Random Regents Friday

Elijah and Avery are solving a math puzzle. They need to simplify the expression (3x² + 4x - 8) + 2(11 - 5x). Can you help them find the equivalent expression?

• 3x² - x + 5

• 3x² - x + 14

• 3x² - 6x + 14

• 3x² + 14x + 14

Answer explanation

To simplify (3x² + 4x - 8) + 2(11 - 5x), first distribute: 2(11 - 5x) = 22 - 10x. Then combine like terms: 3x² + (4x - 10x) + (22 - 8) = 3x² - 6x + 14. The correct answer is 3x² - 6x + 14.

Abigail and Luna are having a math duel! They need to find out the degree of the polynomial 2x + x³ + 5x². Can you help them solve this mystery?

• 1

• 2

• 3

• 4

Answer explanation

The degree of a polynomial is the highest power of the variable. In 2x + x^3 + 5x^2, the term with the highest power is x^3, which has a degree of 3. Therefore, the correct answer is 3.

Benjamin and Maya are playing a game where they need to solve the inequality -3(x - 6) > 2x - 2 to unlock a treasure chest. Can you help them find the correct solution?

• x > 4

• x < 4

• x > -16

• x < -16

Answer explanation

To solve -3(x - 6) > 2x - 2, first distribute: -3x + 18 > 2x - 2. Then, combine like terms: 18 + 2 > 2x + 3x, leading to 20 > 5x. Dividing by 5 gives x < 4, which is the correct solution.

Priya and Ava are exploring the magical world of functions. They stumble upon a mysterious function: f(x) = x² + 2x - 5. Can you help them discover the range of this function in the realm of real numbers?

• less than or equal to -6

• greater than or equal to -6

• less than or equal to -1

• greater than or equal to -1

Answer explanation

To find the range of f(x) = x^2 + 2x - 5, we complete the square: f(x) = (x+1)^2 - 6. The minimum value occurs at x = -1, giving f(-1) = -6. Thus, the range is greater than or equal to -6.

Scarlett and Oliver are having a math duel! If Scarlett's function is f(x) = x² + 3x, which of the following statements is true about her function?

• f(1) = f(-1)

• f(2) = f(-2)

• f(1) = f(2)

• f(-1) = f(-2)

Answer explanation

To verify f(-1) and f(-2): f(-1) = (-1)^2 + 3(-1) = 1 - 3 = -2; f(-2) = (-2)^2 + 3(-2) = 4 - 6 = -2. Thus, f(-1) = f(-2) = -2, making the statement true.

• 3y = -4x + 15

• 3y = -4x + 6

• -3y = 4x + 15

• -3y = 4x + 6

Answer explanation

To find the equation of the line, use the point-slope form: y - y1 = m(x - x1). With point (6, -3) and slope -4/3, we get y + 3 = -4/3(x - 6). Rearranging gives 3y = -4x + 15, which matches the correct choice.

Abigail is planning a road trip and wants to calculate how much gasoline her car will consume for the journey. The function G(m) represents the amount of gasoline consumed by her car traveling m miles. What would be the most suitable domain for this function?

• integers

• rational numbers

• nonnegative integers

• nonnegative rational numbers

Answer explanation

The function G(m) calculates gasoline consumption for a road trip, which requires nonnegative distances. Thus, the most suitable domain is nonnegative rational numbers, as distances can be fractional and cannot be negative.

Avery and Sophia are on a mission to calculate the average rate of change in the number of reported polio cases per year in Nigeria from 2006 to 2013. Can you help them find the answer, rounded to the nearest hundredth?

• -0.01

• -125.44

• -134.50

• -153.71

Answer explanation

To find the average rate of change, subtract the number of cases in 2006 from the number in 2013, then divide by the number of years (7). The calculation yields -153.71, indicating a decrease in cases.

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