Answer:
see explanation
Step-by-step explanation:
consecutive even integers have a difference of 2 between them
for example 2, 4, 6 are 3 consecutive even integers
In general if we let the first integer be k then the next 2 integers are
k + 2 and k + 4
the sum of these equals 4 times the first integer, that is 4k, hence
k + k + 2 + k + 4 = 4k
3k + 6 = 4k ( subtract 3k from both sides )
6 = k
the 3 consecutive integers are
k = 6
k + 2 = 6 + 2 = 8
k + 4 = 6 + 4 = 10
that is 6, 8 and 10
note that sum = 6 + 8 + 10 = 24
and 4 × 6 = 24
confirming the sum of the 3 integers equals 4 times the first integer
<em>Exterior angle of the triangle is equal to the sum of the opposite angles.</em>
9x = 5x + 9 + x
<em>Combine like terms:</em>
9x = 6x + 9
<em>Take away 6x from both sides:</em>
3x = 9
<em>Divide by 3 on both sides:</em>
x = 3
Answer: x = 3
Answer:
5 5/8 miles per hour
Step-by-step explanation:
Martin can run 3 ¾ miles in 2/3 of an hour. Write a unit rate to describe the situation and explain the context.
We are asked to write the unit rate , this means we are to find out how many miles he can run per hour
Hence,
2/3 hour = 3 3/4 miles
1 hour = x
Cross Multiply
2/3 hour × x = 3 3/4 miles × 1 hour
x = 3 3/4 miles × 1 hour/ 2/3 hour
x = 3 3/4 ÷ 2/3
x = 15/4 ÷ 2/3
x = 15/4 × 3/2
x = 45/8
x = 5 5/8 miles per hour