Answer:
The answer would be true.
Step-by-step explanation:
60*40=2400
The answer is D.
Find the scale of each dimension:
B: 6/3 = 2 and 10/5 = 2, both dimensions have the same scale factor of 2.
C: 15/3 = 5 and 25/5 = 5, both dimensions have the same scale factor of 5.
D: 60/3 = 20 and 90/5 = 18, each dimension has a different scale factor so is not an enlargement.
Answer:
Proved
Step-by-step explanation:
Given
![1+5+9+...+[4(n-1)+1]+[4n+1] = (n+1)(2n+1)](https://tex.z-dn.net/?f=1%2B5%2B9%2B...%2B%5B4%28n-1%29%2B1%5D%2B%5B4n%2B1%5D%20%3D%20%28n%2B1%29%282n%2B1%29)
![n \geq 1](https://tex.z-dn.net/?f=n%20%5Cgeq%201)
Required
Prove by induction
![1+5+9+...+[4(n-1)+1]+[4n+1] = (n+1)(2n+1)](https://tex.z-dn.net/?f=1%2B5%2B9%2B...%2B%5B4%28n-1%29%2B1%5D%2B%5B4n%2B1%5D%20%3D%20%28n%2B1%29%282n%2B1%29)
Increment n by 1 on both sides
![1+5+9+...+[4(n-1)+1]+[4n+1]+[4(n+1)+1] = (n+1+1)(2(n+1)+1)](https://tex.z-dn.net/?f=1%2B5%2B9%2B...%2B%5B4%28n-1%29%2B1%5D%2B%5B4n%2B1%5D%2B%5B4%28n%2B1%29%2B1%5D%20%3D%20%28n%2B1%2B1%29%282%28n%2B1%29%2B1%29)
Simplify the right hand side
![1+5+9+...+[4(n-1)+1]+[4n+1]+[4(n+1)+1] = (n+2)(2n+2+1)](https://tex.z-dn.net/?f=1%2B5%2B9%2B...%2B%5B4%28n-1%29%2B1%5D%2B%5B4n%2B1%5D%2B%5B4%28n%2B1%29%2B1%5D%20%3D%20%28n%2B2%29%282n%2B2%2B1%29)
![1+5+9+...+[4(n-1)+1]+[4n+1]+[4(n+1)+1] = (n+2)(2n+3)](https://tex.z-dn.net/?f=1%2B5%2B9%2B...%2B%5B4%28n-1%29%2B1%5D%2B%5B4n%2B1%5D%2B%5B4%28n%2B1%29%2B1%5D%20%3D%20%28n%2B2%29%282n%2B3%29)
Group the left hand side
![(1+5+9+...+[4(n-1)+1]+[4n+1])+[4(n+1)+1] = (n+2)(2n+3)](https://tex.z-dn.net/?f=%281%2B5%2B9%2B...%2B%5B4%28n-1%29%2B1%5D%2B%5B4n%2B1%5D%29%2B%5B4%28n%2B1%29%2B1%5D%20%3D%20%28n%2B2%29%282n%2B3%29)
Recall that
----[Given]
So; Substitute
for
on the left hand side
![(n+1)(2n+1)+[4(n+1)+1] = (n+2)(2n+3)](https://tex.z-dn.net/?f=%28n%2B1%29%282n%2B1%29%2B%5B4%28n%2B1%29%2B1%5D%20%3D%20%28n%2B2%29%282n%2B3%29)
Open All Brackets
![2n^2 + n + 2n + 1 + 4n + 4 + 1 = 2n^2 + 3n + 4n + 6](https://tex.z-dn.net/?f=2n%5E2%20%2B%20n%20%2B%202n%20%2B%201%20%2B%204n%20%2B%204%20%2B%201%20%3D%202n%5E2%20%2B%203n%20%2B%204n%20%2B%206)
Collect Like Terms
![2n^2 + n + 2n + 4n+ 1 + 4 + 1 = 2n^2 + 3n + 4n + 6](https://tex.z-dn.net/?f=2n%5E2%20%2B%20n%20%2B%202n%20%2B%204n%2B%201%20%20%2B%204%20%2B%201%20%3D%202n%5E2%20%2B%203n%20%2B%204n%20%2B%206)
![2n^2 + 7n+ 6 = 2n^2 + 7n + 6](https://tex.z-dn.net/?f=2n%5E2%20%2B%207n%2B%206%20%3D%202n%5E2%20%2B%207n%20%2B%206)
<em>Notice that the expression on both sides are equal;</em>
<em>Hence, the given expression has been proven</em>
First location the diver dove = 6 3/5 meters below sea leavel.
Second location the diver dove = 8 1/5 meters below sea leavel.
Let us convert those mixed fractions into improper fraction.
6 3/5 =
= 33/5.
8 1/5 =
= 41/5.
Now, we need to find the difference in depths of locations diver dove.
41/5 - 33/5 = ![\frac{41-33}{5}=\frac{8}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B41-33%7D%7B5%7D%3D%5Cfrac%7B8%7D%7B5%7D)
So, we got 8/5.
Now, we need to convert 8/5 into mixed fraction.
Dividing 8 by 5, we get quotient=1 and remainder 3.
So, the mixed fraction would be
.
Therefore, we could say
meter is the difference in depths of locations diver dove.
The answer is 361.
This is because you take 731 and subtract 9 and you get 722. Then you divide 722 by two and you get 361.
Hope this helped!!