Algebra 1 Practice EOC

• V = d - m

• V = dm

Answer explanation

To find the volume (V) from the density (d) and mass (m), rearrange the equation d = m/V. Multiplying both sides by V gives dV = m, then dividing by d results in V = m/d. Thus, the correct equation is V = m/d.

Emilio is given the triangle shown below. Emilio represents the perimeter of the triangle with the equation (5w - 13) + (2w + 6) + 2(5w + 15) = P, where P is the perimeter of the triangle. Which equation is correctly solved for w?

Answer explanation

To solve for w, first simplify the perimeter equation: (5w - 13) + (2w + 6) + 2(5w + 15) = P. This simplifies to 17w + 7 = P. Rearranging gives w = (P - 7)/17. The correct choice is w = (P - 23)/17.

Kaylee is building a rectangular enclosure with an area of 90 square yards. She wants the length of the enclosed area to be 6 yards longer than the width, x. To represent this, she writes the equation x² + 6x = 90. She then completes the square to help solve her equation for x. Which equation is equivalent to Kaylee’s equation after she completes the square?

• (x + 3)² = 93

• (x + 3)² = 99

• (x + 6)² = 96

• (x + 6)² = 126

Answer explanation

To complete the square for the equation x² + 6x = 90, we add (6/2)² = 9 to both sides, resulting in (x + 3)² = 99. Thus, the correct choice is (x + 3)² = 99.

Amil is given the equation shown. x² + 14x + 37 = 0. He completes the square and rewrites the given equation. Which equation is equivalent to the given equation?

• (x + 7)² - 12 = 0

• (x - 7)² - 12 = 0

• (x + 7)² + 12 = 0

• (x - 7)²+ 12 = 0

Answer explanation

To complete the square for the equation x² + 14x + 37 = 0, we rewrite it as (x + 7)² = 0 by adding and subtracting 49. Thus, the equivalent equation is (x + 7)² = 0.

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Answer explanation

The inequality y > -2/3x + 2 represents a region above the line y = -2/3x + 2. The correct graph will show a dashed line (indicating 'greater than') and shade the area above this line.

Which graph represents the solutions to 5x – 2y ≥ 10?

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Answer explanation

To solve 5x – 2y ≥ 10, rearrange to y ≤ (5/2)x - 5. Graph A correctly shows the shaded area below the line y = (5/2)x - 5, indicating all solutions satisfying the inequality.

Mark hits a tennis ball into the air. He uses the equation shown to approximate the height, h, in feet, of the ball t seconds after he hits it. h = -16t² + 88t + 4 What does the 4 represent in Mark’s equation?

• The ball was in the air for a total of 4 seconds.

• The ball landed 4 feet away from where Mark hit it.

• The ball was 4 feet above the ground when Mark hit it.

• The ball reached its maximum height 4 seconds after Mark hit it.

Answer explanation

In the equation h = -16t² + 88t + 4, the constant 4 represents the initial height of the ball when Mark hits it, meaning the ball was 4 feet above the ground at that moment.

A website tracks the number of users it has at the end of each of its first 30 days since going online. The equation y = 15(1.03)^x shows the relationship between the number of days since the website went online, x, and the number of users it has, y. What does 1.03 represent in the equation?

• The number of users increases by 3 each day.

• The number of users increases by 103 each day.

• Each day after the first, the number of users is 3% greater than it was the day before.

• Each day after the first, the number of users is 103% greater than it was the day before.

Answer explanation

In the equation, 1.03 indicates that each day, the number of users increases by 3% compared to the previous day. This means the user count grows by a factor of 1.03 daily.

A quadratic expression is shown. x² - 100 Which statement best explains why the quadratic expression can be rewritten as (x + c)(x - c) for some integer value of c?

• The expression is quadratic.

• The quadratic expression is a difference of squares.

• The quadratic expression does not have a linear term.

• The coefficient of the x² term in the quadratic expression is 1.

Answer explanation

The quadratic expression x² - 100 can be rewritten as (x + c)(x - c) because it is a difference of squares, where c is 10. This form arises from the identity a² - b² = (a + b)(a - b).

Answer explanation

The expression x⁴ + 6x² + 9 can be rewritten as (x² + 3)². However, it is also equivalent to (x + 3)⁴ when expanded. Thus, the correct choice is (x + 3)⁴.