Determine if side lengths 24, 21.5, and 55.5 make a triangle. If so, classify the type of triangle it creates.

The distance between New York City, NY, and Louisville, KY is 720 miles. One morning a train traveling 80 mph left from New York

beks73 [17]

Answer:

2 hours

Step-by-step explanation:

Given : The distance between New York City, NY, and Louisville, KY is 720 miles. One morning a train traveling 80 mph left from New York. Two hours later a slower train, traveling at 60 mph, left Louisville.

To find : How many hours will the slower train travel for before both trains will arrive at the same point?

Solution : Let the distance covered by NY is x

and let the distance covered by KY is y

Total distance covered is $x+y=720$ ........[1]

→ New York city,

Distance traveled = x

Speed of the train = 80 mph

Time taken = t+2

Formula is $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$t+2=\frac{x}{80}$ .......[2]

→ Louisville,

Distance traveled = y

Speed of the train = 60 mph

Time taken = t

Formula is $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$t=\frac{y}{60}$ .......[3]

Put the value of t from [3] into [2]

$\frac{x}{80}- \frac{y}{60}=2$ ......[4]

Now, we solve equation [1] and [4],

Put the value of y from [1] and put back in [4], $y=720-x$

$\frac{x}{80}- \frac{y}{60}=2$

$\frac{x}{80}- \frac{720-x}{60}=2$

$\frac{60x-80(720-x)}{80\times60}=2$

$60x-57600+80x=9600$

$140x-57600=9600$

$140x=57600+9600=67200$

$x=\frac{67200}{140}=480$

Put x=480 in [1]

$x+y=720$

$480+y=720$

$y=240$

So, The distance covered by train from New York city is x=480 miles

The distance covered by train from Louisville is y=240 miles.

Now put value of y in [3] to get time,

$t=\frac{y}{60}$

$t=\frac{240}{60}$

$t=4$

So, The time taken by train from Louisville is 4 hr.

The time taken by train from New York city is t+2=4+2=6 hr.

→ 6-4=2 hours will the slower train travel for before both trains will arrive at the same point.

7 0

3 years ago

What is 4and2/14 as an improper fraction in lowest terms

julia-pushkina [17]

Answer: 58 14ths

Step-by-step explanation:

multiply 14 by 4 to get 56 14ths, then add the 2

6 0

3 years ago

Read 2 more answers

Here are two datasets:

fiasKO [112]

Answer:

Option a) Mean

Mean is affected a lot by the change in the last observation as the median remains the same.

Step-by-step explanation:

we are given the following in the question:

Data set A: 64, 65, 66, 68, 70, 71, 72

Data set B: 64, 65, 66, 68, 70, 71, 720

For data set A, the mean and median are 68.

For data set B:

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1124}{7} = 160.57$

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data:

64, 65, 66, 68, 70, 71, 720

$\text{Median} = \dfrac{7+1}{2}^{th} \text{ term} = 4^th\text{ term} = 68$

Clearly, 720 is the is a outlier.

As seen mean is affected a lot by the change in the last observation as the median remains the same.

5 0

3 years ago

Teachers drive a mini-van. what percentage of the teachers drive a mini-van? (6.5B*) There are 60 teachers at Smith Middle Schoo

tekilochka [14]

20 o/o fndjdndbbbbbndndn

5 0

3 years ago

What is the difference between lcm and gcf and all of that help im doing it on my home work pls help i hate this stuff best answ

raketka [301]

greatest common factor=gcf

least common multule=lcm

with 12 and 16

factors of 12=2 times 2 times 3

factors of 16=2 times 2 times 2 times 2

greates common factor is 2 times 2=4

least common multiple means all factors combined minus repeats or 2 times 2 times 2 times 2 time 3=48

4 0

3 years ago