Pop Quiz Practice Test: Boost Your Skills

To solve the equation, subtract 3 from both sides to obtain 2x = 8, and then divide by 2, giving x = 4. This method isolates x with simple inverse operations.

Following the order of operations, multiplication comes before subtraction. Calculating 4 Ã - 2 gives 8, then 7 - 8 results in -1, which is the correct answer.

The area of a rectangle is calculated by multiplying its length by its width. Multiplying 8 by 3 gives 24 cm², which is the correct area.

Combining like terms involves subtracting the coefficients of x. Subtracting 2 from 5 yields 3x, which is the simplified form.

In the slope-intercept form y = mx + b, the slope is indicated by m. Since the equation is y = 3x + 2, the slope is 3.

Dividing both sides by 3 simplifies the equation to x - 2 = 3, and adding 2 to both sides gives x = 5. This method efficiently isolates the variable.

The distributive property requires multiplying the term outside the parentheses with each term inside. Multiplying 2 by a and 2 by 4 gives 2a + 8, which is the correct application.

The slope is determined by the formula (y2 - y1) / (x2 - x1). Using the points (2, 3) and (6, 11), the slope is (11 - 3)/(6 - 2) which simplifies to 8/4 = 2.

First, distribute the multiplication in both expressions to get 12x - 8 and 10x + 2. Then, subtracting the second expression from the first results in 2x - 10.

Multiplying both sides by the reciprocal, 3/2, isolates x and gives x = 8 Ã - (3/2) which simplifies to 12. This straightforward calculation produces the correct value of x.

A quadratic equation must include an x² term as its highest degree. Option B fits this definition, making it the only quadratic equation among the choices.

By adding 4 to both sides, the equation becomes x² = 4. Taking the square root of both sides gives two solutions: x = 2 and x = -2.

When two points share the same y-coordinate, the distance between them is the absolute difference of their x-coordinates. Calculating |1 - (-3)| gives 4.

Substituting x = 4 into the function f(x) = 2x + 3 gives f(4) = 2(4) + 3 = 8 + 3, which equals 11. This confirms that the correct value is 11.

The associative property states that the way numbers are grouped in addition does not change the sum. Changing the grouping from a + (b + c) to (a + b) + c has no effect on the final result.

Using the quadratic formula, x = (8 ± √(64 - 48))/(4) simplifies to x = (8 ± 4)/4, which leads to x = 3 and x = 1. Both solutions satisfy the original equation.

The vertex is found using h = -b/(2a), which for this equation gives h = 3. Substituting h back into the function gives k = -1, so the vertex is (3, -1).

The logarithm logâ‚‚(8) asks for the power to which 2 must be raised to produce 8. Since 2 raised to the 3rd power equals 8, the value of x is 3.

By expressing y from the equation x - y = 1 as y = x - 1 and substituting into 2x + y = 7, you can solve for x to get x = 8/3. Substituting back gives y = 5/3, which is the unique solution for the system.

This triangle satisfies the Pythagorean theorem since 7² + 24² equals 25². Therefore, it is a right triangle, which is the correct classification.