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3 years ago

Create a linear equation for the following data:

Mathematics

1 answer:

djverab [1.8K]3 years ago

4 0

Answer:

y=-.386x + 2.879

Explanation:

For these type of calculations, you would have to use a graphing calculator to use the linear regression function. What this does is, it takes the x & y values given on the chart and it gives you the best possible linear equation for the given data set.

The exact results were:

y = -0.3862928349 + 2.869158879

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Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an averag

azamat

Answer:

It takes 0.619 hours (approximately 37 minutes) for the van to catch up with the storm.

They have driven 33.43 miles

They will catch up when their distances are equal.

Step-by-step explanation:

The speed of the van is 54 mph, and the speed of the storm is 33 mph. They are going in the same direction, so the relative speed is the difference of their speeds:

relative speed = 54 - 33 = 21 mph

Now, to find the time when the van reaches the storm, we just need to use the equation:

distance = speed * time

13 = 21 * t

t = 13 / 21 = 0.619 hours

The distance traveled by the van is:

distance = 54 * 0.619 = 33.43 miles

The van will catch up when the distances are equal (the distance of the storm is 13 + 33*0.619 = 33.43 miles)

6 0

4 years ago

Find the cube of 12.

enot [183]

The cube of 12 is (12 x 12 x 12) = 1,728 .

The volume of a cube with side-length of 7 units is
(7 units x 7 units x 7 units) = 343 cubic units.

The volume of a cube with side-length of 14 units is
(14 units x 14 units x 14 units) = 2,744 cubic units.

The number of 1 by 1 unit cubes that would equal the volume
of the figure shown can't be determined, because the figure is 
not shown.

The volume of the figure can't be determined, because the figure
is not shown.

7 0

3 years ago

The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:

Soloha48 [4]

Part A: What do the x-intercepts and maximum value of the graph represent?

There are two x-intercepts: x = 0 and x = 36

Those values are the points at which the height of the tunnel is 0.

That means that the width of the tunnel at the ground level is 36 - 0 = 36.

The maximum value of the graph is 32, at x= 18. That, represents that at the center, x= 18, the tunnel has a height of 32.

What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height? (6 points)

The interval where the function is increasing is (0,18) and the interval where teh function is decreasing is (18,36)

That represents that the height starts to increase with the distance (from 0 to 18) reaches a maximum of 32, at x = 18, and starts to decrease with the distance until x = 36.

Part B: What is an approximate average rate of change of the graph from x = 5 to x = 15, and what does this rate represent? (4 points)

The average rate of change from x = 5 to x = 15 is the change in height divided by the change in distance

=> average rate of change = Δy / Δx

Δy ≈ 31 -14 = 17

Δx = 15 - 5 = 10

=> Δy / Δx ≈ 17 / 10 = 1.7

7 0

4 years ago

Solve each system of equation by substitution

marishachu [46]

You substitute in an expression by filling in the desired and accustomed unknown value to the value you're trying to find. An example below can better elaborate what I want to say above. In the equation below, 7 - 2n = 5 the unknown is represented by n moreover, the equation suggest to find the missing to make it equilateral on both sides.

In mathematical expression, the equation then becomes 7 - 2n = 5

The next procedure is to find the unknown.
1. 7 - 2n = 5
2. -2n = 5 - 7
3. -2n = -2
4. n = -2/-2
5. n = 1

Check:
Substitute n = 1

7 - 2 (1) = 5
7-2 = 5
5=5

3 0

4 years ago

find three numbers whos sum is 86, if the first number is three times the difference between the second and the third, and the s

agasfer [191]

Answer: 45,28,13

Step-by-step explanation:

Firstly let’s call integer 3

‘x’

Following the information given the following equations can be constructed:

integer 3 = x

integer 2 = 2+2x because 2x represents 2 times integer 3 (which is x) and plus two

integer 1 =3((2x+2)-x) what we have written is the difference between integer 2 (which was (2x+2)) and integer 3 which was x and simply multiply the result of that subtraction by 3

next we can treat them like their own variables almost.

integer 1 + integer 2 + integer 3 =86

so now plug in the equations we have constructed for each integer:

(3((2x+2)-x)) + (2x+2) + x = 86

to make it easier to read please see the image attached below to solve for x

After you have gone through the image I have included you should notice x= 13 great we got one integer! (Integer 3)

now plug in 13 into our integer equations :

integer 2: 2(13)+2= 28

Therefore integer 2 is 28

integer 1: 3((2(13)+2)-(13))=
3((28-13)

3(15)

Therefore integer 1 is 45.

and integer 3 is x which as we now know is equal to 13

3 0

3 years ago