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scZoUnD [109]
3 years ago
9

Two trains leave stations 306 miles apart at the same time traveling toward each other one is traveling at 90 mph the other at 8

0 mph how long before they meet
Mathematics
1 answer:
Sergeu [11.5K]3 years ago
3 0

Answer:

They will meet in 1.8 hours.

Step-by-step explanation:

Given that, distance between trains = 306 miles

Let they take time 't' to meet each other.

Speed of first train = 90 mph

Speed of second train = 80 mph

Let distance traveled by first train = D_1 miles

Formula for distance:

Distance = Speed \times Time

Distance traveled by first train, D_1 = 90t

Let distance traveled by first train = D_2 miles

Formula for distance:

Distance = Speed \times Time

Distance traveled by first train, D_2 = 80t

Total distance traveled is 306 miles.

i.e.

D_1+D_2=306\\\Rightarrow 90t +80t=306\\\Rightarrow 170t=306\\\Rightarrow t =\dfrac{306}{170}\\\Rightarrow \bold{t=1.8\ hr}

They will meet in 1.8 hours.

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The interval (-1, 1) is best described as
Bad White [126]

Answer: There's an increasing interval between -1 and 1

While x goes from -1 to 1, the value of y increases (from -2 to 2).

7 0
3 years ago
2x+3y=1 and y=-2 - 9 solve using linear combination method. Please explain steps.
kaheart [24]

Answer:

x=17

Step-by-step explanation:

2x+3y=1

y=-2-9

  • In order to combine these two equations, an idea you need to keep in mind is finding a way of setting these equations as equal to each other. I saw that each equation shared a common value, y. In this case, we need to isolate y in the first equation so that both equations =y.

2x+3y=1

3y=-2x+1

\frac{3y}{3}=\frac{-2x+1}{3}

y=-\frac{2}{3}x+\frac{1}{3}

  • With this, we now know that both -2-9 and -\frac{2}{3}x+\frac{1}{3} are equal to y, so we can set them equal to each other.

y=-\frac{2}{3}x+\frac{1}{3}

y=-11

-\frac{2}{3}x+\frac{1}{3}=-11

  • Reply to this if anything I'm saying or doing is confusing in any way, or if you find a mistake. :) Solve for x.

-\frac{2}{3}x+\frac{1}{3}=-11

-\frac{2}{3}x=-11-\frac{1}{3}

-\frac{2}{3}x =-\frac{33}{3}-\frac{1}{3}

-\frac{2}{3}x =-\frac{34}{3}

-\frac{2}{3}x(-\frac{3}{2})=-\frac{34}{3}(-\frac{3}{2})

x=\frac{102}{6}=17

x=17

  • Hopefully this answer is correct AND makes sense in terms of how I achieved it. Again, reply to this with any questions or mistakes I made and I'll do my best to answer or fix them.

 

4 0
3 years ago
F(x) = x(x - 1)<br><br> g(x) = 3x<br> find (f*g)(6)
svetlana [45]

Step-by-step explanation:

<u>Given functions:</u>

  • f(x) = x(x - 1)
  • g(x) = 3x

<u>Find (f*g)(6):</u>

  • (f*g)(6) = f(6)*g(6) = 6(6 - 1)*3(6) = 30*18 = 540

<u>In case it is a composite function (f · g)(6) the answer is different:</u>

  • (f · g)(6) = f(g(6)) = f(3*6) = f(18) = 18*(18 - 1) = 306
4 0
2 years ago
Read 2 more answers
HELP A.S.A.P!!!! The data to represent average test scores for a class of 16 students includes an outlier value of 78. If the ou
kolezko [41]

When the outlier is removed The mean would increase.

<u>Step-by-step explanation:</u>

Outliers are the value that lies outside the set of data. i.e. the data doesn't fit in the group.

Removing outliers can affect mean more than median. Because outlier removal sometimes affect the median but in a small percentage or sometimes it will remain the same.

Let us prove, consider 16 values one with 78 and other 15 with values nearly 85, 84 that will give the mean value as 84.

78, 84, 82, 86, 84, 85, 83, 86, 82, 85, 84, 83, 86, 85, 86, 85.

Mean =\frac{Sum of the values}{Number of values}.

Mean =\frac{78+84+82+86+84+85+83+86+82+85+84+83+86+85+86+85}{16}.

Mean =\frac{1344}{16}.

Mean = 84.

Remove 78 from the data set then the data set is 84, 82, 86, 84, 85, 83, 86, 82, 85, 84, 83, 86, 85, 86, 85 and number of data is reduced to 15.

Mean =\frac{84+82+86+84+85+83+86+82+85+84+83+86+85+86+85}{15}.

Mean =\frac{1266}{15}.

Mean = 84.4.

The mean is increased.

8 0
3 years ago
A recipe calls for 3 cups of flour to make 2 batches of dinner rolls. One batch makes 15 rolls. Laura is making dinner for 12 pe
Maru [420]

Answer:

A

Step-by-step explanation:

3 cups of flour produces 2 batches of dinner rolls. So, if one batch makes 15 rolls, then 2 batches makes 30 rolls. Therefore, 3 cups of flour produces 30 rolls.

Laura wants to find how much flour she needs to make 12 rolls.

Here's the setup:

Let x be the number of cups of flour needed. Then,

(3 cups of flour)/(30 rolls)=(x cups of flour)/(12 rolls)

This is the set up for all equations involving ratios. The units should be consistent. Notice how I have flour/rolls=flour/rolls.

It is not necessary to solve the equation, but you should to make sure your answer makes sense. By cross-multiplying, we get x=(3*12)/30 or 1.2 cups.

This solution makes sense. Because 3 cups of flour produces 30 rolls, one cup produces 10 rolls. We need slightly more than 1 cup to get 12 rolls.

4 0
2 years ago
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