During a family trip, you share the driving with your dad. At most, you are allowed to drive for three hours. While driving, your maximum speed is 55 miles per hour.Part A) Write a system of inequalities describing the possible numbers of hours “t” and distance “d” you may have to drive.

Part B) Is it possible for you to have driven 160 miles?

Please help and if you don’t mind to explain how you got all of the answers to each part. Offering 20 Points!

Thank you!

Answers

Answer 1

Answer:

Final answer:

In this question, we create a system of inequalities to describe the possible number of hours and distance you may have to drive. It is not possible to have driven 160 miles.

Explanation:

Part A:

Let t represent the number of hours you drive and d represent the distance you drive.

The constraints for the number of hours are: 0 ≤ t ≤ 3, which means you can drive for at most 3 hours.

The constraints for the distance are: 0 ≤ d ≤ 55t, which means the distance you drive cannot exceed 55 miles per hour multiplied by the number of hours you drive.

Part B:

No, it is not possible for you to have driven 160 miles. Let's substitute t = 3 into the distance constraint:

d ≤ 55t

d ≤ 55(3)

d ≤ 165

Since 160 is greater than 165, it is not within the range of possible distances you can drive.

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Answer 2

Answer:

Final answer:

The system of inequalities describing the possible numbers of hours and distance is t ≤ 3 and d = t × 55. It is not possible to have driven exactly 160 miles.

Explanation:

Part A:

To describe the possible numbers of hours and distance you may have to drive, we can create a system of inequalities based on the given conditions. Let's denote 't' as the number of hours you drive and 'd' as the distance you cover.

The maximum allowed driving time is 3 hours, so we can write the inequality: t ≤ 3.

Since your maximum speed is 55 miles per hour, the distance 'd' can be calculated using the formula: d = t × 55.

Combining these two inequalities, we have: t ≤ 3 and d = t × 55.

Part B:

To determine if it is possible to have driven 160 miles, we substitute the distance 'd' with 160 in the inequality: d = t × 55. By solving for 't', we can find the allowed range of hours. Plugging in the values, we get: 160 = t × 55. Rearranging the equation, we find t = 160 / 55, which gives t ≈ 2.91.

Therefore, it is not possible to have driven exactly 160 miles, as it falls outside the allowed range of t.

Learn more about system of inequalities here:

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Answers

Answer:

583$

Step-by-step explanation:

6% is equal to 0.06, so you multiply 550 by 0.06. which equals 33. Then, because it asks for how much Katie played, including the tax and TV, you add 33 to 550.

A circle is centered at the point (5, -4) and passes through the point (-3, 2).The equation of this circle is (x + ___)2 + (y + ___)2 = ___

Answers

Answer: $(x-5)^2+(y+4)^2=100$

Step-by-step explanation:

We know that the general equation of a circle can be written as :

$(x-h)^2+(y-k)^2=r^2$ (1), where (center )= (h,k) and r= radius

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(h,k) = (5,-4)

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$(-3-5)^2+(2-(-4))^2=r^2\n\n\Rightarrow\ (-8)^2+(2+4)^2=r^2\n\n\Rightarrow\ 64+6^2=r^2\n\n\Rightarrow\ 64+36=r^2\n\n\Rightarrow\ 100=r^2\n\n\Rightarrow\ r=√(100)=\pm10$

Since radius cannot be negative , thus r= 10 units

Put value of $r^2$ and (h,k) in equation (1), we get

$(x-5)^2+(y+4)^2=100$

Thus , the equation of given circle is $(x-5)^2+(y+4)^2=100$ .

you have to use the distance formula in order to find the radius. By doing that you get the answer 10. so the equation is:

(x-4)^2 + (y+5)^2 = 10

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A. 75/21
B. 7/9
C. 7/25
D. 21/75

Answers

In this question there is nothing complicated. Only thing is to know the way fractions can be divided. Once that is known the problem would be one of the easiest to solve. Now let us get back to the problem and look at all the information's that are given in the question.
Divide 7/15 by 3/5 = (7/15)/(3/5)
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   = (35/45)
Dividing the numerator and the denominator by 5 for simplifying purpose, we get
   = 7/9
So from the above deduction we can easily conclude that 7/9 is the correct answer and option "B" is the correct option among all the options given in the question.

If you would like to solve 7/15 / 3/5, you can calculate this using the following steps:

7/15 / 3/5 = 7/15 * 5/3 = 7/9

The correct result would be B. 7/9.

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D.The graph of the function is 1 unit up and 2 units to the left Efrom the graph of y = x2.
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Answers

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B. The range is all real numbers greater than or equal to 1.

This is false. Instead, the range is all real numbers greater than or equal to 2, that is the $y-coordinate$ of the vertex.

C. The y-intercept is 3.

This is true. We can find the $y-intercept$ letting $x=0$ , so:

$x=0 \n \n y-intercept \rightarrow f(0)=(0+1)^2+2=3$

D. The graph of the function is 1 unit up and 2 units to the left from the graph of $y=x^2$

This is false. The correct statement is that the graph of the function is 2 units up and 1 unit to the left from the graph of $y=x^2$

E. The graph has two x-intercepts.

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Answer:

A and C

Step-by-step explanation:

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Answers

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