Answer with Step-by-step explanation:
Since we have given that
a + b = c
and a|c
i.e. a divides c.
We need to prove that a|b.
⇒ a = mb for some integer m
Since a|c,
So, mathematically, it is expressed as
c= ka
Now, we put the above value in a + b = c.
So, it becomes,
a=mb, here, m = k-1
Hence, proved.
D 28 miles you want to multiply by 4 so 7x4 =28
Answer:
False, the dilation factor is 2.
Step-by-step explanation:
Notice how each measure of the segments for the red quadrilateral is 2x the amount of the segments for the blue triangle? That right there is the dilation factor.
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
Answer:
The length and width of another rectangular field with same perimeter but a larger area is 80 m by 70 m
Step-by-step explanation:
The perimeter of the existing field is
2(l + b)
= 2(90 + 60) = 2(150) = 300 yards
So we want another field having the same perimeter but a larger area
The area we have here is 90 * 60 = 5,400 square yards
If we had 80 by 70
Perimeter will still be 2(70 + 80) = 150
But the area will be 80 * 70 = 5,600 square yards
