HS Math Flashcards

What phrase can be used in place of √176?

Answer: 4√11

To simplify the square root of 176, you need to find the largest perfect square factor of 176. The number 176 can be expressed as the product of 16 and 11 (16 × 11 = 176). Therefore, √176 can be rewritten as √(16 × 11), which simplifies to √16 × √11, resulting in 4√11.

What expression can be used in place of 64x2 – 225?

Answer: (8x – 15)(8x + 15)

The expression 64x² – 225 is a classic example of a difference of two squares. Recognize that 64x² is the square of 8x, and 225 is the square of 15. Applying the difference of squares formula, a² – b² = (a – b)(a + b), we factor the expression as (8x – 15)(8x + 15).

Which of the following best depicts the equation of the line that crosses (32,24) and (-10,-8)?

Answer: y = 16/21x – 8/21

To find the equation of the line, first calculate the slope (m) using the two given points (32, 24) and (-10, -8). The slope is (24 - (-8)) / (32 - (-10)) = 32 / 42 = 16/21. Then, use the point-slope form y - y₁ = m(x - x₁) with one of the points, for example (32, 24): y - 24 = (16/21)(x - 32). Simplifying this equation yields y = 16/21x - 8/21.

In a grocery store, a customer purchased 58 products for a total of $4.20. Bananas made up the majority of the products, with some apples included. ‥ Each apple costs $0.05 ‥ Each banana costs $0.10 Which set of equations may be used to determine, from the customer's purchases at the grocery shop, a) the number of apples and b) the number of bananas?

Answer: a + b = 58 0.05a + 0.10b = 4.20

Let 'a' represent the number of apples and 'b' represent the number of bananas. The first equation represents the total number of items purchased: a + b = 58. The second equation represents the total cost based on the price of each item: 0.05a (cost of apples) + 0.10b (cost of bananas) = 4.20 (total cost). This system accurately models the given scenario.

Which of the following represents 6x² – 17x + 5 in factored form?

Answer: (2x – 5)(3x – 1)

To factor the quadratic expression 6x² – 17x + 5, we look for two binomials that multiply to this trinomial. By testing combinations of factors for 6x² (e.g., 2x and 3x) and 5 (e.g., -5 and -1), we find that (2x – 5)(3x – 1) correctly expands to 6x² - 2x - 15x + 5, which simplifies to 6x² – 17x + 5.

Which of the following inequality best characterizes the part's range and domain?

Answer: Domain: -3 ≤ x ≤ 3 Range: -2 ≤ f(x) ≤ 1

The domain of a function refers to all possible input (x) values, and the range refers to all possible output (f(x) or y) values. For the described part, the x-values extend from -3 to 3, inclusive, meaning -3 ≤ x ≤ 3. The corresponding y-values extend from -2 to 1, inclusive, meaning -2 ≤ f(x) ≤ 1.

Which of the following statements most accurately depicts the line's grid equation and its relationship to the y-axis?

Answer: The equation of the line is x = -3, and the line is parallel to the y-axis.

A vertical line has an equation where x is equal to a constant value. If the line passes through x = -3, its equation is x = -3. A vertical line is always parallel to the y-axis and perpendicular to the x-axis, as it maintains a constant x-coordinate regardless of the y-coordinate.

Which of the following expressions is 9x² + 72x + 144?

Answer: (3x + 12)²

The expression 9x² + 72x + 144 is a perfect square trinomial. This can be recognized because 9x² is (3x)², 144 is 12², and the middle term, 72x, is twice the product of 3x and 12 (2 * 3x * 12 = 72x). Therefore, it factors into the form (a + b)² = a² + 2ab + b², which is (3x + 12)².

Take a look at the function f(x) = x² – 9x + 20. Which of these claims about the following is true?

Answer: The zeros are 4 and 5 because the factors of f are (x – 4) and (x – 5).

To find the zeros of the function f(x) = x² – 9x + 20, you need to factor the quadratic expression. The factors are (x – 4) and (x – 5), because (-4) * (-5) = 20 and (-4) + (-5) = -9. Setting each factor to zero, x – 4 = 0 gives x = 4, and x – 5 = 0 gives x = 5. These are the zeros of the function.

In the solution set of -5x – 25y < -30, which of the following ordered pairs is present?

Answer: {1 – 2√2, 1 + 2√2}

The question asks for an ordered pair in the solution set of a two-variable inequality, but the options provided are sets of single values, typically representing solutions to a quadratic equation. Assuming the question is flawed and intends to ask for the solution set of a quadratic equation, the form {1 – 2√2, 1 + 2√2} represents conjugate surds. These are common solutions when using the quadratic formula for equations that do not have rational roots.