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Subtract and from the both sides to get .

Divide both sides by , to get

The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.

Perimeter A = 45” and perimeter B = 135”

The proportion of Perimeter A to Perimeter B is .

This applies to the sides of the triangle. Therefore to get the any side of Triangle B, just multiply the correlating side by 3.

15” x 3 = 45”

10” x 3 = 30“

First write the equation in slope intercept form. Add to both sides to get . Now divide both sides by to get . The slope of this line is , so any line that also has a slope of would be parallel to it. The correct answer is .

Solve for by merging the equations so that gets factored out. To do so, multiply the lower equation by (so that at the top is subtracted by )

First, solve this equation for y and then substitute the answer into the second equation:

Now substitute into the second equation and solve for x:

To solve for x, add the coefficients on the x variables together then divide both sides by three.

We define the variables as and .

We substitute these values into the equation for the area of a rectangle and get .

or

Lengths cannot be negative, so the only correct answer is . If , then .

Therefore, .

Let x be the number of pencils and y be the number of pens Sally purchased. We are told that each pencil costs 25 cents. Because, the total amount she spent was given in dollars, we want to convert 25 cents to dollars. Because there are 100 cents in one dollar, 25 cents = $0.25. Similarly, each pen costs $0.50.

The amount that Sally spent on pencils is equal to the product of the number of pencils and the cost per pencil. We can model the amount of money spent on pencils as 0.25x.

Likewise, the amount Sally spent on pens is equal to the product of the number of pens and the cost per pen, or 0.5y.

Since we are told that Sally spent $5.75 total on pens and pencils combined, we can write the following:

We are also told that the number of pens is one greater than the number of pencils. We can thus write:

We now have two equations and two unknowns. In order to solve this system of equations, we can take the value of y = x + 1 and substitute it into the other equation.

Distribute.

Combine x terms.

Subtract 0.5 from both sides.

Divide both sides by 0.75.

This means Sally bought 7 pencils and 8 pens. The question asks us to find the number of pens and pencils purchased altogether, which would equal

The answer is 15.

AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.

Since we have a triangle, the opposites sides of those angles will be in the ratio .

Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to .

which also means

Use the substitution method to solve the system of equations. There are two ways to do this - either substitute the first equation into the second, or the second equation into the first. Since the second equation is already solved for one variable, we will choose the latter.

Now factor the equation:

or

For this particular question, you could stop right here, as you can only need to know the number of solutions not the ordered pair of the solutions. Here there are two solutions. The ordered pairs would be:

and

Subtracting the second equation from the first, we acquire .

Adding this equation to the third equation, we get .

Therefore, .

This problem can be solved by using substitution. Write the first equation in terms of and substitute it into the second equation.

So and thus and solving for and then .

So the sum of and is 7.

The area of the walls is given by

One gallon of paint covers 400 and the remaining 140 would be covered by two quarts.

So one gallon and two quarts of paint would cost

Look for perfect cubes within each term. This will allow us to factor out of the radical.

Simplify.

This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.

Add like terms together:

has no like terms.

Combine these terms into one expression to find the answer:

We can solve either by substitution or by elimination. We will solve by elimination.

Line up both equations so the variables are in the same order.

Because we have a negative and a positive , if we were to add these two equations straight up and down, the values would cancel out.

Solve for .

Plug back in to one of the original equations to solve for .

The final answer will be . We can check this answer by plugging it back into either of the original equations.

For this system, it will be easiest to solve by substitution. The variable is already isolated in the second equation. We can replace in the first equation with , since these two values are equal.

Now we can solve for .

Now that we know the value of , we can solve for by using our original second equation.

The final answer will be the ordered pair .

Find the product:

Step 1: Use the distributive property.

Step 2: Combine like terms.

With quadratic equations, always begin by getting it into standard form:

Therefore, take our equation:

And rewrite it as:

You could use the quadratic formula to solve this problem. However, it is possible to factor this if you are careful. Factored, the equation can be rewritten as:

Now, either one of the groups on the left could be and the whole equation would be . Therefore, you set up each as a separate equation and solve for :

OR

The sum of these values is: