<em>Factor -1.5 out of -4.5n + 3</em>
Answer: D. -1.5(3n + 2)
Easy
ok, so
for y=a(x-h)^2+k
the vertex is (h,k)
given that the the vertex is (-2,-20)
y=a(x-(-2))^2+(-20)
y=a(x+2)^2-20
find a
when x=0, then y=-12
-12=a(0+2)^2-20
-12=a(2)^2-20
8=4a
2=a
equation is
y=2(x+2)^2-20
if the last term is positive, then maybe y=2(x+2)^2+(-20)?
unless you typed something wrong, then you are right that the last term is -20
Answer:
13/18
Step-by-step explanation:
1. ![\frac{5}{6} -\frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D%20-%5Cfrac%7B1%7D%7B9%7D)
2. ![\frac{n}{54} - \frac{n}{54}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7B54%7D%20-%20%5Cfrac%7Bn%7D%7B54%7D)
3. ![\frac{45}{54} - \frac{6}{54}](https://tex.z-dn.net/?f=%5Cfrac%7B45%7D%7B54%7D%20-%20%5Cfrac%7B6%7D%7B54%7D)
4. ![= \frac{39}{54}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B39%7D%7B54%7D)
5. ![Simplify: \frac{13}{18}](https://tex.z-dn.net/?f=Simplify%3A%20%5Cfrac%7B13%7D%7B18%7D)
G(-3) = 2(-3) - 2
= - 6 - 2
= - 8
Answer:
36 milliliters of rain.
Step-by-step explanation:
The rate at which rain accumluated in a bucket is given by the function:
![r(t)=10t-t^2](https://tex.z-dn.net/?f=r%28t%29%3D10t-t%5E2)
Where r(t) is measured in milliliters per minute.
We want to find the total accumulation of rain from <em>t</em> = 0 to <em>t</em> = 3.
We can use the Net Change Theorem. So, we will integrate function <em>r</em> from <em>t</em> = 0 to <em>t</em> = 3:
![\displaystyle \int_0^3r(t)\, dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E3r%28t%29%5C%2C%20dt)
Substitute:
![=\displaystyle \int_0^3 10t-t^2\, dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%20%5Cint_0%5E3%2010t-t%5E2%5C%2C%20dt)
Integrate:
![\displaystyle =5t^2-\frac{1}{3}t^3\Big|_0^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D5t%5E2-%5Cfrac%7B1%7D%7B3%7Dt%5E3%5CBig%7C_0%5E3)
Evaluate:
![\displaystyle =(5(3)^2-\frac{1}{3}(3)^3)-(5(0)^2-\frac{1}{3}(0)^3)=36\text{ milliliters}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D%285%283%29%5E2-%5Cfrac%7B1%7D%7B3%7D%283%29%5E3%29-%285%280%29%5E2-%5Cfrac%7B1%7D%7B3%7D%280%29%5E3%29%3D36%5Ctext%7B%20milliliters%7D)
36 milliliters of rain accumulated in the bucket from time <em>t</em> = 0 to <em>t</em> = 3.