Algebra II

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Algebra 2 › Algebra II

Questions 1 - 10
1

Divide the following fractions:

Explanation

In order to solve this, we will need to evaluate term by term. First rewrite the complex fractions by using a division sign.

Change the sign from a division to multiplication and take the reciprocal of the second term.

Evaluate the second complex fraction.

This means that:

The answer is:

2

Solve for .

Explanation

To solve for the variable , isolate the variable on one side of the equation with all other constants on the other side. To accomplish this perform the opposite operation to manipulate the equation.

First cross multiply.

Next, divide by four on both sides.

3

Solve

Explanation

First we rewrite the equation in exponential form:

Now we take the cube root of :

4

Divide the fractions:

Explanation

Change the division sign in the expression and take the reciprocal of the second term.

Reduce the three and nine in the numerator and denominator.

The fractions become:

The answer is:

5

Solve the system of equations.

None of the other answers are correct.

Explanation

Isolate in the first equation.

Plug into the second equation to solve for .

Plug into the first equation to solve for .

Now we have both the and values and can express them as a point: .

6

Add:

Explanation

Determine the least common denominator in order to add the numerator.

Each denominator shares an term. The least common denominator is since it is divisible by each coefficient of the denominator.

Convert the fractions.

Simplify the top and bottom.

The answer is:

7

Simplify the expression:

Explanation

Factor the second denominator, then simplify:

8

Evaluate:

Explanation

When dealing with exponents, we convert as such: . Therefore, .

9

Solve.

Explanation

When adding and subtracting radicals, make the sure radicand or inside the square root are the same.

If they are the same, just add the numbers in front of the radical.

Since they are not the same, the answer is just the problem stated.

10

Multiply the fractions:

Explanation

When multiplying fractions, multiply the numbers on the top together and the numbers on the bottom together. Then simplify accordingly.

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