Answer:Let n = the smallest integer
Then the other integers are n+1, n+2, n+3 and n+4
Sum = n + n+1 + n+2 + n+3 + n+4 = 5n + 10 = 5(n + 2)
So the sum is always divisible by 5, for any value of n
Step-by-step explanation:
The answer is B! Hoped I help
Answer:
![New\ Lengths = (14,21)](https://tex.z-dn.net/?f=New%5C%20Lengths%20%3D%20%2814%2C21%29)
![New\ Scale\ Factor = \frac{1}{7}](https://tex.z-dn.net/?f=New%5C%20Scale%5C%20Factor%20%3D%20%5Cfrac%7B1%7D%7B7%7D)
Step-by-step explanation:
Given
Rectangle:
Length = 2 in
Width = 3 in
Scale Factor = 7
Solving (a):
The side lengths of the new scale is calculated as follows;
New Lengths = Old Lengths * Scale Factor
![New\ Lengths = (2,3) * 7](https://tex.z-dn.net/?f=New%5C%20Lengths%20%3D%20%282%2C3%29%20%2A%207)
![New\ Lengths = (2 * 7,3* 7)](https://tex.z-dn.net/?f=New%5C%20Lengths%20%3D%20%282%20%2A%207%2C3%2A%207%29)
![New\ Lengths = (14,21)](https://tex.z-dn.net/?f=New%5C%20Lengths%20%3D%20%2814%2C21%29)
Solving (b): To go back to the original length
Given that the initial scale factor is 7;
The new scale factor is the reciprocal of the old factor;
Hence;
![New\ Scale\ Factor = \frac{1}{7}](https://tex.z-dn.net/?f=New%5C%20Scale%5C%20Factor%20%3D%20%5Cfrac%7B1%7D%7B7%7D)
Answer:
(-4,-11)
Step-by-step explanation:
Given an equation of a circle
![x^{2} +y^{2} +8x+22y+37 =0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2By%5E%7B2%7D%20%2B8x%2B22y%2B37%20%3D0)
To find the centre and radius of the circle.
We group x terms to gether and y terms to gether first.
![x^{2} +8x+y^{2}+22y+37 =0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B8x%2By%5E%7B2%7D%2B22y%2B37%20%3D0)
Now completion of squares method is used for both x and y.
![x^{2} +8x+16-16+y^{2}+22y+121-121+37 =0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B8x%2B16-16%2By%5E%7B2%7D%2B22y%2B121-121%2B37%20%3D0)
![(x+4)^{2} +(y+11)^{2}-100 =0](https://tex.z-dn.net/?f=%28x%2B4%29%5E%7B2%7D%20%20%2B%28y%2B11%29%5E%7B2%7D-100%20%3D0)
![(x+4)^{2} +(y+11)^{2} =10^{2}](https://tex.z-dn.net/?f=%28x%2B4%29%5E%7B2%7D%20%20%2B%28y%2B11%29%5E%7B2%7D%20%3D10%5E%7B2%7D)
Thus we find that the centre = (-4,-11) and radius
= 10
Answer:
27
Step-by-step explanation:
#3 is 1/3^3, and #4 is 1/x. The x is obviously 3^3 simplified, which is 27.
I see that you are in high school. Im in 7th grade and i can do this lol.