NJSLA Practice Quiz Essentials

Since the denominators are the same, you add the numerators directly. 3/4 plus 1/4 gives (3+1)/4 which simplifies to 1.

Subtracting 7 from both sides of the equation gives x = 12 - 7. Therefore, x equals 5.

The area of a rectangle is found by multiplying the length by the width. Multiplying 8 by 3 gives 24, which is the area.

Raising 2 to the power of 3 means multiplying 2 by itself three times. Thus, 2 Ă - 2 Ă - 2 equals 8.

By substituting a = 4 into the equation, you get 4 + b = 10. Solving for b yields b = 6.

Distribute 3 to obtain 3x - 6 = 9. Adding 6 to both sides and dividing by 3 yields x = 5.

First, distribute the 2 to get 6x + 8, then subtract 5x to simplify the expression to x + 8. This shows the proper use of the distributive property.

Multiply both sides by 3 to eliminate the fraction giving 2y = 24, then divide by 2 to find y = 12. This problem requires simple manipulation of an equation.

The slope is calculated by the change in y over the change in x: (11 - 3) divided by (6 - 2) equals 8/4, which simplifies to 2. This represents the steepness of the line.

Let the width be w so that the length is 2w. The perimeter formula 2(w + 2w) equals 6w; setting 6w = 36 leads to w = 6. This problem combines algebra with geometry.

Subtract 3 from both sides of the equation to obtain 0.5x = 4, and then multiply by 2 to solve for x, resulting in x = 8. This demonstrates basic equation solving.

Calculating 3/5 of 20 involves multiplying 20 by 3/5, which equals 12. This tests the understanding of fractions applied to real-world situations.

The numerator is a difference of squares and can be factored as (x - 3)(x + 3). Canceling the (x - 3) term leaves x + 3 as the simplified expression.

When the data is ordered from smallest to largest (2, 3, 5, 7, 9), the middle value, or median, is 5. This is a basic concept from statistics.

To find 15% of 200, multiply 200 by 0.15 to get 30. This question applies percentage calculations in a straightforward manner.

Multiplying the entire equation by 12 clears the fractions, resulting in 8x - 3 = 60. Adding 3 and then dividing by 8 gives x = 63/8, which is approximately 7.875.

Substitute x = 3 into the function to get 2(3)² - 3(3) + 1, which simplifies to 18 - 9 + 1 = 10. This is a typical evaluation of a quadratic function.

Using the area formula A = πr², set πr² equal to 49π. Dividing both sides by π yields r² = 49, so the radius r is 7.

First, solve x - y = 1 to get x = y + 1 and substitute into 2(y + 1) + 3y = 12. This results in 5y + 2 = 12, so y = 2 and x = 3, giving the ordered pair (3, 2).

Set the function equal to 19 by writing 3x + 4 = 19. Subtracting 4 from both sides gives 3x = 15, so x = 5. This tests solving a simple linear equation using function evaluation.