Acceleration, a, in meters per second squared (m/5}), is found by the formula a= (V2-V2)/t where V1, is the beginning velocity, V2 is the end velocity, and t is time. What is the acceleration, in m/s^2, of an object with a beginning velocity of 14 m/s and end velocity of 8 m/s over a time of 4 seconds?
- A. 1.5
- B. -1.5
- C. 4.5
- D. -12
Correct Answer & Rationale
Correct Answer: B
To find acceleration, use the formula \( a = \frac{V2 - V1}{t} \). Here, \( V1 = 14 \, \text{m/s} \) and \( V2 = 8 \, \text{m/s} \). Plugging in the values gives \( a = \frac{8 - 14}{4} = \frac{-6}{4} = -1.5 \, \text{m/s}^2 \). Option A (1.5) is incorrect as it does not account for the decrease in velocity. Option C (4.5) miscalculates the difference between velocities and does not reflect the negative change. Option D (-12) results from incorrect arithmetic, misapplying the formula. Thus, the only accurate calculation shows the object is decelerating at -1.5 m/s².
To find acceleration, use the formula \( a = \frac{V2 - V1}{t} \). Here, \( V1 = 14 \, \text{m/s} \) and \( V2 = 8 \, \text{m/s} \). Plugging in the values gives \( a = \frac{8 - 14}{4} = \frac{-6}{4} = -1.5 \, \text{m/s}^2 \). Option A (1.5) is incorrect as it does not account for the decrease in velocity. Option C (4.5) miscalculates the difference between velocities and does not reflect the negative change. Option D (-12) results from incorrect arithmetic, misapplying the formula. Thus, the only accurate calculation shows the object is decelerating at -1.5 m/s².
Other Related Questions
Factor the expression completely: 45bcx - 10ax
- A. 5x(9bc - 2a)
- B. 5(9bc - 2a)
- C. x(45bc - 10a)
- D. 5x(9bc + 2a)
Correct Answer & Rationale
Correct Answer: A
To factor the expression 45bcx - 10ax completely, we start by identifying the greatest common factor (GCF). The GCF of the coefficients 45 and 10 is 5, and both terms contain the variable x. Thus, we can factor out 5x, resulting in 5x(9bc - 2a). Option A accurately reflects this factorization. Option B lacks the variable x, which is essential in the original expression. Option C incorrectly factors out only x, missing the GCF of 5. Option D alters the sign of the second term, which does not represent the original expression correctly.
To factor the expression 45bcx - 10ax completely, we start by identifying the greatest common factor (GCF). The GCF of the coefficients 45 and 10 is 5, and both terms contain the variable x. Thus, we can factor out 5x, resulting in 5x(9bc - 2a). Option A accurately reflects this factorization. Option B lacks the variable x, which is essential in the original expression. Option C incorrectly factors out only x, missing the GCF of 5. Option D alters the sign of the second term, which does not represent the original expression correctly.
How many more tickets did Larry buy than Jim?
- A. 3
- B. 12
- C. 6
- D. 1
Correct Answer & Rationale
Correct Answer: C
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.
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 \(-118\).
Which graph represents a function?
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A.
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B.
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C.
Correct Answer & Rationale
Correct Answer: B
To determine which graph represents a function, we apply the Vertical Line Test. This test states that if a vertical line intersects the graph at more than one point, the graph does not represent a function. Option A fails this test, as a vertical line can intersect the graph at multiple points, indicating it is not a function. Option C also does not satisfy the criteria, showing multiple intersections with vertical lines. In contrast, Option B passes the Vertical Line Test, as any vertical line drawn will intersect the graph at only one point, confirming it represents a function.
To determine which graph represents a function, we apply the Vertical Line Test. This test states that if a vertical line intersects the graph at more than one point, the graph does not represent a function. Option A fails this test, as a vertical line can intersect the graph at multiple points, indicating it is not a function. Option C also does not satisfy the criteria, showing multiple intersections with vertical lines. In contrast, Option B passes the Vertical Line Test, as any vertical line drawn will intersect the graph at only one point, confirming it represents a function.