It will take her 62.5 min to finish her homework
(4,-2) (6,-2) (4,1) are co ordinates for the triangle after the movement
Answer:
t(total amount) = 8 + 0.5x
Step-by-step explanation:
9514 1404 393
Answer:
positive
Step-by-step explanation:
The exponent 12 tells you how many times (-1 3/4) is a factor in the product. The number 12 is even, so there will be an even number of minus signs in the product. That results in a positive product.
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The value is ...
825.005006849765777587809625
ANSWER TO QUESTION 1
.
EXPLANATION
The function given to us is,
![f(x)=x^4-x^3-7x^2+13x-6](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4-x%5E3-7x%5E2%2B13x-6)
According to rational roots theorem,
are possible rational zeros of
.
We find out that,
![f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6](https://tex.z-dn.net/?f=f%28-3%29%3D%28-3%29%5E4-%28-3%29%5E3-7%28-3%29%5E2%2B13%28-3%29-6)
![f(-3)=81+27-63-39-6](https://tex.z-dn.net/?f=f%28-3%29%3D81%2B27-63-39-6)
![f(-3)=6-6](https://tex.z-dn.net/?f=f%28-3%29%3D6-6)
![f(-3)=0](https://tex.z-dn.net/?f=f%28-3%29%3D0)
Also
![f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6](https://tex.z-dn.net/?f=f%282%29%3D%282%29%5E4-%282%29%5E3-7%282%29%5E2%2B13%282%29-6)
![f(2)=16-8-28+26-6](https://tex.z-dn.net/?f=f%282%29%3D16-8-28%2B26-6)
![f(2)=6-6](https://tex.z-dn.net/?f=f%282%29%3D6-6)
![f(2)=0](https://tex.z-dn.net/?f=f%282%29%3D0)
This implies that
are factors of
and hence
is also a factor.
We perform the long division as shown in the diagram.
Hence,
.
ANSWER TO QUESTION 2
Sketching the graph
We can see from the factorization that the roots
and
have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.
Also the root
has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.
Now we determine the position of the graph on the following intervals,
![x\le -3](https://tex.z-dn.net/?f=x%5Cle%20-3)
![f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6](https://tex.z-dn.net/?f=f%28-4%29%3D%28-4%29%5E4-%28-4%29%5E3-7%28-4%29%5E2%2B13%28-4%29-6)
![f(-4)=150\:>0](https://tex.z-dn.net/?f=f%28-4%29%3D150%5C%3A%3E0)
![-3\le x \le 1](https://tex.z-dn.net/?f=-3%5Cle%20x%20%5Cle%201)
![f(0)=-6\:](https://tex.z-dn.net/?f=f%280%29%3D-6%5C%3A%3C0)
![1\le x\le 2](https://tex.z-dn.net/?f=1%5Cle%20x%5Cle%202)
![f(1.5)=-0.56\:](https://tex.z-dn.net/?f=f%281.5%29%3D-0.56%5C%3A%3C0)
![x \ge 2](https://tex.z-dn.net/?f=x%20%5Cge%202)
![f(3)=24\:>0](https://tex.z-dn.net/?f=f%283%29%3D24%5C%3A%3E0)
We can now use these information to sketch the function as shown in diagram