80 because if you divide 24 by 3 and multiply it by 2, you get the second value (16), then divide 24 by 3 and multiply it by five, you get the third value (40). Then you add all three values (24,16,40) and you get 80
Answer:
a. The side lengths are the same.
b. The perimeter is the same.
Step-by-step explanation:
Translating does not change the shape of the pentagon.
Answer:
15
Step-by-step explanation:
123=x+x+12+(x+12)*3
123=5x+48
75=5x
15=x
Answer:
C
Step-by-step explanation:
By tracing the figure, we see that we go around a semicricle twice and go in a straight path twice. So the perimeter of this figure consists of two semicircles and two line segments, hence the answer is C.
First, notice that the series you wrote is
∑ (-3)(n) for n ∈ [0,5]
There is a general formula for the sum of a basic geometric series that you should know or learn.
Here's a hint: How can you simplify the product of (1-x) and a summation, for n∈ [0,N], of all the n'th powers of x ((1-x)·∑ xn for n∈ [0,N])?
You can see you have to perform a distributive multiplication here, and if you write out the first three or four terms, and the last three or four terms, you should see a lot of cancellation going on. Pay special attention to what happens at n=0, n=N.
(x0+x1+x2+...+xN-2+xN-1+xN)-(x1+x2+...+xN-1+xN+xN+1)
Notice how all the values in between end up cancelling?
You can use your result to find an appropriate formula. In your case, x is 3. N is 5.
If your answer is correct, your formula will work for summing up any number of terms of any geometric series (any value of x and any value N). It is easy to compare your answer using your formula to the answer found manually by actually adding up all the terms.
