Calculate the area of the shape shown.
Round your answer to two decimal places .

We have three shapes: A half circle, a rectangle, and a triangle.

Calculate the area of each and add them up.

Circle:

The diameter is 4 feet so the radius is 2 feet.

Rectangle:

The length is 4 feet and the width is 3 feet.

Triangle:

The base is 4 feet and the hypotenuse is 5 feet. We can use the Pythagorean Theorem to find
the height.

The total area is the sum:

2x³ -2x + 4 divided by x - 3

First, factor out the greatest common factor, which is 4:

Now, find two integers whose product is 6 • (-2) = !12 and whose sum is 1.

Perform the indicated operations and simplify:

Factor each denominator and form the LCD:

Now, convert each given fraction into an equivalent fraction but with the LCD in the denominator:

We need to see if the numerator can be factored. If it can, we may be able to reduce.

Find two integers whose product is

(-2)(-3) = 6 and whose sum is –4. Whole number pairs
whose product is 6 are 1 • 6 and 2 • 3. We cannot add or subtract any pair of factors to get -4 so
we cannot factor the numerator using integers. Thus, we cannot reduce the fraction .

Solve:

Clear the fractions by multiplying each term by the LCD of all the terms. Then, solve as usual.

Simplify completely:

Follow the order of operations for simplifying arithmetic expressions:

Step 1 Simplify expressions inside grouping symbols, which include parentheses ( ), brackets [ ],
the fraction bar → , absolute value bars , and radicals .

Step 2 Simplify exponents, square roots, and absolute values.

Step 3 Simplify multiplication and division, working left to right.

Step 4 Simplify addition and subtraction, working left to right.

A store sells peanuts for $1.20 per pound and cashews for $3.40 per pound. How many pounds of
peanuts should be mixed with 20 pounds of cashews so that the mixture should sell for $2.00 per
pound? Be sure to define your variables, clearly write the equation, and be careful solving it! Using
our 9 step process would be a really good idea.

1. Read the problem several times carefully until you fully understand it.

2. Draw a diagram if appropriate.

3. Identify any formulas you might need (e.g., area, perimeter, simple interest).

4. Assign a variable to represent what you are looking for.

x = number of pounds of peanuts

5. Express any other unknown quantities in terms of your variable .

20 + x = # pounds of mix

6. Write an equation that models a relationship between your expressions.

We have a relationship between the values of the nuts:

Value of peanuts +Value of cashews =Value of nuts

7. Solve the equation.

8. Write the final answer, including units.

35 pounds

9. Check the answer with the facts in the problem.

The value of 35 pounds of peanuts is 35 • 1.20 = $42.00

The value of 20 pounds of cashews is 20 • 3.40 = $68.00

The value of the 35 + 20 = 55 pounds of mixture is 55 • $2.00 = $110.00

$42.00 + $68.00 = $110.00.