1.
An expression of the form

is called a "compound fraction"
Compound fractions can be written as simple fractions by multiplying c to a, and then adding the product to c as follows:

for example,

can be written as:

2.
when we subtract or add a fraction

from an integer k,
we first write k as a fraction with denominator n. We can do this as follows:

for example, if we want to subtract

from 8,
we first write 8 as a fraction with denominator 2:

3.
Thus,

4.
The simple fraction 7/2 is not an option, so we write it as a compound fraction as follows:

(So write 7 as the sum of the largest multiple of 2, smaller than 7 + what is left. In our case these numbers are 6 and 1, then proceed as shown)
5. Answer: D
Answer:
Step-by-step explanation:
-3x + 4y = 12
12(1/4x - 1/3y = 1)
-3x + 4y = 12
3x - 4y = 12
there is no solution
Let X be the normal variable with mean μ =50 and standard deviation σ =2
We have to find probability that x is between 47 and 54
P(47 < X < 54) = P(X < 54) - P(X < 47)
=
- 
= P(Z < 2) - P(Z < -1.5)
Using standard normal z score table to find probabilities we get
P(Z < 2) = 0.9772
P(Z < -1.5) = 0.0668
P(47 < X < 54) = P(Z < 2) - P(Z < -1.5)
= 0.9772 - 0.0668
P(47 < X < 54) = 0.9104
The probability that x is between 47 and 54 is 0.9104
I will show all the steps to lead to the solution.
1) 10b = 5 (√c + 2) <---- starting equation
2) divide by 5 => 2 b = √c + 2
3) subtract 2 => 2b - 2 = √c
4) raise to the power 2 => (2b - 2)^2 = c, which is the expression given.
Now these are two equivalent forms:
1) extract 2 from the parentheses: c = 4 (b -1)^2
2) expand the parentheses: c = 4b^2 - 8b + 4)
To determine if the ordered pair (3 , -2) is a solution to 4x = 3y + 18,
plug in the point into the equation.
4x = 3y + 18 (Plug in 3 for "x", and plug in -2 for "y")
4(3) = 3(-2) + 18
12 = -6 + 18
12 = 12
This is a solution because in the end, the number is the same on both sides