The correct answer is A.
You have direct variation if x and y are modeled by the equation
In this case, m is the constant of proportionality. So, if the constant has to be 2, the equation becomes
A side note: Actually, option C has a constant of proportionality of two as well, except the roles of x and y are interchanged. I chose option A because usually you want the y = mx form, but the names of the variables are obviously meaningless.
First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.
"Four times..." means we're multiplying something by 4.
"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.
"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.
So, the resulting inequality is 4(x + 15) ≤ 120.
Simplify the inequality.
4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4
Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.
In interval notation it would look something like this:
[15, ∞)
In set builder notation it would look something like this:
{x | x ∈ R, x ≤ 15}
It is read as "the set of all x, such that x is a member of the real numbers and x is less than or equal to 15".
The inverse is f¯¹(x)=x/7.
Answer:
The answer will be 64.5
Step-by-step explanation:
