Choose the best answer. If necessary, use the paper you were given.
If (2w + 7)(3w - 1) = 0 which of the following is a possible value of w?
- A. -3
- B. -0.28571
- C. 01-Mar
- D. 07-Feb
Correct Answer & Rationale
Correct Answer: D
To solve the equation (2w + 7)(3w - 1) = 0, we set each factor to zero. 1. For 2w + 7 = 0, solving gives w = -3. This corresponds to option A, which is a valid solution. 2. For 3w - 1 = 0, solving gives w = 1/3, approximately 0.333. Option B, -0.28571, does not match this value. 3. Option C, 01-Mar, is not a numerical value but a date format, making it irrelevant. 4. Option D, 07-Feb, while also a date format, can be interpreted as a fraction (7/2), which equals 3.5, not a solution to the equation. Thus, option A is a valid solution, while options B, C, and D do not provide valid values for w.
To solve the equation (2w + 7)(3w - 1) = 0, we set each factor to zero. 1. For 2w + 7 = 0, solving gives w = -3. This corresponds to option A, which is a valid solution. 2. For 3w - 1 = 0, solving gives w = 1/3, approximately 0.333. Option B, -0.28571, does not match this value. 3. Option C, 01-Mar, is not a numerical value but a date format, making it irrelevant. 4. Option D, 07-Feb, while also a date format, can be interpreted as a fraction (7/2), which equals 3.5, not a solution to the equation. Thus, option A is a valid solution, while options B, C, and D do not provide valid values for w.
Other Related Questions
If the trend shown in the graph above continued into the next year, approximately how many sport utility vehicles were sold in 1999?
- A. 3 million
- B. 2.5 million
- C. 2 million
- D. 3 thousand
Correct Answer & Rationale
Correct Answer: A
To determine the approximate number of sport utility vehicles sold in 1999, analyzing the trend in the graph is essential. If the upward trend continued, sales would likely increase compared to previous years. Given the data, 3 million aligns with the projected growth rate, reflecting a significant rise consistent with market trends. Option B, 2.5 million, underestimates the growth, while C, 2 million, does not account for the upward trajectory. Option D, 3 thousand, is far too low and unrealistic, failing to represent the scale of SUV sales during that period. Thus, 3 million is the most reasonable estimate.
To determine the approximate number of sport utility vehicles sold in 1999, analyzing the trend in the graph is essential. If the upward trend continued, sales would likely increase compared to previous years. Given the data, 3 million aligns with the projected growth rate, reflecting a significant rise consistent with market trends. Option B, 2.5 million, underestimates the growth, while C, 2 million, does not account for the upward trajectory. Option D, 3 thousand, is far too low and unrealistic, failing to represent the scale of SUV sales during that period. Thus, 3 million is the most reasonable estimate.
If a +√x= b then x =
- A. √b-√a
- B. √(b-1)
- C. (b-a)²
- D. b²-a²
Correct Answer & Rationale
Correct Answer: C
To solve for \( x \) in the equation \( a + \sqrt{x} = b \), we first isolate \( \sqrt{x} \) by rearranging the equation to \( \sqrt{x} = b - a \). Squaring both sides gives \( x = (b - a)^2 \), which corresponds to option C. Option A, \( \sqrt{b} - \sqrt{a} \), does not account for squaring the expression and thus cannot represent \( x \). Option B, \( \sqrt{(b-1)} \), is unrelated to the original equation and lacks the necessary operations. Option D, \( b^2 - a^2 \), applies the difference of squares incorrectly and does not solve for \( x \) directly.
To solve for \( x \) in the equation \( a + \sqrt{x} = b \), we first isolate \( \sqrt{x} \) by rearranging the equation to \( \sqrt{x} = b - a \). Squaring both sides gives \( x = (b - a)^2 \), which corresponds to option C. Option A, \( \sqrt{b} - \sqrt{a} \), does not account for squaring the expression and thus cannot represent \( x \). Option B, \( \sqrt{(b-1)} \), is unrelated to the original equation and lacks the necessary operations. Option D, \( b^2 - a^2 \), applies the difference of squares incorrectly and does not solve for \( x \) directly.
Allison drives her car at an average speed of x miles per hour for y hours and travels 150 miles. Which of the following equations represents this situation?
- A. x + y = 150
- B. xy = 150
- C. y/x = 150
- D. x/y = 150
Correct Answer & Rationale
Correct Answer: B
The relationship between speed, time, and distance is expressed by the formula: distance = speed × time. In this scenario, Allison travels 150 miles at an average speed of x miles per hour for y hours, which translates to the equation xy = 150. Option A (x + y = 150) incorrectly suggests that speed and time add up to distance, which is not accurate. Option C (y/x = 150) misrepresents the relationship by implying that the ratio of time to speed equals distance, which is incorrect. Option D (x/y = 150) also misinterprets the relationship, suggesting that the ratio of speed to time equals distance. Thus, option B correctly captures the relationship among the variables.
The relationship between speed, time, and distance is expressed by the formula: distance = speed × time. In this scenario, Allison travels 150 miles at an average speed of x miles per hour for y hours, which translates to the equation xy = 150. Option A (x + y = 150) incorrectly suggests that speed and time add up to distance, which is not accurate. Option C (y/x = 150) misrepresents the relationship by implying that the ratio of time to speed equals distance, which is incorrect. Option D (x/y = 150) also misinterprets the relationship, suggesting that the ratio of speed to time equals distance. Thus, option B correctly captures the relationship among the variables.
(a ^ 9 * b ^ 12)/(a ^ 3 * b) =
- A. a ^ 3 * b ^ 11
- B. a ^ 6 * b ^ 12
- C. a ^ 3 * b ^ 12
- D. a ^ 6 * b ^ 11
Correct Answer & Rationale
Correct Answer: D
To simplify the expression \((a^9 * b^{12})/(a^3 * b)\), apply the laws of exponents. For the \(a\) terms, subtract the exponents: \(9 - 3 = 6\), giving \(a^6\). For the \(b\) terms, also subtract the exponents: \(12 - 1 = 11\), resulting in \(b^{11}\). Thus, the simplified expression is \(a^6 * b^{11}\). Option A is incorrect because it miscalculates the exponent of \(b\). Option B incorrectly maintains the exponent of \(b\) at 12. Option C fails to adjust the exponent of \(a\) correctly. Only option D accurately reflects the simplification.
To simplify the expression \((a^9 * b^{12})/(a^3 * b)\), apply the laws of exponents. For the \(a\) terms, subtract the exponents: \(9 - 3 = 6\), giving \(a^6\). For the \(b\) terms, also subtract the exponents: \(12 - 1 = 11\), resulting in \(b^{11}\). Thus, the simplified expression is \(a^6 * b^{11}\). Option A is incorrect because it miscalculates the exponent of \(b\). Option B incorrectly maintains the exponent of \(b\) at 12. Option C fails to adjust the exponent of \(a\) correctly. Only option D accurately reflects the simplification.