43](https://tex.z-dn.net/?f=6%283%29%2B5%285%29%3D43)
![18+25=43](https://tex.z-dn.net/?f=18%2B25%3D43)
![43=43](https://tex.z-dn.net/?f=43%3D43)
CHECKS