An advertisement poster in the window of a shoe store is in the shape of a rectangle. The length of the poster is 9 less than 4 times the width. Which expression represents the length of the poster when w is the width
- A. 4w - 9
- B. 9 - 4w
- C. 4w + 9
- D. 9w - 4
Correct Answer & Rationale
Correct Answer: A
The expression for the length of the poster is determined by the relationship given in the problem. The length is described as "9 less than 4 times the width," which translates mathematically to \(4w - 9\). Option A (4w - 9) accurately reflects this relationship. Option B (9 - 4w) incorrectly suggests that the length is greater than 9 and decreases as width increases, which contradicts the problem's description. Option C (4w + 9) implies that the length increases by 9, rather than decreasing, which is not aligned with the original statement. Option D (9w - 4) introduces an incorrect multiplication factor and does not adhere to the given relationship, making it invalid.
The expression for the length of the poster is determined by the relationship given in the problem. The length is described as "9 less than 4 times the width," which translates mathematically to \(4w - 9\). Option A (4w - 9) accurately reflects this relationship. Option B (9 - 4w) incorrectly suggests that the length is greater than 9 and decreases as width increases, which contradicts the problem's description. Option C (4w + 9) implies that the length increases by 9, rather than decreasing, which is not aligned with the original statement. Option D (9w - 4) introduces an incorrect multiplication factor and does not adhere to the given relationship, making it invalid.
Other Related Questions
What is the slope of the line shown on the graph
- A. -0.333333333
- B. -3
- C. 3
- D. 1\3
Correct Answer & Rationale
Correct Answer: D
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.
What is the value of x^3 - 2y + 3 if x = -5 and y = -2?
Correct Answer & Rationale
Correct Answer: A
To find the value of \( x^3 - 2y + 3 \) when \( x = -5 \) and \( y = -2 \), substitute the values into the expression. Calculating \( x^3 \): \[ (-5)^3 = -125 \] Calculating \( -2y \): \[ -2(-2) = 4 \] Now, substituting these values into the expression: \[ -125 + 4 + 3 = -118 \] Thus, the value of the expression is \(-118\), corresponding to option A. Other options are incorrect due to miscalculations in either \( x^3 \), \( -2y \), or the final sum, leading to values that do not match the correct result of \(-118\).
To find the value of \( x^3 - 2y + 3 \) when \( x = -5 \) and \( y = -2 \), substitute the values into the expression. Calculating \( x^3 \): \[ (-5)^3 = -125 \] Calculating \( -2y \): \[ -2(-2) = 4 \] Now, substituting these values into the expression: \[ -125 + 4 + 3 = -118 \] Thus, the value of the expression is \(-118\), corresponding to option A. Other options are incorrect due to miscalculations in either \( x^3 \), \( -2y \), or the final sum, leading to values that do not match the correct result of \(-118\).
What is the value of the expression 2j - 7jkm when j = 5, k = -14, and m = -3?
Correct Answer & Rationale
Correct Answer: A
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
Which pair of equations represents parallel lines?
- A. -2x + y + 2 = 0, y = -(1/2)x - 4
- B. 3x + y = -8, y = 3x - 8
- C. x + 2y = 8, -x - 2y = 3
- D. -(2/3)x + y = 12, y = -(3/2)x - 1
Correct Answer & Rationale
Correct Answer: C
To identify parallel lines, the slopes of the equations must be equal. Option A has slopes of 1/2 and -1/2, which are not equal. Option B has slopes of 3 and 3, indicating the lines are parallel; however, it is not the correct answer as it does not match the requirement for both equations. Option C has the first equation rearranged to slope -1/2 and the second to slope -1/2, confirming they are parallel. Option D features slopes of 2/3 and -3/2, which are also not equal, indicating the lines intersect. Thus, only option C accurately represents parallel lines.
To identify parallel lines, the slopes of the equations must be equal. Option A has slopes of 1/2 and -1/2, which are not equal. Option B has slopes of 3 and 3, indicating the lines are parallel; however, it is not the correct answer as it does not match the requirement for both equations. Option C has the first equation rearranged to slope -1/2 and the second to slope -1/2, confirming they are parallel. Option D features slopes of 2/3 and -3/2, which are also not equal, indicating the lines intersect. Thus, only option C accurately represents parallel lines.