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3 years ago

Write an equation in slope intercept form that passes through (-5, -4) and (-2,-7).

Mathematics

1 answer:

liubo4ka [24]3 years ago

7 0

Answer:

y = x + 1

Step-by-step explanation:

slope/m = -3/3 = -1

b/y-inter = 1

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It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel

Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

Solution:

The speed is given by formula:

$speed = \frac{distance}{time}$

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

The total distance travelled by the train across the bridge is given by:

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 1260}{60}$

The total distance travelled by the train through the tunnel is given by:

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 2010}{90}$

The speed of the train was the same in both cases.

Equate both speeds

$\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}$

$\frac{x+630}{30} = \frac{x+1005}{45}$

$45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120$

Thus length of train is 120 meters

Find the speed of train:

$speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25$

Thus speed of train is 25 meter per second

5 0

3 years ago

What is the equation of the line that is parallel to y-3x=2 and that passes through (6,1)?

Artemon [7]

Try this solution (analytic method):

1. if new line is parallel to the given one (y=3x+2) it means the new line has a form y=3x+b, where b - number.

2. In order to calculate 'b', it need to substitute the coordinates of point (6;1) into the equation of the new line:

1=3*6+b, ⇒ b=-17.

3. If to make up the equation of the new line:

y=3x-17

Answer: A

8 0

4 years ago

Find the sum of these polynomials. (x^2 - x + 7) + (9x^2 + 6)

Rina8888 [55]

The answer is 10x^2-x+13

3 0

3 years ago

A firm has the marginal-demand function where D(x)=-1400x÷√25-x² is the number of units sold at x dollars per unit. Find the dem

borishaifa [10]

The equation of the demand function is D(x) = 1400√(25-x²) + 11400

<h3>How to determine the demand function?</h3>

From the question, we have the following parameters that can be used in our computation:

Marginal demand function, D'(x) = -1400x÷√25-x²

Also, we have

D = 17000, when the value of x = 3

To start with, we need to integrate the marginal demand function, D'(x)

So, we have the following representation

D(x) = 1400√(25-x²) + C

Recall that

D = 17000 at x = 3

So, we have

17000 = 1400√(25-3²) + C

Evaluate

17000 = 5600 + C

Solve for C

C = 17000 - 5600

So, we have

C = 11400

Substitute C = 11400 in D(x) = 1400√(25-x²) + C

D(x) = 1400√(25-x²) + 11400

Hence, the function is D(x) = 1400√(25-x²) + 11400