Okay so basically the axis of symmetry is the h (technically where x is on the graph)nvalue so for the first one the answer is -4 for the second one because in vertex form the value of h (x-h) is in the parenthesis. For the second one you will have to turn the equation from standard to vertex. First step is to factor out the first two terms' coefficients. if you factor out two the equation turns into 2(x^2-8x) +15 The next step is you take 8 and divide it by 2 and then square it which equals 16. You add this term into the parenthesis so you can factor out like a quadratic. The equation turns into 2(x^2-8x+16) +15 to balance out the equation you have to subtract the term that you put in the parenthesis outside the parenthesis. Since 16 is the parenthesis you need to multiply it by 2, so your equation will turn into y=2(x^2-8x+16) -17 then factor out like a regular polynomial and get y=2(x-4)^2 -17 now that it's in vertex form you can see your answer is positive 4. For the third problem just look where the vertex is and see the x coordinate. The answer is 1.
The order is the g(x), the graph and the f(x)
In the figure we have three parallel lines cut by two transversals
The theorem stares:
If two or more parallel lines are cut by two transversals, then they divide the transversals proportionally.
Applying this theorem we have:
To solve for x we cross multiply
6x=20
Dividing both sides by 6 we have:
The second option x=
is the right answer
Answer:
![\int_{-\infty}^0 5 e^{60x} dx = \frac{1}{12}[e^0 -0]= \frac{1}{12}](https://tex.z-dn.net/?f=%20%5Cint_%7B-%5Cinfty%7D%5E0%205%20e%5E%7B60x%7D%20dx%20%3D%20%5Cfrac%7B1%7D%7B12%7D%5Be%5E0%20-0%5D%3D%20%5Cfrac%7B1%7D%7B12%7D)
Step-by-step explanation:
Assuming this integral:
We can do this as the first step:
Now we can solve the integral and we got:
![\int_{-\infty}^0 5 e^{60x} dx = \frac{e^{60x}}{12}\Big|_{-\infty}^0 = \frac{1}{12} [e^{60*0} -e^{-\infty}]](https://tex.z-dn.net/?f=%20%5Cint_%7B-%5Cinfty%7D%5E0%205%20e%5E%7B60x%7D%20dx%20%3D%20%5Cfrac%7Be%5E%7B60x%7D%7D%7B12%7D%5CBig%7C_%7B-%5Cinfty%7D%5E0%20%3D%20%5Cfrac%7B1%7D%7B12%7D%20%5Be%5E%7B60%2A0%7D%20-e%5E%7B-%5Cinfty%7D%5D)
So then we see that the integral on this case converges amd the values is 1/12 on this case.
Answer:
The amount of money he owes when he begins making payments:
A = 13000 x ( 1 + rate/12)^month
= 13000 x (1 + (3.6/100)/12)^15
= 13597.45 dollar
Hope this helps!
:)
