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Mamont248 [21]
3 years ago
6

A train traveled 300 miles at a constant speed. It took 5 hours. What is the constant of proportionality that describes the trai

n's speed?
Mathematics
1 answer:
Fudgin [204]3 years ago
5 0

Answer:

60 miles an hour

Step-by-step explanation:

^^^^^^^^

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Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four
gregori [183]

Answer and step-by-step explanation:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = -5x + 750

Next we divide both sides by 2:

2y/2 = -5x/2 + 750/2

y = -2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width.  In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x(-2.5x+375)

A = -2.5x² + 375x

This is a quadratic equation, with values a = -2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex.  First we find the axis of symmetry, using the equation

x = -b/2a

x = -375/2(-2.5) = -375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = -2.5x² + 375x

A = -2.5(75)² + 375(75) = -2.5(5625) + 28125 = -14062.5 + 28125 = 14062.5

6 0
3 years ago
While riding her bike to the ocean and back home 5 times, Kimberly timed herself at 53min, 48min, 56min, 54min, and 45min. She h
alex41 [277]

Answer:

Kim will need to spend 67 minutes on her sixth ride

Step-by-step explanation:

Represent the number of minutes of her sixth ride by m.

Then the average number of minutes is

53 + 43 + 56 + 54 + 45 + m

---------------------------------------- = 53

                      6

Multiplying both sides of this equation by 6 yields

6(53 + 43 + 56 + 54 + 45 + m)

--------------------------------------------- = 6(53)

                        6

which simplifies to

 251 + m

---------------- = 318

         

or  251 + m = 318.  Subtract 251 from both sides to obtain the value of m:

m  = 318 - 251 = 67

Kim will need to spend 67 minutes on her sixth ride to attain an average ride length of  53 minutes.i

4 0
2 years ago
Solve for y. 3=7(1-1)<br><br>(it isn't 2)​
laiz [17]

Answer:

First off, I can't solve for y, there is no y variable.

Second, 3 = 7 ( 1 - 1 ) is not true because 3 ≠ 0 ( 3 doesn't equal 0 ) :

3 = 7 ( 1 - 1 )

3 = 7 ( 0 )  ( Simplify Parenthesis )

3 = 0 ( Multiply 7 and 0 )

3 ≠ 0

4 0
3 years ago
Find the volume of the figure in question #2 if the figure was half filled
telo118 [61]
The volume is 12x20x10 then divide by 2

200x12=2400

2400/2= 1200
4 0
3 years ago
Does the point (-2, -5) satisfy the equation y = x − -3?
Verizon [17]
No because (-2, -5) is negative and the y coordinate needs to be positive.
4 0
3 years ago
Read 2 more answers
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