Answer:
Step-by-step explanation:
To be rational means to be able to express the result as the ratio of two whole numbers.
a) 4/7 + (-1/3) = 12/21 - 7/21 = 5/21 so rational
b) √(4) • 2/5 = ±2 • 2/5 = ±4/5 so both solutions are rational
We are given ratio 456:8.
The given ratio can be written in fraction form as 
In order to find the rate, we need to divide 456 by 8, because it would give the unit value.
When we divide 456 by 8, we first take multiple of 8 closer to the number 45.
8*6=48 but it's greater than 45, so we would take 8*5 =40.
Subtracting 40 from 45, we get 5.
Getting 6 down, we get 56. Take multiple of 8 upto 56.
8*7= 56.
56 -56=0.
So, on dividing 456 by 8 we got 57.
Therefore, rate is 57 per unit.
Remember you can do anyting to an equation as long as ou do it to both sides
-6x+4=-50
minus 4 both sides
-6x=-54
divide both sides by -6
x=9
5x+6=-44
minus 6 both sides
5x=-50
divide both sides by 5
x=-10
-3(7+6x)=-201
normally you would distribute (that works) but it's easier to divide both sides by -3
7+6x=67
minus 7 both sides
6x=60
divide by 6 both sides
x=10
35a. We're asked to compute the ratio between the enlarged width and the original width. So we literally perform the operation:

35b. If the order is wrong the image would be shrunk instead of enlarged, with a ratio of 
36. We know that

Observe that

If you were to take both halves of the carpet and place them on top of each other you can see that the two triangle sections would cover each over up and fill in to make a rectangle. So first, lets compute the size of the middle section, then we will compute the size of the end pieces.
The center section of the carpet is 30 ft x 31 ft = 930 sq ft
The ends of the carpet are 12 ft x 15.5 ft = 186 sq ft
Since there are two side to the carpet like this we multiply this by 2
186 * 2 = 372 sq ft
Adding these two values together gives
930 + 372 = 1302 sq ft