Compare the zeros of function P and function Q. Which statement about the zeros of the functions is true?
- A. Function P has the greater zero, which is 9.
- B. Function P has the greater zero, which is 1.
- C. Function Q has the greater zero, which is 5.
- D. Function Q has the greater zero, which is 4.
Correct Answer & Rationale
Correct Answer: C
To determine which statement is true regarding the zeros of functions P and Q, it's essential to analyze the values given. Option A claims that function P's greater zero is 9; however, this contradicts the provided information, as 9 is not a zero for P. Option B asserts that function P's greater zero is 1, which is also incorrect if 1 is not the highest zero of P. Option D states that function Q's greater zero is 4, but if Q's zeros are higher, this option cannot be true. In contrast, option C correctly identifies that function Q has a greater zero, specifically 5, which aligns with the provided data about the functions' zeros.
To determine which statement is true regarding the zeros of functions P and Q, it's essential to analyze the values given. Option A claims that function P's greater zero is 9; however, this contradicts the provided information, as 9 is not a zero for P. Option B asserts that function P's greater zero is 1, which is also incorrect if 1 is not the highest zero of P. Option D states that function Q's greater zero is 4, but if Q's zeros are higher, this option cannot be true. In contrast, option C correctly identifies that function Q has a greater zero, specifically 5, which aligns with the provided data about the functions' zeros.
Other Related Questions
Solve the equation for x: (2x-3)/5 = x/10
- A. 2
- B. 3
- C. 1\5
- D. 10
Correct Answer & Rationale
Correct Answer: A
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).
To solve the equation \((2x-3)/5 = x/10\), first eliminate the fractions by multiplying both sides by 10, resulting in \(2(2x - 3) = x\). Simplifying gives \(4x - 6 = x\). Rearranging leads to \(4x - x = 6\), or \(3x = 6\), giving \(x = 2\). Option B (3) does not satisfy the equation when substituted back. Option C (1/5) results in a negative left side, while Option D (10) leads to an incorrect balance in the original equation. Thus, the only solution that holds true is \(x = 2\).
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 \(-118\).
The world's highest suspension bridge spans the Arkansas River at a height of 1,053 feet above the water. If a ball is dropped from the bridge. The height of the ball, In feet, after t seconds can be modeled by the equation f(t)= -16(t)^2 + 1053. How many feet above the water is the ball 7 seconds after being dropped?
Correct Answer & Rationale
Correct Answer: A
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
To determine the height of the ball 7 seconds after being dropped, substitute \( t = 7 \) into the equation \( f(t) = -16(t)^2 + 1053 \). Calculating this gives \( f(7) = -16(7)^2 + 1053 = -16(49) + 1053 = -784 + 1053 = 269 \) feet. Option A provides this correct height of 269 feet. Other options are incorrect because they result from miscalculations or incorrect substitutions into the equation. For example, using an incorrect value for \( t \) or failing to properly apply the formula leads to heights that do not reflect the physics of the scenario.
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.