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Questions 1 - 10

Simplify:

$\left (2x^{-4} \right )^{-2}$

$\frac{x^{8}}{4}$

$\frac{1}{4x^{8}}$

$\frac{x^{8}}{256}$

$\frac{1}{256x^{8}}$

Explanation

$\left (2x^{-4} \right )^{-2}$

$=\left ( \frac{2}{x^{4}} \right )^{-2}$

$=\left ( \frac{x^{4}}{2} \right )^{2}$

$= \frac{\left (x^{4}\right )^{2}}{2^{2}}$

$= \frac{ x^{4 \cdot 2} }{2^{2}}$

$= \frac{ x^{8} }{4}$

If a circle has an area of , what is its radius?

Explanation

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: $A=\pi \cdot r^2$ , where r is the radius.

This means that we can directly solve for radius through substituting in the value for the area.

$64.8= \pi \cdot r^2$

$\frac{64.8}{\pi}= r^2$

Remember that you need to take the square root in order to solve for r.

Therefore, the radius is

Evaluate:

Do not use a calculator.

Explanation

Add vertically, aligning the decimal points:

$\begin{matrix} ; ;109.10 \ +; \underline{55.67} \ ; ; 164.77 \end{matrix}$

A hexagon has a perimeter of 198cm. Find the length of one side.

$33\text{cm}$

$32\text{cm}$

$29\text{cm}$

$31\text{cm}$

$28\text{cm}$

Explanation

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is

where a is the length of any side. To find the length of one side, we solve for a.

Now, we know the perimeter of the hexagon is 198cm. So, we can substitute and solve for a. We get

$198\text{cm} = 6a$

$\frac{198\text{cm}}{6} = \frac{6a}{6}$

$33\text{cm} = a$

$a = 33\text{cm}$

Therefore, the length of one side of the hexagon is 33cm.

What is the circumference of a circle with an area of $12\pi$ ?

$4\pi\sqrt{3}$

$2\pi\sqrt{3}$

$\pi\sqrt{3}$

$2\sqrt{3}$

$6\pi\sqrt{3}$

Explanation

For this question, you need to first use the area to calculate your circle's radius. From that, you can then calculate the circumference of the circle. Recall that the area of a circle is defined as:

$A=\pi r^2$

For your data, this means:

$12\pi=\pi r^2$

Solving for , you get...

$r=\sqrt{12}=\sqrt{4*3}=2\sqrt{3}$

Now, the circumference of a circle is calculated as:

$C=2\pi r$

For your data, this is:

$C=2\pi*2\sqrt{3}=4\pi\sqrt{3}$

If two angles are complementary, and one angle is measured $\frac{\pi}{3}$ radians, what is the other angle in radians?

$\frac{1}{6}\pi$

$\frac{1}{3}\pi$

$\frac{1}{4}\pi$

$\frac{1}{5}\pi$

$\frac{2}{3}\pi$

Explanation

If the set of angles are complementary, they must add up to $\frac{\pi}{2}$ radians, which is equivalent to 90 degrees.

Subtract $\frac{\pi}{3}$ radians from $\frac{\pi}{2}$ radians.

$\frac{\pi}{2}-\frac{\pi}{3} = \frac{3\pi}{6}-\frac{2\pi}{6}$

The answer is: $\frac{1}{6}\pi$

A rectangle has length 10 inches and width 5 inches. Each dimension is increased by 3 inches. By what percent has the area of the rectangle increased?

Explanation

The area of a rectangle is its length times its width.

Its original area is $10 \times 5 = 50$ square inches; its new area is $13 \times 8 = 104$ square inches. The area has increased by

$\frac{104 - 50}{50 } \times 100 = \frac{54}{50 } \times 100 = 108 %$ .

Determine the area of a circle with a radius of $9\sqrt{2}$ .

$162\pi$

$81\pi$

$\textup{The answer is not given.}$

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (9\sqrt{2})^2=\pi (9\sqrt{2})(9\sqrt{2}) = 81\cdot 2 \pi$

The answer is: $162\pi$

Give the expanded form of the following scientific notation.

Explanation

Give the expanded form of the following scientific notation.

To expand this, we need to move the decimal point. Because our exponent is positive, we will be moving it 7 spaces to the right.

In order to do so, we need to add a couple zeros

$7.9881*10^7\rightarrow 7.9881000*10^7\rightarrow79,881,000$

So, our answer is

In the figure above, $a\parallel b$ . If the measure of $\measuredangle 1=6x^{\circ}$ and $\measuredangle 6=4x^{\circ}$ , what is the measure of $\measuredangle8$ ?

$108^{\circ}$

$122^{\circ}$

$72^{\circ}$

$58^{\circ}$

Explanation

Since we have two parallel lines, we know that $\measuredangle1=\measuredangle4$ since they are opposite angle.

We also know that $\measuredangle 4 \text{ and }\measuredangle 6$ are supplementary because they are consecutive interior angles. Thus, we know that $\measuredangle 1$ is also supplementary to $\measuredangle6$ .