Knowledge Check: Chapters 7–11

Simplify $\sqrt{144}$ to show that it is a whole number, and therefore rational.

Write $-5$ as the ratio of two integers.

Simplify $\sqrt{49}$ to show that it is a whole number, and therefore rational.

Rewrite the expression $x \cdot 14$ using the commutative property. Enter the resulting expression.

Rewrite the expression $(8 \cdot 2) \cdot 5$ using the associative property. Enter the resulting expression.

For the number $\tfrac{2}{5}$, find the additive inverse.

For the number $\tfrac{2}{5}$, find the multiplicative inverse.

Simplify using the distributive property: $6(5x - 4)$.

Simplify using the distributive property: $\tfrac{1}{4}(8a + 12)$.

Simplify using the distributive property: $8(6p - 1) + 2(9p + 3)$.

Find the additive inverse of $19.4$.

Simplify: $0/8$.

Simplify: $0 \div \tfrac{2}{3}$.

One cup of milk contains 276 milligrams of calcium. Convert this to grams. (1 milligram = 0.001 gram)

Janice ran 15 kilometers. Convert this distance to miles. Round to the nearest hundredth of a mile. (1 mile = 1.61 kilometers)

Use the formula $F = \tfrac{9}{5}C + 32$ to convert $35°C$ to degrees Fahrenheit.

Solve the equation using the Subtraction Property of Equality: $x + 7 = 19$.

Solve the equation: $n - 12 = 32$.

Translate the sentence into an algebraic equation and then solve it: The sum of $-6$ and $m$ is 25.

Translate the sentence into an algebraic equation and then solve it: The difference of twice $x$ and 4 is 16.

Solve the equation: $9c = 144$.

Solve the equation: $\tfrac{2}{3}x = 6$.

Solve the equation: $-8x - 15 + 9x - 1 = -21$.

Solve the equation: $10y = -5y + 60$.

Solve the equation: $-(d + 9) = 23$.

Solve the equation: $2(6x + 5) - 8 = -22$.

Solve the equation: $\tfrac{1}{4}p + \tfrac{1}{3} = \tfrac{1}{2}$.

Solve the equation by clearing the fractions: $\tfrac{2}{5}n - \tfrac{1}{10} = \tfrac{7}{10}$.

Solve the equation by clearing the decimals: $0.8x - 0.3 = 0.7x + 0.2$.

The sum of 13 and twice a number is −19. Find the number.

The sum of a number and three is forty-one. Find the number.

One number is nine less than another. Their sum is twenty-seven. Find the smaller number.

One number is nine less than another. Their sum is twenty-seven. Find the larger number.

Bonita has $2.95 in dimes and quarters in her pocket. If she has 5 more dimes than quarters, find the number of quarters.

Bonita has $2.95 in dimes and quarters in her pocket. If she has 5 more dimes than quarters, find the number of dimes.

Paulette has $140 in $5 and $10 bills. The number of $10 bills is one less than twice the number of $5 bills. Find the number of $5 bills.

Paulette has $140 in $5 and $10 bills. The number of $10 bills is one less than twice the number of $5 bills. Find the number of $10 bills.

Find the complement of a 52° angle.

The perimeter of an equilateral triangle is 145 feet. Find the length of each side. Round to the nearest tenth.

A right triangle has legs of length 24 and 10. Find the length of the hypotenuse.

A baseball diamond is shaped like a square with sides 90 feet long. How far is it from home plate to second base (the diagonal)? Round to the nearest tenth.

A triangular poster has base 80 centimeters and height 55 centimeters. Find the area of the poster.

Find the area of a triangle with base 18 inches and height 15 inches.

The height of a trapezoid is 8 feet and the bases are 11 and 14 feet. What is the area?

A circular pool has diameter 90 inches. What is its circumference? Round to the nearest tenth.

A circular mosaic has radius 3 meters. Find the circumference of the mosaic. Round to the nearest hundredth.

A circular mosaic has radius 3 meters. Find the area of the mosaic. Round to the nearest hundredth.

Find the diameter of a circle with circumference 150.72 inches.

Find the volume of a rectangular room with width 12 feet, length 15 feet, and height 8 feet.

A rectangular solid has length 14 centimeters, width 4.5 centimeters, and height 10 centimeters. Find the volume.

A rectangular solid has length 14 centimeters, width 4.5 centimeters, and height 10 centimeters. Find the surface area.

A traffic cone has height 75 centimeters. The radius of the base is 20 centimeters. Find the volume of the cone. Round to the nearest tenth.

The Catalina Express takes $1\tfrac{1}{2}$ hours to travel from Long Beach to Catalina Island, a distance of 22 miles. To the nearest tenth, what is the speed of the boat (in miles per hour)?

Solve the formula $A = \tfrac{1}{2}bh$ for $h$, when $A = 1716$ and $b = 66$.

Solve the formula $P = 2L + 2W$ for $W$.

For the polynomial $8y^4 - 3y^2 + 1$: how many terms does it have?

For the polynomial $8y^4 - 3y^2 + 1$: what is its degree?

Simplify: $(10x^2 - 3x + 5) - (4x^2 - 6)$

Simplify: $n \cdot n^4$

Simplify: $(8xy^3)(-6x^4y^6)$

Multiply: $(s + 8)(s + 9)$

Multiply: $(11a - 6)(5a - 1)$

Multiply: $(4a + 9b)(6a - 5b)$

Simplify: $\left(\tfrac{x^3 \cdot x^9}{x^5}\right)^2$

Simplify: $\tfrac{24r^3s}{6r^2s^7}$

Simplify: $(15xy^3 - 35x^2y) \div 5xy$

Simplify: $(2y)^{-3}$

Simplify: $x^4 / x^{-5}$

Convert $5.25 \times 10^{-4}$ to decimal form.

Simplify, and write your answer in decimal form: $(9 \times 10^4) / (3 \times 10^{-1})$

Factor the greatest common factor from the polynomial: $-6x^2 - 30x$

Factor the greatest common factor from the polynomial: $16u - 24$

Factor the greatest common factor from the polynomial: $6p^2 + 6p$

Complete the table of solutions to $y = 4x - 1$: what is $y$ when $x = 1$?

Complete the table of solutions to $x + 2y = 5$: what is $x$ when $y = 0$?

To check whether $(1, 3)$ is a solution to $x + 4y = 12$, substitute $x = 1$ and $y = 3$ into the left side. What value does $x + 4y$ equal? (Since it does not equal 12, $(1, 3)$ is not a solution.)

Complete the table of solutions to $4x + y = 8$: what is $y$ when $x = 2$?

Complete the table of solutions to $4x + y = 8$: what is $y$ when $x = 3$?

Find the $x$-intercept and $y$-intercept of $x - y = -1$. Enter the $x$-intercept as an ordered pair.

Find the $x$-intercept and $y$-intercept of $y = 3x$. Enter the $y$-intercept as an ordered pair.

Find the $x$-intercept and $y$-intercept of the equation $3x - y = 6$. Enter the $x$-intercept as an ordered pair.

Find the slope of the line graphed above, which passes through $(-4, 6)$ and $(2, -6)$.

Find the slope of the line $y = 2$.

A bicycle route climbs 20 feet for 1,000 feet of horizontal distance. What is the slope of the route?