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Question:

Solve: \((-3)^3\)

A −27

explanation

Remember the basic rules of exponents:
\(n^3 = n \times n \times n\)
\((-3)^3 = (-3) \times (-3) \times (-3)\)
When you multiply a negative and a negative you get a positive:
\(= 9 \times (-3)\)
When you multiply a negative and a positive you get a negative: = −27

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Which number sentence is true?

0.006262 < 0.062

The more zeroes to the right of the decimal point, the smaller the number.

A scoutmaster is preparing his troop for their annual fishing expedition. He surveys each of his scouts to find out how many fishing poles they own. What is the mode of this data set?

0

The mode of the data is the number that appears the most often. In this case the largest number of scouts (7) own 0 fishing poles.

What angle is complementary to 47 degrees?

43 degrees

Two angles are complementary if they add up to 90 degrees. This means that the complementary angle to 47 degrees is equal to 90-47 = 43 degrees.

If (3.2 + 3.3 +3.5)w = w, then what is the value of w?

0

First add up the three numbers that are in parentheses:
10w=w
10w=w will only be true when w=0.

(x+4)(x+4) =

\(x^2 + 8x + 16\)

Use the FOIL method (First, Outside, Inside, Last) to solve. \(x^2 + 4x + 4x + 16 = x^2 + 8x + 16\)

If one plant requires 2 liters of water each day, how many liters are required to water the plant for 13 days?

26 liters

To calculate this value, multiply the number of liters the plant needs each day (2) by the number of days it must be watered (13): \(2 \times 13 = 26\) liters

Solve for x: \(x^2+10x+9=0\)

-1 or -9

Factor the quadratic equation: \(x^2+10x+9=0\)
\((x+1)(x+9)=0\)
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x + 9) must equal zero:
If (x + 1) = 0, x must equal -1
If (x + 9) = 0, x must equal -9
So the solution is that x = -1 or -9.

What is the perimeter of the shape seen in the figure?

70 cm

The angles in the figure tell you that the triangle must be equilateral (All of corners of the triangle is 60 degree (150 - 90 = 60)). That means all three sides of the triangle are 10 cm. This also means the base of the figure is 10 cm + 6 cm = 16 cm. The left side is 14 cm, adding up the values given on the right side. Thus, the total perimeter is 10 cm + 10 cm + 14 cm + 16 cm + 6 cm + 6 cm + 8 cm, which is 70 cm total.

Calculate the area of the trapezoid in the figure in square feet.

6.5

The area of a trapezoid is equal to \([ \frac{\mathrm{(b_1 + b_2)h} }{\mathrm{2} }]\). For this trapezoid, that is \(\frac{\mathrm{(2+4.5) \times 2} }{\mathrm{2} }\) = 6.5 square feet.

If XY=YZ and angle Y measures 90 degrees in the figure above, which of the following CANNOT be concluded?

XZ

Here we are looking for the choice that is NOT true. Since the triangle is isosceles (XY=YZ), then a=b=45. This means that a+b=90.
For all right triangles, the Pythagorean Theorem applies.
It is NOT true that XZ

Simplify: \(x^6 \times x^5\)

\(x^{11}\)

Recall that the multiplication of terms sharing the same base can be simplified by adding the exponents:
\(x^a + x^b = x^{(a+b)} \)
If this rule is forgotten, you can quickly derive it by considering the simple case of \(2^1 2^2\) , which can be rewritten as \(2 \times 2 \times 2\), or \(2^3\). The expression in this case, then, can be simplified as: \(x^6 \times x^5 = x^{(6+5)} = x^{11}\)

The circumference of a circle is 20 cm. What is the approximate radius of the circle?

3.2 cm

The formula for the circumference of a circle is \(C=2 \pi r\). Plug in the given circumference and solve for the radius.
\(C=2 \pi r\)
\(20=2 \pi r\)
\(10= \pi r\)
Use 3.14 as an approximate value for π and divide to solve. Round to the nearest tenth. r = 3.2

When two lines intersect, adjacent angles are ____ (they add up to 180°) and angles across from each other are ____ (they're equal).

supplementary, vertical

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from each other are vertical (they're equal).

Which of the following numbers is the greatest?

\(\frac{\mathrm{2} }{\mathrm{3} }\)

To determine which value is the greatest, convert the fractions to decimals and compare each value. The fraction \(\frac{\mathrm{2} }{\mathrm{3} }\) is equivalent to \(2 \div 3\) or 0.66; the fraction \(\frac{\mathrm{13} }{\mathrm{22} }\) evaluates to 0.59.

A square has one side with length 4.5 feet. The area of the square is ____.

20.25 square feet

Squares have 4 sides that are the same length, and the area of a square is equal to its side squared, in this case 4.5*4.5, which is equal to 20.25.