Answer:
1822
Step-by-step explanation:
The fraction 1822 is equal to 911 when reduced to lowest terms.
18
22
is equivalent to 9
11
because 9 x 2 = 18 and 11 x 2 = 22
27
33
is equivalent to 9
11
because 9 x 3 = 27 and 11 x 3 = 33
36
44
is equivalent to 9
11
because 9 x 4 = 36 and 11 x 4 = 44
Option b: 10 in, 18.5 in, 31.5 in.
Explanation:
The three sides of a triangle are
and ![7y](https://tex.z-dn.net/?f=7y)
The perimeter of the triangle is
.
Since, Perimeter = all sides of the triangle
Let us add all the three sides to determine the length of each side.
![Perimeter=2y+1+3y+5+7y](https://tex.z-dn.net/?f=Perimeter%3D2y%2B1%2B3y%2B5%2B7y)
Substituting the value of Perimeter and simplifying, we get,
![60=12y+6\\54=12y\\4.5=y](https://tex.z-dn.net/?f=60%3D12y%2B6%5C%5C54%3D12y%5C%5C4.5%3Dy)
Substituting
in the three sides of the triangle
and
, we get,
![2y+1=2(4.5)+1=10 in](https://tex.z-dn.net/?f=2y%2B1%3D2%284.5%29%2B1%3D10%20in)
![3y+5=3(4.5)+5=18.5 in](https://tex.z-dn.net/?f=3y%2B5%3D3%284.5%29%2B5%3D18.5%20in)
![7y=7(4.5)=31.5 in](https://tex.z-dn.net/?f=7y%3D7%284.5%29%3D31.5%20in)
Thus, the lengths of each side are 10 in, 18.5 in, 31.5 in.
Answer:
7/12
Step-by-step explanation:
Divide both the numerator & denoniminator by 7.
49 / 7 = 7
84 / 7 = 12
7/12
Answer:
The constant of proportionality is 54.
k = 54
c as a function of d:
![c(d) = \dfrac{54}{d^2}](https://tex.z-dn.net/?f=c%28d%29%20%3D%20%5Cdfrac%7B54%7D%7Bd%5E2%7D)
![c(7) = \dfrac{54}{49}](https://tex.z-dn.net/?f=c%287%29%20%3D%20%5Cdfrac%7B54%7D%7B49%7D)
Step-by-step explanation:
We are given the following in the question:
c is inversely proportional to the square of d.
![\Rightarrow c\propto \dfrac{1}{d^2}\\\\\Rightarrow c = \dfrac{k}{d^2}\\\\\text{where k is constant of proportionality}](https://tex.z-dn.net/?f=%5CRightarrow%20c%5Cpropto%20%5Cdfrac%7B1%7D%7Bd%5E2%7D%5C%5C%5C%5C%5CRightarrow%20c%20%3D%20%5Cdfrac%7Bk%7D%7Bd%5E2%7D%5C%5C%5C%5C%5Ctext%7Bwhere%20k%20is%20constant%20of%20proportionality%7D)
When c = 6, d = 3.
Plugging the values, we get,
![6 = \dfrac{k}{3^2}\\\\\Rightarrow k = 6\times 3^2 = 54](https://tex.z-dn.net/?f=6%20%3D%20%5Cdfrac%7Bk%7D%7B3%5E2%7D%5C%5C%5C%5C%5CRightarrow%20k%20%3D%206%5Ctimes%203%5E2%20%3D%2054)
Thus, the constant of proportionality is 54.
c as a function of d can be written as:
![c(d) = \dfrac{54}{d^2}](https://tex.z-dn.net/?f=c%28d%29%20%3D%20%5Cdfrac%7B54%7D%7Bd%5E2%7D)
We have to find value of c when d = 7.
Putting values, we get,
![c(7) = \dfrac{54}{(7)^2}=\dfrac{54}{49}](https://tex.z-dn.net/?f=c%287%29%20%3D%20%5Cdfrac%7B54%7D%7B%287%29%5E2%7D%3D%5Cdfrac%7B54%7D%7B49%7D)
is the required value of c.