Answer:
Step-by-step explanation:instead, try making the subscripts and superscripts stand out:
n-1
a = a * r
n n-1
Believe me, it's worth the extra work to do this!!
Given the sequence -3, -6, -12, -24, you can easily see that the first term,
a is -3. The common factor is 2. Note how (-3)*2=-6, and so on.
1
So, a = -3 and r=2.
1
So the formula for this geometric sequence is
n-1
a = -3*2
n
Answer:
37 kilograms alr recycled this year
Plan:
1 kilogram each week
After 13 weeks he would of recycled 13 kilograms
37+13=50
In total his office wesley's have recycled 50 kilograms of paper
Hope this helps
Answer:
1079
Step-by-step explanation:
Answer:
The height is 2 units
Step-by-step explanation:
Find the area of the base of the square pyramid
we know that
The volume of the square pyramid is equal to
![V=\frac{1}{3}BH](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7DBH)
where
B is the area of the base and H is the height of the pyramid
we have
![H=6\ units](https://tex.z-dn.net/?f=H%3D6%5C%20units)
![V=70\ units^{3}](https://tex.z-dn.net/?f=V%3D70%5C%20units%5E%7B3%7D)
substitute in the formula and solve for B
![70=\frac{1}{3}B(6)](https://tex.z-dn.net/?f=70%3D%5Cfrac%7B1%7D%7B3%7DB%286%29)
![B=70/2=35\ units^{2}](https://tex.z-dn.net/?f=B%3D70%2F2%3D35%5C%20units%5E%7B2%7D)
step 2
Find the height of the square prism
we know that
The volume of the square prism is equal to
![V=Bh](https://tex.z-dn.net/?f=V%3DBh)
where
B is the area of the base and h is the height of the prism
we have
![B=35\ units^{2}](https://tex.z-dn.net/?f=B%3D35%5C%20units%5E%7B2%7D)
![V=70\ units^{3}](https://tex.z-dn.net/?f=V%3D70%5C%20units%5E%7B3%7D)
substitute in the formula and solve for h
![70=(35)h](https://tex.z-dn.net/?f=70%3D%2835%29h)
![h=2\ units](https://tex.z-dn.net/?f=h%3D2%5C%20units)
Answer:
Chantal and Trisha will have both traveled 105 miles in 20 minutes.
Step-by-step explanation:
is distance in miles,
is time in hours.
The two equations are:
![y = \frac{20}{x} + 45](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B20%7D%7Bx%7D%20%2B%2045)
![y = \frac{35}{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B35%7D%7Bx%7D)
Set them equal to each other and solve for x:
![\frac{35}{x} = \frac{20}{x} + 45](https://tex.z-dn.net/?f=%5Cfrac%7B35%7D%7Bx%7D%20%3D%20%5Cfrac%7B20%7D%7Bx%7D%20%2B%2045)
![\frac{35}{x} - \frac{20}{x} = 45](https://tex.z-dn.net/?f=%5Cfrac%7B35%7D%7Bx%7D%20-%20%5Cfrac%7B20%7D%7Bx%7D%20%3D%2045)
![\frac{35-20}{x} = 45](https://tex.z-dn.net/?f=%5Cfrac%7B35-20%7D%7Bx%7D%20%3D%2045)
![\frac{15}{x} = 45](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7Bx%7D%20%3D%2045)
![x = \frac{15}{45} = \frac{1}{3} hours = 20 minutes](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B15%7D%7B45%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20hours%20%3D%2020%20minutes)
Plug that back into the equations to confirm this
gives the same
:
![y = \frac{20}{1/3} + 45 = 105 miles](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B20%7D%7B1%2F3%7D%20%2B%2045%20%3D%20105%20miles)
![y = \frac{35}{1/3} = 105 miles](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B35%7D%7B1%2F3%7D%20%3D%20105%20miles)