A car travels at an average speed of 68 miles per hour. How long does it take to travel 357 miles?

What is the perimeter of a rectangle that is 2m 10cm by 45cm?

Amiraneli [1.4K]

$P=2l+2w\\
l=2\text{ m }10\text{ cm}=210 \text{ cm}\\
w=45\text{ cm}\\\\
P=2\cdot210+2\cdot45\\
P=420+90\\
P=510 \text{ cm}$

6 0

4 years ago

If f(x)=x^3-x, what is the average rate of change of f(x) over the interval [1,5]?

RSB [31]

Answer:

30

Step-by-step explanation:

Average rate of change=Δf(x)/Δx = [f(x2)-f(x1]/[x2-x1]

Δf(x)/Δx = [f(5)-f(1]/[5-1]

f(5)=5³-5=120

f(1)=1³-1=0

Δf(x)/Δx = [120-0]/[5-1]=120/4=30

4 0

3 years ago

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

Henry has 12 diamonds of the same shape and size in a bowl.how many diamonds represent 3/4 of the bowl

zhuklara [117]

Answer:

9

Step-by-step explanation:

12 divided by 4=3 3X3=9

7 0

3 years ago

A biologist is comparing the growth of a population of flies per week to the number of flies a bullfrog will consume per week. S

Lubov Fominskaja [6]

Realize that since 2x and 3x - 1 are equal to each other, they are also equal to y. This means that we can craft two equations, y = 2x and y = 3x - 1.

When you want to solve a systems of equations via a graph, you need to plot both equations on a graph and determine the x- and y-value of where the lines intersect. In this case, we would plot both y = 2x and y = 3x - 1. These lines intersect at the point (1, 2).

Since we are trying to find the day the bullfrog will be able to eat the entire population, or x, we are going to use the x-value of our point as our answer. Thus, our answer is 1 day.

3 0

4 years ago