A scientist uses the expression 5/9(F - 32) to convert temperatures from degrees Fahrenheit (°F), F, to degrees Celsius (°C). To the nearest degree, what is the temperature, in °F, of a substance at -25°C?
- A. 13
- B. -32
- C. -13
- D. 18
Correct Answer & Rationale
Correct Answer: C
To find the Fahrenheit equivalent of -25°C, use the formula \( F = \frac{9}{5}C + 32 \). Substituting -25 for C gives \( F = \frac{9}{5}(-25) + 32 = -45 + 32 = -13 \). Thus, the temperature in Fahrenheit is -13°F. Option A (13°F) is incorrect as it does not reflect the negative temperature conversion. Option B (-32°F) is too low and does not correspond to the calculated value. Option D (18°F) is also incorrect as it is significantly higher than the expected result for -25°C.
To find the Fahrenheit equivalent of -25°C, use the formula \( F = \frac{9}{5}C + 32 \). Substituting -25 for C gives \( F = \frac{9}{5}(-25) + 32 = -45 + 32 = -13 \). Thus, the temperature in Fahrenheit is -13°F. Option A (13°F) is incorrect as it does not reflect the negative temperature conversion. Option B (-32°F) is too low and does not correspond to the calculated value. Option D (18°F) is also incorrect as it is significantly higher than the expected result for -25°C.
Other Related Questions
The graph of the equation y = x^2 + 4x - 5 is shown on the grid. Which statement is true when y = 0?
- A. x= -5 and x=1
- B. x= -2
- C. x= -5 and x = 0
- D. x= -9
Correct Answer & Rationale
Correct Answer: A
To find the values of x when y = 0, we need to solve the equation \(x^2 + 4x - 5 = 0\). Factoring this quadratic gives \((x + 5)(x - 1) = 0\), leading to the solutions \(x = -5\) and \(x = 1\). Option A correctly identifies these solutions. Option B states \(x = -2\), which is not a solution to the equation. Option C suggests \(x = -5\) and \(x = 0\); while it includes one correct solution, \(x = 0\) is incorrect. Option D claims \(x = -9\), which does not satisfy the equation. Thus, only option A accurately reflects the solutions when y = 0.
To find the values of x when y = 0, we need to solve the equation \(x^2 + 4x - 5 = 0\). Factoring this quadratic gives \((x + 5)(x - 1) = 0\), leading to the solutions \(x = -5\) and \(x = 1\). Option A correctly identifies these solutions. Option B states \(x = -2\), which is not a solution to the equation. Option C suggests \(x = -5\) and \(x = 0\); while it includes one correct solution, \(x = 0\) is incorrect. Option D claims \(x = -9\), which does not satisfy the equation. Thus, only option A accurately reflects the solutions when y = 0.
The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?
- A. 36
- B. 16
- C. 40
- D. 13
Correct Answer & Rationale
Correct Answer: A
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.
What is the value of f(-3) for f(x) = 2x^2 + x + 1
Correct Answer & Rationale
Correct Answer: -20
To find \( f(-3) \) for the function \( f(x) = 2x^2 + x + 1 \), substitute \(-3\) for \(x\): \[ f(-3) = 2(-3)^2 + (-3) + 1 = 2(9) - 3 + 1 = 18 - 3 + 1 = 16. \] The correct answer is -20, which is incorrect based on the calculation. Examining the other options: - If an option were 16, it would be correct as shown in the calculation. - Any other number, like -10 or 0, would arise from miscalculations or incorrect substitutions, thus not representing the function's value at \(-3\). The accurate evaluation confirms that \( f(-3) = 16 \).
To find \( f(-3) \) for the function \( f(x) = 2x^2 + x + 1 \), substitute \(-3\) for \(x\): \[ f(-3) = 2(-3)^2 + (-3) + 1 = 2(9) - 3 + 1 = 18 - 3 + 1 = 16. \] The correct answer is -20, which is incorrect based on the calculation. Examining the other options: - If an option were 16, it would be correct as shown in the calculation. - Any other number, like -10 or 0, would arise from miscalculations or incorrect substitutions, thus not representing the function's value at \(-3\). The accurate evaluation confirms that \( f(-3) = 16 \).
Which expression is undefined over the real numbers?
- A. (-3)^0
- B. 0/4
- C. |-2|
- D. (-7)^(1/2)
Correct Answer & Rationale
Correct Answer: D
The expression (-7)^(1/2) is undefined over the real numbers because it represents the square root of a negative number, which does not yield a real result. Option A, (-3)^0, equals 1, as any non-zero number raised to the power of 0 is defined. Option B, 0/4, simplifies to 0, which is a defined real number. Option C, |-2|, equals 2, as the absolute value of any number is always defined and non-negative. Thus, only (-7)^(1/2) fails to produce a real number, making it the only undefined expression in this context.
The expression (-7)^(1/2) is undefined over the real numbers because it represents the square root of a negative number, which does not yield a real result. Option A, (-3)^0, equals 1, as any non-zero number raised to the power of 0 is defined. Option B, 0/4, simplifies to 0, which is a defined real number. Option C, |-2|, equals 2, as the absolute value of any number is always defined and non-negative. Thus, only (-7)^(1/2) fails to produce a real number, making it the only undefined expression in this context.