Answer:
Step-by-step explanation:
Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that
1 gallon of gas would be used to drive 392/14 = 28 miles
a) The number of miles traveled varies directly with the number of gallons of gas used.
Let x =number of gallons of gas you use.
Let y = the number of miles travelled.
Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,
y = kx
If 28 miles will require 1 gallon of gas, it means
28 = 1×k
k = 28
So y = 28x
b) we want to determine how far you can drive with 3.7 gallons of gas.
x = 3.7
y = 28x = 28×3.7
y = 103.6 miles
Answer:

Step-by-step explanation:
This is a multiplication problem.
We want to multiply 
We factor to get:

We now cancel out the common factors to get:

We now multiply the numerators and the denominators separately to get.
This simplifies to 
Therefore the simplified expression is 
Answer:

Step-by-step explanation:
A direct variation equation has the following format:

Where k is a constant.
We know that y is 12 when x is -2. Thus, substitute:

Divide both sides by -2:

So, our direct variation equations is:

To find what x is when y equals -6, substitute in -6 for y:

Divide both sides by -6:

So, our answer is 1 :)
Answer: 25
explanation:
7² + 24² = c²
49 + 576 = c²
625 = c²
c = √625
c= 25
or just know some pythagorean triples
Answer:
4
Explanation:
The amplitude of a sine function is the absolute value of the coefficient of sin(in other words, the absolute value of the number multiplying the sin)
In this case, that is |-4|=4