Question

1. a bus is traveling at a constant speed along a straight portion of road. the equation (d = 30t) gives the distance (d), in feet from a road - marker, that the bus will be (t) seconds after passing the marker. how many feet from the marker will the bus be 2 seconds after passing the marker? a) 30 b) 32 c) 60 d) 90
2. for a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. a bead produced by the machine will be selected at random. what is the probability of selecting a bead that has a defect? a) (\frac{1}{2900}) b) (\frac{1}{29}) c) (\frac{29}{100}) d) (\frac{2}{10})
3. what is the (y) - intercept of the graph shown? a) ((-8,0)) b) ((-6,0)) c) ((0,6)) d) ((0,8)
4. which expression is equivalent to ((2x^{2}+x - 9)+(x^{2}+6x + 1))? a) (2x^{2}+7x + 10) b) (2x^{2}+6x - 8) c) (3x^{2}+7x - 10) d) (3x^{2}+7x - 8)

Explanation:

1. First question:

• Explanation:
• Step1: Identify the formula and variable - value
• The formula for the distance of the bus from the road - marker is \(d = 30t\), where \(d\) is the distance in feet and \(t\) is the time in seconds. We need to find \(d\) when \(t = 2\).
• Step2: Substitute the value of \(t\) into the formula
• Substitute \(t = 2\) into \(d = 30t\), so \(d=30\times2 = 60\).
• Answer: C. 60

1. Second question:

• Explanation:
• Step1: Recall the definition of the \(y\) - intercept
• The \(y\) - intercept of a graph is the point where the graph crosses the \(y\) - axis. At this point, \(x = 0\). Looking at the graph, when \(x = 0\), \(y = 6\). The \(y\) - intercept is the point \((0,6)\).
• Answer: C. \((0,6)\)

1. Third question:

• Explanation:
• Step1: Recall the probability formula
• The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of defective beads (favorable outcomes) is 29, and the total number of beads is 100.
• Answer: C. \(\frac{29}{100}\)

1. Fourth question:

• Explanation:
• Step1: Combine like - terms
• \((2x^{2}+x - 9)+(x^{2}+6x + 1)=(2x^{2}+x^{2})+(x + 6x)+(-9 + 1)\).
• Step2: Simplify each group of like - terms
• \(2x^{2}+x^{2}=3x^{2}\), \(x + 6x = 7x\), and \(-9 + 1=-8\). So the result is \(3x^{2}+7x - 8\).
• Answer: D. \(3x^{2}+7x - 8\)

Answer:

1. First question:

• Explanation:
• Step1: Identify the formula and variable - value
• The formula for the distance of the bus from the road - marker is \(d = 30t\), where \(d\) is the distance in feet and \(t\) is the time in seconds. We need to find \(d\) when \(t = 2\).
• Step2: Substitute the value of \(t\) into the formula
• Substitute \(t = 2\) into \(d = 30t\), so \(d=30\times2 = 60\).
• Answer: C. 60

1. Second question:

• Explanation:
• Step1: Recall the definition of the \(y\) - intercept
• The \(y\) - intercept of a graph is the point where the graph crosses the \(y\) - axis. At this point, \(x = 0\). Looking at the graph, when \(x = 0\), \(y = 6\). The \(y\) - intercept is the point \((0,6)\).
• Answer: C. \((0,6)\)

1. Third question:

• Explanation:
• Step1: Recall the probability formula
• The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of defective beads (favorable outcomes) is 29, and the total number of beads is 100.
• Answer: C. \(\frac{29}{100}\)

1. Fourth question:

• Explanation:
• Step1: Combine like - terms
• \((2x^{2}+x - 9)+(x^{2}+6x + 1)=(2x^{2}+x^{2})+(x + 6x)+(-9 + 1)\).
• Step2: Simplify each group of like - terms
• \(2x^{2}+x^{2}=3x^{2}\), \(x + 6x = 7x\), and \(-9 + 1=-8\). So the result is \(3x^{2}+7x - 8\).
• Answer: D. \(3x^{2}+7x - 8\)