Help :C Two cities are 45 miles apart. Two trains, traveling at speeds of 70 mph and 60 mph, leave the two cities at the same time and travel in the same direction so that the faster train will catch up to the other one. How long after the trains leave will the distance between them be 10 miles? How long after the trans leave will they be 10 miles apart for the first time? Help :(

Answers

Answer 1
Answer: 3.5 hours

=======================================================

Explanation:

Draw a horizontal number line. Plot point A at 0 and point B at 45 on the number line. The distance from A to B is 45 units to represent that 45 mile gap between the cities.

Let's say the trains travel to the right (aka to the east) along this number line train track. We'll place the faster train at location A, and the slower train at location B. This allows the slower train a head start. Eventually the faster train will catch up. If this was swapped and the trains still aimed to the right, then the trains will never be 10 miles apart.

-----------------------

Now we'll define two variables

x = number of hours that have elapsedy = the train's location on the number line

For the faster train at location A, which I'll just refer to "train A" from now on, we can form the equation y = 70x. I'm using the idea that distance = rate*time to help form this equation.

For example, if x = 2 hours have passed by, then train A is at location y = 70*2 = 140 miles on the number line train track.

Train B will have the equation y = 60x+45. The 60x is formed in a similar manner compared to the 70x. The plus 45 at the end is due to the 45 mile head start. In other words, train B travels 60x miles on top of the 45 miles already done so far.

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The two key takeaways from that last section is that we have these equations

y = 70xy = 60x+45

which correspond to the locations of train A and train B in that order.

Now to the question at hand: how can we determine when the trains are 10 miles apart? The short answer is through subtraction. Moreover, we'll need to involve absolute value to ensure that distance is never negative.

So the distance expression between the trains at any given time x is:

distance between trains = |trainA - trainB|

distance = |70x - (60x+45)|

distance = |70x-60x-45|

distance = |10x-45|

Next, we set that distance expression equal to 10 and solve for x.

distance = 10 miles

|10x-45| = 10

10x-45 = 10 or 10x-45 = -10

10x = 10+45 or 10x = -10+45

10x = 55 or 10x = 35

x = 55/10 or x = 35/10

x = 5.5 or x = 3.5

-----------------------

Those two results mean that at the hour marks of 3.5 hours and 5.5 hours is when the two trains are 10 miles apart exactly.

The two trains start off being 45 miles apart. They both take off and train A will catch up to train B. Their gap will be 10 miles at the 3.5 hour mark. That gap shrinks to 0 at some point, and then grows again afterward. By the 5.5 hour mark is when the trains are again 10 miles apart. This time is when train A is in the lead and will remain so assuming the speeds stay the same.  

It seems like your teacher is only concerned with when the trains are 10 miles apart for the first time and not the second. So your teacher is likely only expecting one answer and that would be 3.5 hours

Side notes:

3.5 hours = 3 hours, 30 minutes = 210 minutes.5.5 hours = 5 hours, 30 minutes = 330 minutes.Multiply by 60 to convert from hours only to minutes only.

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1 /5

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Answer:

12(2A+B)=12*3

Step-by-step explanation:

Answer:

[tex]12[/tex]

Step-by-step explanation:

We know that [tex]24=12*2[/tex], [tex]12=12*1[/tex], and [tex]36=12*3[/tex].

So, we can re-write the equation as [tex]12*2*A+12*1*B=12*3[/tex].

We can factor out a [tex]12[/tex] from both sides to get [tex]12(2A+B)=12(3)[/tex].

The insides can't be simplified anymore, so the final equation is [tex]12(2A+b)=12(3)[/tex] and the gcf is [tex]\boxed{12}[/tex]

Please help me with number 1!

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How do I use FOIL? I get lost every time...especially with exponents

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Here is the foil method, I hope it helped

i need to find the values of X but there isn’t another expression to find x for 180°

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Answer:

x=5

Step-by-step explanation:

In this equation, we need to find x. According to the Vertical Angles Congruence Theorem, all vertical angles are congruent. Therefore, because angles (2x+12) and (8x-18) are vertical angles, they are congruent. We can set this up as an equation and simply solve for x:

2x+12=8x-18   Subtract 2x from both sides.

-2x      -2x

12=6x-18         Add 18 to both sides.

+18    +18

30=6x             Divide both sides by 6.

/6   /6

5=x

I hope this helps!! Have an amazing day :)

Answer:

x = 5

Step-by-step explanation:

The two angles have the same degree because of the Vertical Angles rule. This means that if angles are vertical, then they are congruent. Therefore, we can solve for x by setting the two angles equal to each other.

2x + 12 = 8x - 18

    + 18         + 18

2x + 30 = 8x

-2x          -2x

30 = 6x

÷6    ÷6

5 = x

We can then double check this by inputing x back into the equations

2x + 12 = 2(5) + 12 = 10 + 12= 22

8x - 18 = 8(5) - 18 = 40 - 18 = 22

These check out so x = 5

I hope this helped :)

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Answer:

x=15

Step-by-step explanation:

Rate as BRAINLIEST

JM = 4x-29

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4x -29 = 1 +2x

2x -29 = 1

2x = 30

x = 15

ײ+6×+9=0 in Discriminant and nature of the roots

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Answer:

D = 0, x = -3

Step-by-step explanation:

D = b*b - 4ac = 36 - 4*9 = 36 - 36 = 0

x = -b/2a since D = 0, so

x = -6/2 = -3

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Answer:

5^7 or 78125

Step-by-step explanation:

100+1133232323232332323232

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Answer:

1133232323232332323332

Step-by-step explanation:

Answer: 1133232323232332323332

Step-by-step explanation:

Ben wants to have his birthday at the bowling alley with a few of his friends, but he can spend no more than $80. The bowling alley charges a flat fee of $45 for a private party and $5.50 per person for shoe rentals and unlimited bowling. Write an inequality that represents the total cost of Ben's birthday for p people given his budget. Use your inequality to solve for how many people Ben can pay for (including himself) while staying within the limitations of his budget? *

Answers

Answer:

He can pay for 5 friends plus himself while staying within the budget.

Step-by-step explanation:

No parents are allowed in.

45 + 5.5p = 80    80-45=35   5.5p = 35   35/5.5 = 6.4

So he can pay for himself plus 5 people, and probably a drink.

Hope this helps!

Solve the system.
x + 4y +z = 12
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z = 3
Enter your answer as an ordered triple.
([ ? ], [ ], [ ]

Answers

Answer:

([ 1 ], [ 2 ], [ 3 ])

Step-by-step explanation:

y – 3z = -7; z = 3 => y = 2

x + 4y +z = 12 => x + 4(2) + 3 = 12 => x = 1

([ 1 ], [ 2 ], [ 3 ])

[tex](x^{2} +1)(x^{2} -1)^{6}[/tex]

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X^4 - 5x^12 + 9x^10 - 5x^8 - 5x^6 + 9x^4 - 5x^2 + 1

Answer:

(x²+1)(x²-1)⁶ = x¹⁴-5x¹²+9x¹⁰-5x⁸-5x⁶+9x⁴-5x²+1

Step-by-step explanation:

Pascal triangle 6th row for (a + (-b))⁶;  ... for (x²-1)⁶

a⁶+6a⁵(b)¹+15a⁴(b)²+20a³(b)³+15a²(b)⁴+6a(b)⁵+1*(b)⁶   .. a=x²   b = -1

= x¹²+6x¹⁰(-1)¹+15x⁸(-1)²+20x⁶(-1)³+15x⁴(-1)⁴+6x²(-1)⁵+1*(-1)⁶

= x¹²-6x¹⁰+15x⁸-20x⁶+15x⁴-6x²+1

(x²+1)(x²-1)⁶ = (x²+1)(x¹²-6x¹⁰+15x⁸-20x⁶+15x⁴-6x²+1)

                  = x¹⁴-5x¹²+9x¹⁰-5x⁸-5x⁶+9x⁴-5x²+1

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Answer:

[tex]\sf The \: answers\: are \:attached[/tex]

_________________

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Answers

Answer:
X = -30,000

Step by step explanation;

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- 31424. -31424
(Subtract 31424 on both sides)

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a baker is making cupcakes. he has 36 pounds of dough. each cupcake is made from ⅙ pound of dough. how many cupcakes can be made?

explain with answer​

Answers

Answer:

First you have to understand a one cupcake has 1/6 pound of dough.

Then to calculate the number of cupcakes, divide the total 36 pounds of dough by a 1/6 pound.

36/(1/6)

= 36 ×(6/1)

= 216 cupcakes

Answer: 216 cupcakes can be made

Step-by-step explanation:

Given information

36 pounds of dough in total

⅙ pound of dough per cupcake

Set variables

Let x be the number of cupcakes that could be made

Set equations from given information

Total = unit × number

36 = (1/6) × x

Multiply 6 on both sides to isolate [x] variable

36 × 6 = (1/6) × x × 6

216 = 1 × x

[tex]\boxed{x=216}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

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Answer:

Step-by-step explanation:

9x-1 + 5x-15 =180, 14x-16=180, x = 14

9x-1 + y-20 = 180, 126-1-20+y =180, y = 105

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An input-output machine generates the information below

a- Find the values to fill in the table for variables a and b
b- write up a rule that describes the relationship between the input output.
c- what is the value of the output and input in 20?
d- what is the value of the input when the output is 77.

Answers

Using a linear function, we have that:

a) The values are: a = 11 and b = 5.

b) The rule is:

[tex]y = 3x + 2[/tex]

c) The value of the output is 62.

d) The value of the input is 25.

The equation of a linear function is given by:

[tex]y = mx + b[/tex]

In which

m is the slope, which is the rate of change.b is the y-intercept, which is the initial value.

First, we are going to solve item b to find the rule, then we solve other items.

Item b:

In the table, we have two points: (1,5) and (2,8).

The slope is given by change in y divided by change in x, thus:

[tex]m = \frac{8 - 5}{2 - 1} = 3[/tex]

Then

[tex]y = 3x + b[/tex]

Point (1,5) means that when [tex]x = 1, y = 5[/tex], and this is used to find b.

[tex]5 = 3(1) + b[/tex]

[tex]b = 2[/tex]

Thus, the rule is:

[tex]y = 3x + 2[/tex]

Item a:

a is the value of y when x = 3, thus:

[tex]y = a = 3(3) + 2 = 11[/tex]

Thus, a = 11.

b is the value of x when y = 17, thus:

[tex]3b + 2 = 17[/tex]

[tex]3b = 15[/tex]

[tex]b = 5[/tex]

The values are: a = 11 and b = 5.

Item c:

The value of the output is y when x = 20, thus:

[tex]y = 3(20) + 2 = 60 + 2 = 62[/tex]

Thus, the value of the output is 62.

Item d:

The value of the input is x when y = 77, thus:

[tex]3x + 2 = 77[/tex]

[tex]3x = 75[/tex]

[tex]x = \frac{75}{3}[/tex]

[tex]x = 25[/tex]

The value of the input is 25.

A similar problem is given at https://brainly.com/question/25004958

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The picture is to small.

Step-by-step explanation:

To small.

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If the bigger one is 24 inches, and the bigger one is two times the size of the smaller one, the smaller one is 12 iches

If 1llm, find the value of y

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Answer:

y = 70°

Step-by-step explanation:

4x - 50 and 2x + 30 are equal, because they are corresponding angles

4x - 50 = 2x + 30

4x = 2x + 80

2x = 80

x = 40°

The angle below 2x + 30 = y, because they are vertical angles

Since we know what x is, we can substitute x from 2x + 30

And since two angles that take up a line are 180°, we can add them

2(40) + 30 + y = 180

80 + 30 + y = 180

110 + y = 180

y = 180 - 110

y = 70

-Chetan K

Describe how to solve d = rt for t

Answers

Answer:

t = d/r

Step-by-step explanation:

Given the equation, d = rt for t:

Switch sides:

rt = d

Divide both sides by r to isolate t:  

[tex]\frac{rt}{r} = \frac{d}{r}[/tex]

t = d/r

the distance of a trip
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Answer:

T-.5 = x (200)

Step-by-step explanation:

Let T = total time in hours

30 mn = .5 hours  30 /60 = .5

$ 2.00 is the rate per hour.

so  T − .5 =  the time that will be charged at the rate

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Answer:

4m8n8p6

Step-by-step explanation:

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it is 2.35

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Answer:

60000

Step-by-step explanation:

56763 so you're going to take that number and you're going to run it to the nearest thousands by doing that you're going to take the six and six is either closest to zero or 10 and it is closer to 10 which would be your answer so you're going to add these zero replacing the six seven six and three in the equation and making me five of six by adding the one from the number 10 if you have any other questions text me if that doesn't make sense

the answer is 57,000 !!

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Find the angle
25 points for you plus a brainliest, thanks and 5 star

Answers

Answer:

? =64.62306

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent side / hypotenuse

cos ? = 3/7

Taking the inverse cos of each side

cos ^-1 ( cos ? ) = cos ^-1 (3/7)

? =64.62306

Answer:

The angle is approximately 23°

Step-by-step explanation:

let the angle be ∆

using trigonometrical identity,

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Answers

Answer:

6.71

Step-by-step explanation:

Using the distance formula:

[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

= √(-1-5)^2 + (8-5)^2

= √36 + 9

= √45

= 3√5 <- Optional

= 6.70820393

≈ 6.71

Hope this helps and be sure to have a wonderful time ahead at Brainly! :D

Answer:

[tex]3\sqrt{5}[/tex]

Decimal form: 6.70820393 …

Step-by-step explanation:

The length of this line can be found by using the distance formula:

[tex]{\sqrt (}(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})[/tex]

Step 1: Plot the coordinates of both points.

Step 2:  Evaluate the x-axis and y-axis distance between the points.

Step 3:  Square both results.

Step 4: Add the squared results.

Step 5: The answer lies in the square root of the equation.


7)
Is MNO similar to PQO

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Answer:

Where is your attachment or question

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