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Question:

Factor: 4y(3x + 2) − 2(3x + 2)

A (4y − 2)(3x + 2)

explanation

Any part of an expression that is common to every term in the expression can be factored out. In this case, (3x + 2) is a common term and can be factored out from both parts of the expression:
4y(3x + 2) − 2(3x + 2)
= (3x + 2)(4y − 2) .
Notice that distributing (3x + 2) through [4y − 2] yields the original expression; this verifies the answer.

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What is the value of x in the rhombus seen in the figure?

145 degrees

A rhombus has two pairs of equal angles that are supplementary. This means that this rhombus must have two 35 degree angles, and the remaining two angles must be supplementary to 35 degrees. Thus, the angle of x is 180 = 35 = 145 degrees.

Which of the following means 3n + 7 = 16?

7 more than 3 times a number is 16

The expression 3n means 3 times n. The addition sign before the 7 indicates the phrase more than.

15y -20 = 110 y = ?

8.66

First, we add 20 to the right side to arrive at 15y = 130. Then, we divide both sides by 15 to arrive at \(y = 130 \div 15 = 8.66\)

The surface area of a rectangular prism with sides 3 x 5 x 5 inches is:

110 square inches

The area of each of the three unique sides are 15, 15, and 25. We need to double this area because each side is mirrored in a rectangular solid. This gives us a total surface area of 110 square inches.

If 3(x−4)=18, what is the value of x?

10

Begin by dividing both sides by 3 to open the parenthesis:
x−4=6
Add 4 to both sides to find x:
x=10.

What is the distance between the points (2, 4) and (-1, 8)?

5

To find the distance, we use pythagorean theorem. First calculate the distances in terms of x and y. The x difference is 3 and the y difference is 4. Then, \(\sqrt{ 3^2+ 4^2 }\) distance, which is 5.

A medium pizza has a diameter of 14 inches. What is its circumference?

14π

The circumference of a circle is equal to the diameter multiplied by π.

Which of the following angles is obtuse?

130 degrees

An obtuse angle is one which is greater than 90 degrees. Acute angles are less than 90 degrees, and right angles are exactly equal to 90 degrees.

How much water could a container hold that measures 8cm by 12cm by 10cm?

960 mL

The volume of the container is equal to the length times the width times the height. \(V=lwh=8 \times 12 \times 10 =960\) Cubic centimeters are equal to mL, so a container with a volume of 960 cc can hold 960 mL.

A trapezoid is a quadrilateral with one set of __________ sides.

parallel

A trapezoid is a quadrilateral with one set of parallel sides.

The dimensions of this rectangular parallelepiped are height h = 8, length l = 4, and width w= 6. What is the volume?

192

The volume of a rectangular parallelepiped is height x length x width: v = hlw = 8 * 4 * 6 = 192.

Which of the following statements about a parallelogram is not true?

opposite sides and adjacent angles are equal

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

\(6 \frac{\mathrm{1} }{\mathrm{3} } + 5\frac{\mathrm{3} }{\mathrm{10} } \)=

\(6 \frac{\mathrm{10} }{\mathrm{30} } + 5\frac{\mathrm{9} }{\mathrm{30} } = 11\frac{\mathrm{19} }{\mathrm{30} }\)

You must convert both fractions to thirtieths before adding. Thus, with the fractions converted the numbers are \(6 \frac{\mathrm{10} }{\mathrm{30} } + 5\frac{\mathrm{9} }{\mathrm{30} } = 11\frac{\mathrm{19} }{\mathrm{30} }\)

In the figure below, line A is parallel to line B. What is the value of angle x?

140 degrees

First, we find the supplementary angle to 40 degrees, which is 140 degrees. That tells us the angle opposite is 140 degrees. Because they are two parallel lines, then the mirrored angle must also be 140 degrees.