Which expressions are equivalent to $$\frac{1}{2^6}$$ ?

a. $$2^{-5} \cdot 2^{-1}$$ b. $$2^{-2} \cdot 2^{-4}$$ c. $$2^{1} \cdot 2^{5}$$ d. $$2^{1} \cdot 2^{6}$$ e. $$2^{2} \cdot 2^{-8}$$ f. $$2^{2} \cdot 2^{3}$$

For each expression shown, determine an equivalent expression written as a common factor multiplied by the sum of two algebraic expressions: a. $$125x^2 + 15x$$ b. $$-24 - 36y^3$$ c. $$\frac{3}{4}xy - \frac{1}{4}x^2y^3$$

Factor each expression to find the common factor and the sum of two expressions.

Solve and graph the inequality -225 \leq 320 - 0.5x.

Solve the inequality and represent the solution on the number line.

For each equation, state whether there is no solution, one solution, or infinitely many solutions. Equations: $$\frac{1}{3}x - 6 = \frac{1}{3}(x - 3) - 1$$ , $$2x + 7 = -2x + 7$$ , $$0.8x + 1.4 = 0.8x$$

Determine the number of solutions for each equation and provide reasoning.

Solve for x: a. -3.5(10x - 2) = -176.75 b. 15(2x - 10) + 4x = -3(15x + 4)

Find the value of x for each equation.

The volume of a large cube is 125 cubic inches. The volume of a small cube is 27 cubic inches. What is the difference between the length of one side of the large cube and the length of one side of the small cube?

Calculate the side lengths of both cubes and find the difference.

The measure of angle 1 is 12 more than the measure of angle 2. What is the degree measure of angle 3?

Use the given information to find the measure of angle 3.

In triangle LMN, the measure of angle L is 50° and the measure of angle M is 70°. What is the measure of the exterior angle to angle N?

Calculate the exterior angle using the given angle measures.

One measure of an angle in a triangle is 96°. The other two angle measures are represented by 2x and x + 12. Determine the other two degree measures for the missing angles.

Solve for x and find the measures of the other two angles.

Find the number of degrees for the sum of the interior angles of a regular 12-sided figure.

Use the formula for the sum of interior angles of a polygon to find the answer.

Given the two triangles, are they similar?

Yes, the triangles are similar by the AA (Angle-Angle) similarity criterion.

The bottom of a ladder must be placed 3 feet from a wall. The ladder is 10 feet long. The height above the ground where the ladder touches the wall is 9.54 feet.

The ladder touches the wall 9.54 feet above the ground.

Using the figure, the length of side AB in meters is 8 meters.

The length of side AB is 8 meters.

On a coordinate plane, the distance between the points (-3, 4) and (0, -3) is 7.62 units.

The distance between the points is 7.62 units.

Using the Pythagorean Theorem, the distance from point (8, -6) to the origin is 10 units.

The distance from the point to the origin is 10 units.

The side lengths of a triangle cannot be 2, 4, and 8 because they do not satisfy the triangle inequality theorem.

No, these side lengths cannot form a triangle because they do not satisfy the triangle inequality theorem.

John can prove to Bryan that the triangle with side lengths of 5, 12, and 13 is a right triangle using the Pythagorean Theorem: $$5^2 + 12^2 = 13^2$$ .

John can use the Pythagorean Theorem: $$5^2 + 12^2 = 13^2$$ , which confirms it is a right triangle.

The theoretical probability of choosing one red marble and one green marble from a bag with 3 red, 1 blue, and 2 green marbles is $$\frac{1}{6}$$ .

The probability is $$\frac{1}{6}$$ .

The sample space for a quiz containing 2 multiple-choice questions with five possible answers each is 25 possible outcomes.

The sample space is 25 possible outcomes.

The probability the student guesses wrong answers for both questions is $$\frac{16}{25}$$ .

The probability is $$\frac{16}{25}$$ .

The probability the student guesses the correct answers for both questions is $$\frac{1}{25}$$ .

The probability is $$\frac{1}{25}$$ .

The sample space for flipping a round, flat game piece with yellow on one side and white on the other side four times includes 16 possible outcomes.

The sample space includes 16 possible outcomes.

The probability of guessing at least one correct answer is calculated by considering all possible outcomes.

Calculate the probability of guessing at least one correct answer by considering all possible outcomes.

Joanna is spinning a spinner twice with 4 equal sections numbered 1 to 4. The sample space consists of all possible pairs of numbers from 1 to 4.

The sample space consists of all possible pairs of numbers from 1 to 4, such as (1,1), (1,2), ..., (4,4).

A student is making trail mix for each serving size in the table given. The relationship is linear if the difference between servings is constant.

Check if the difference between servings is constant. If so, the relationship is linear, and the constant rate of change is the difference.

A relationship is proportional if the ratio between the quantities is constant.

The number of cups of nuts and fruit in a serving size of zero can be determined by extrapolating the pattern in the table.

Extrapolate the pattern in the table to determine the number of cups at zero serving size.

A proportional relationship is represented by a straight line through the origin.

Alexia earns $14.75 an hour as a hostess at a local restaurant and an additional $30 in tips each night from take-out orders. This is not proportional due to the additional fixed amount.

This is not proportional because of the additional fixed amount ($30) added to the hourly earnings.

The circumference of a circle is directly proportional to its diameter, expressed by the equation C = πd.

This is a proportional relationship because the circumference is directly proportional to the diameter.

The slope of a linear relationship can be determined using the formula (y_2 - y_1) / (x_2 - x_1) from the given table values.

Calculate the slope using the formula (y_2 - y_1) / (x_2 - x_1) from the given table values.

Jack charges $1.75 for every 2 gallons of water a pail holds, plus a $2 service fee. Identify the slope of Jack's relationship and determine if it is proportional.

Identify the slope of Jack's relationship and write an equation. Determine if it is proportional.

The slope of Jill's graph can be analyzed to find the slope and determine if the line passes through the origin for proportionality.

Analyze the graph to find the slope and determine if the line passes through the origin for proportionality.

A table of values for Jack's prices can be created and plotted on the graph with Jill's prices.

Create a table of values for Jack's prices and plot them on the graph with Jill's prices.

To determine the better deal between Jack and Jill, compare the total costs for the same amount of water.

Compare the total costs for the same amount of water to determine the better deal.

The equation representing the graph can be written using the slope-intercept form.

Use the slope-intercept form y = mx + b to write the equation based on the graph.

Graph the equation in slope-intercept form.

Graph $y = x - 2$ on the coordinate plane.

Supplies for the car wash cost $25. The booster club charges $10 per car.

Graph the relationship between the amount of money earned and the number of cars washed.

Mathematics Concepts and Calculations Flashcards

Student preview

68 questions

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1.

FLASHCARD QUESTION

Front

Back

Approximate locations to the nearest hundredth.

2.

FLASHCARD QUESTION

Front

Back

Use the chart to determine which is greater.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Estimate the distance in kilometers to Proxima Centauri, the closest star to Earth, as an integer power of 10.

Back

39,900,000,000,000 km

5.

FLASHCARD QUESTION

Front

Express the Bohr radius of a hydrogen atom, 0.0000000000529, in scientific notation.

Back

6.

FLASHCARD QUESTION

Front

How many times heavier is a blue whale than an elephant in pounds?

Back

7.

FLASHCARD QUESTION

Front

How many gallons of water does the Amazon River release into the ocean in one year?

Back

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