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Nutka1998 [239]
3 years ago
5

The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph Which of the follo

wing best describes the motion of the car shown? (15 points)
A) It travels for 2 hours, then stops for 3 hours, and finally travels again for 2 hours. B)It travels for 2 hours, then stops for 3 hours, and finally travels again for 5 hours.
C)It travels for 2 hours, then stops for 1 hour, and finally travels again for 5 hours.
D)It travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours.

Mathematics
1 answer:
Agata [3.3K]3 years ago
5 0

Answer: It travelled at a steady speed for 2 hours then stopped for 1 hour and then it went at a steady speed for 2 hours making the journey in total 6 hours

Step-by-step explanation:

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Find two positive numbers whose difference is 30 and whose product is 2584.
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Answer:

38 and 68.

Step-by-step explanation:

Let x be the smaller one of the two number.

x must be a positive integer. The other number would be (x + 30).

The question states that the product of the two numbers is 2584. In other words:

x\, (x + 30) = 2584.

Rearrange this equation and solve for x:

x^{2} + 30\, x - 2584 = 0.

The first root of this quadratic equation would be:

\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}.

Similarly, the second root of this quadratic equation would be:

\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}.

Since the question requires that both numbers should be positive, x > 0. Therefore, only x = 38 is valid.

Hence, the two numbers would be 38 and (38 + 30), which is 68.

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1/5

Step-by-step explanation:

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B) 12

Step-by-step explanation:

C is the circumference, d is the diameter, and r is the radius.  They are related by the following equations:

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Step-by-step explanation:

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