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2 years ago

The graph shows the distance $y$ (in miles) that a bus travels in $x$ hours. Find and interpret the slope of the line.

Mathematics

1 answer:

faust18 [17]2 years ago

5 0

Answer:

Slope= 30

Speed = 30 miles per hour

Step-by-step explanation:

Given two points the slope will be change in y over change in x

OR (y-y1)/(x-x1)

(120-60)/(2-1) = 60/2 = 30miles/hr

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4x + 12 = -7y -y + 12 = 4x Solve with elimination

statuscvo [17]

Take the second equation and flip it around so the y on the left ends up on the right and the 4x on the right ends up on the left. This makes all negatives positive and all positives negative. -4x + 12 = y

Then add the first equation to the second equation
4x +12 = -7y
-4x + 12 = y this eliminates the x's
24 = - 6y then divide by - 6
- 6 - 6
- 4 = y

So if you know that y = negative 4, you can substitute into either equation. I pick the second one because I am a lazy person.
-y + 12 = 4 x
-(-4) + 12 = 4 x combine your numbers
 16 = 4 x then divide by 4
 4 = x
So your solution is: x = 4 and y = -4 or this is also written (4, -4)

Does that work for you?

4 0

3 years ago

Read 2 more answers

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

Rupert drove home at an average rate of 58 miles per hour. find his rate in feet per second

leva [86]

5280 feet in 1 mile
3600 seconds in an hour

58(5280) / 3600 = 306240/3600 = 85.06 ft per sec or if u need it rounded, it is 85.1

6 0

3 years ago

Two pools are leaking After 15 minutes pool A has leaked 2/3 gallon After 20 minutes pool B has 3/4 gallon Which pool is leaking

Nataly [62]

hope it will help you...........

8 0

3 years ago

Sammy wants to deposit into a 7% annual simple interest account she will also deposit twice as much in a certificate of deposit

antiseptic1488 [7]

Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.

Step-by-step explanation:

Let x represent the amount that he would deposit in the simple interest account.

Let y represent the amount that he would deposit in the certificate of deposit.

she will deposit twice as much in the certificate of deposit. It means that

y = 2x

Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x

Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.

The total interest from both accounts would be $390. It means that

0.07x + 0.05y = 390- - - - - - - - - - 1

Substituting y = 2x into equation 1, it becomes

0.07x + 0.05 × 2x = 390

0.07x + 0.1x = 390

0.17x = 390

x = 390/0.17 = $2294

y = 2x = 2 × 2294

y = 4588

4 0

3 years ago