Distribute the monomial through the polynomial.

The answer is:

Distribute the monomial through each term inside the parentheses.

In order to multiply this, we can simply multiply the coefficients together and the变量联系在一起。当我们把一个变量of the same base, we can add the exponents.

Simplify the right side.

The answer is:

Distribute the monomial to each part of the polynomial, paying careful attention to signs:

Find the product:

Step 1: Multiply the numerators and denominators using the properties of exponents. (When multiplying exponents, add them.)

Step 2: Simplify the expression.

Every minute Phillip completes anothersquare feet of painting. To solve for the total area that he completes, we need to find the number of minutes that he works.

There are 60 minutes in an hour, and he paints for 2.5 hours. Multiply to find the total number of minutes.

如果he completessquare feet per minute, then we can multiplyby the total minutes to find the final answer.

Let's consider the general case whenyvaries directly withx. Ifyvaries directly withx, then we can express their relationship to one another using the following formula:

y=kx, wherekis a constant.

Therefore, ify成正比的平方xand the cube ofz, we can write the following analagous equation:

y=kx²z³, wherekis a constant.

The problem states thaty= 24 whenx= 1 andz= 2. We can use this information to solve forkby substituting the known values fory,x, andz.

24 =k(1)²(2)³=k(1)(8) = 8k

24 = 8k

Divide both sides by 8.

3 =k

k= 3

Now that we havek, we can findyif we knowxandz. The problem asks us to findywhenx= 3 andz= 1. We will use our formula for direct variation again, this time substitute values fork,x, andz.

y=kx²z³

y= 3(3)²(1)³= 3(9)(1) = 27

y= 27

The answer is 27.

We know that the initial population is 3, and that every week the population will triple.

The equation to model this growth will be, whereis the initial size,is the rate of growth, andis the time.

In this case, the equation will be.

Alternatively, you can evaluate for each consecutive week.

Week 1:

Week 2:

Week 3:

Week 4:

如果andare the diameter and circumference, respectively, of the same circle, then

.

By substitution,

Taking the square root of both sides:

Taking作为the constant of variation, we get

,

meaning thatvaries directly as.

The volume of a cone can be calculated from the radius of its base, and the height, using the formula

, so.

, so.

, so by substitution,

Square both sides:

如果we take作为the constant of variation, then

,

andvaries directly as the fifth power of.