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Questions 1 - 10

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

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

What is the next number in the series?

Explanation

To pattern uses the formula $\small \small x_n=2x_{n-1}+1$ .

$\small x_6=2(31)+1=62+1=63$

Evaluate:

Do not use a calculator.

Explanation

Add vertically, aligning the decimal points:

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

Determine the circumference of a circle with a radius of $\frac{\pi}{4}$ .

$\frac{\pi ^2}{2}$

$\frac{\pi }{2}$

$\frac{\pi}{8}$

$\frac{\pi^2}{8}$

$\frac{1}{2}$

Explanation

Write the formula for the circumference of a circle.

$C=\2\pi r$

Substitute the radius.

$C=\2\pi (\frac{\pi}{4}) = \frac{\pi ^2}{2}$

The answer is: $\frac{\pi ^2}{2}$

The image is not to scale.

If the sum of two angles results in a complementary angle, what is the measure of the unknown angle?

Capture2

$60^{\circ}$

$150^{\circ}$

$30^{\circ}$

$90^{\circ}$

$20^{\circ}$

Explanation

With the provided image, we are asked to solve for the measure of the unknown angle.

Capture2

First, we must understand some information before attempting to solve the problem. The problem provides the information that the two angles summed up result in a complimentary angle. This is another way to say that when we add the measures of the two angles, it will equal $90^{\circ}$ .

This becomes a problem where we solve for a missing variable now. We can call the unknown angle x. We would set this up in equation format accordingly:

Now, we can solve for x.

$x+30{\color{Red} -30}=90{\color{Red} -30}$

$x=60^{\circ}$

Therefore, the unknown angle is $60^{\circ}$ .

What is the radius with a diameter of $\frac{\sqrt3}{2}$ ?

$\frac{\sqrt3}{4}$

$\frac{\sqrt3}{6}$

$\sqrt3$

$\sqrt6$

$\frac{\sqrt6}{4}$

Explanation

The radius is half the diameter.

Multiply the diameter by one-half.

$\frac{\sqrt3}{2} \cdot \frac{1}{2} = \frac{\sqrt3}{4}$

The answer is: $\frac{\sqrt3}{4}$

If two angles are complementary, and one angle is measured degrees, what must be the other angle?

Explanation

Complementary angles sum up to degrees.

Simply subtract the given angle from to determine the expression.

Combine like-terms.

The answer is:

Two angles are complementary if they add up to:

$90^{\circ}$

$180^{\circ}$

$270^{\circ}$

$360^{\circ}$

$45^{\circ}$

Explanation

Two angles are complementary if they add up to $90^{\circ}$ .

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

A square and a circle share a center as shown by the figure below.

If the length of a side of the square is and is half the length of the radius of the circle, to the nearest hundredths place, find the area of the shaded region.

Explanation

In order to find the area of the shaded region, we will need to find the area of the circle then subtract the area of the square from it.

Start by finding the area of the square. Since we know the side length of the square, we can write the following:

$\text{Area of Square}=4^2=16$

Next, we find the area of the circle. Since the question states that the length of a side of the square is half the radius of the circle, the radius of the circle must be . Thus, we can find the area of the circle.