5. A train travels two different routes: the North Route and the South Route. • On Monday, the train traveled the North Route 8 times and the South Route 10 times, traveling a total of 410 miles. • On Tuesday, the train traveled the North Route 15 times and the South Route 11 times, traveling a total of 575 miles. How long is each route?

Answers

Answer 1

Answer:

North Route is 20 miles, and South Route is 25 miles.

Step-by-step explanation:

Let the length of the North route be represented by x and that of the South route be represented by y.

On Monday,

8x + 10y = 410

On Tuesday,

15x + 11y = 575

So that,

8x + 10y = 410 .............. 1

15x + 11y = 575 ......... 2

Using substitution method, from equation 1;

x = [tex]\frac{410 - 10y}{8}[/tex] ................. 3

Substitute the expression for x into equation 2,

15([tex]\frac{410 - 10y}{8}[/tex]) + 11y = 575

multiply through by 8,

6150 - 150y + 88y = 4600

6150 - 62y = 4600

6150 - 4600 = 62y

1550 = 62y

divide through by 62 to have,

y = 25

Substitute the value of y in equation 3

x = [tex]\frac{410 - 10y}{8}[/tex]

  = [tex]\frac{410 - 10(25)}{8}[/tex]

  = 20

x = 20

Thus, North Route is 20 miles, and South Route is 25 miles.


Related Questions

Please answer correctly !!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

Answer:

snisisbshdgsbsjsiejbebdbxhhxdyud

Step-by-step explanation:

sorryrydhehsindebbdhddhdb

plz help me asap i need help plz i will mark you as brainlist

Answers

Answer:

the third one

Which range contains the value of sqrt(25-4+16)?
A. Between 6.0and 6.2
B. Between 6.9 and 7.1
C. Between 2.1 and 2.3
D. Between 18.4 and 18.6

Answers

Answer:

I wanna say C. But I'm not exactly sure.

Step-by-step explanation:

I hope it's right :(

NEED HELP ASAP! GIVING BRAINLEST TO THE CORRECT ANSWER! MY BRAINLEST IS GIVING 100 POINTS TO THE PPL WHO ANSWER CORRECTLY
Select the real-world problem that could be solved using a proportion.

A Sheila travels 180 miles in 3 hours. At this rate, how far will she travel in 7 hours?

B Sheila must pay $180 for a phone and then $60 each month for service. How much will she have paid after 7 months?

C Sheila has 3 pens and 7 pencils. How many more pens does she need to make the number of pens and pencils she has equivalent?

D Sheila has 3 dogs and adopts 1 more. How many dogs does she have in total?

Answers

Answer:

A Sheila travels 180 miles in 3 hours. At this rate, how far will she travel in 7 hours?

Step-by-step explanation:

[tex]\frac{180 miles}{3 hours} = \frac{x miles}{7 hours}[/tex]

Find the value of 16 2/3% of Rs.4500​

Answers

Answer:

Rs 750 .

Step-by-step explanation:

We need to find 16 ⅔ % of Rs 45,00 .

So , we can write 16 ⅔ % as 50/3 %.

= [tex]\dfrac{50}{\cancel3}\times Rs ,\cancel{ 4500 }^{1500}\times\dfrac{1}{100}[/tex]

=[tex]\red{ Rs 750 }[/tex]

Please help me solve these problems! I'll give you all my brain points. IM DESPERATE!!!
:-;

Answers

Answer: kg

Step-by-step explanation:

please help thanks in advance

Answers

Answer:

43.25

Step-by-step explanation:

Since sides DF and FE are congruent, their opposite angles D and E are also congruent.

m<D + m<E + m<F = 180

x + x + 93.5 = 180

2x = 86.5

x = 43.25

Answer: 43.25


[tex]( \sin^{2} ( \frac{\pi}{ 4 } - \alpha ) ) = \frac{1}{2} (1 - \sin(2 \alpha ) )[/tex]
Prove​

Answers

Step-by-step explanation:

[tex] \sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

Use the identity

[tex] \sin^2 \theta = \dfrac{1 - \cos 2\theta}{2} [/tex]

on the left side.

[tex] \dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

[tex] \dfrac{1 - \cos (\frac{\pi}{2} - 2\alpha)}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

Now use the identity

[tex] \sin \theta = \cos(\frac{\pi}{2} - \theta) [/tex]

on the left side.

[tex] \dfrac{1 - \sin 2\alpha}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

[tex] \frac{1}{2}(1 - \sin 2\alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

Can a negative number have a positive factor?

Answers

Answer:

The laws of multiplication state that when a negative number is multiplied by a positive number, the product will be negative. So, if considering a factor pair of a negative product, one of these factors must be negative and the other factor must be positive.

one has to be positive one has to be negative

five and six eights + four and 4 fiths please answer ill give 10 points

Answers

Answer:

29/5

Step-by-step explanation:

Answer:

10 11/20

Step-by-step explanation:

ten and eleven twentieths

what is the awnser pls help

Answers

Answer:

I think its B 216

Step-by-step explanation:

Because you multiply 12×9×2 and get 216 (I dont know if im right)

The average person laughs 15 times per day.

Answers

really? i didn’t know.
Gosh I need to start laughing more then

NEED HELP ASAP PLEASEE

Answers

Answer:

can u make a more clear picture ?

Step-by-step explanation:

Create an expression that would represent the area of the triangle

Answers

Answer:

96cm

Step-by-step explanation:

A=1/2bxh (Area=BasexHeight) is the formula to find it.

A=1/2x192

A=96

Nadine and her sister received the
same amount of money to go out to
eat. Each girl spent $12. After
lunch, the girls had a total of $16.
Write and solve an equation to find
the amount of money each girl
received.

Answers

Answer:

2(x - 12) = 16

Step-by-step explanation:

They each had $20 to spend.

Please only answer if you know

Answers

Answer:

A, C

Step-by-step explanation:

A.)

32 / 8 * 5.25 ----> 4 * 5.25 ----> 21

C.)

4 * 12.5 / 2----> 49 / 2 ----> 24.5

Answer:

between 20 & 30?

A & C  

Step-by-step explanation:

A) 32 / 8 * 5.25 = 21

B) -18 / 6 * 9 = -27

C) 4 * 12.5 / 2 = 25

D) 12 * 4[tex]\frac{1}{3}[/tex] / -2 = -26

The quotient of a number increased by 9and 4 is -2 TRANSLATE DO NOT SOLVE please answer I really need this

Answers

Answer: From your questions it's stand like factors of that Number so it is one

3=1

5/9=1

4=1,2

Addition point

Quotient is the number remained after divident is divided by divisor

Step-by-step explanation:

John bought a play station game for $54.50. The tax on the game is 5%. What
is the total cost of the play station game, including the tax?

Answers

Answer:

1089/20 (Decimal: 54.45)

Answer:

$57.22

Step-by-step explanation:

$2.72 would be 5% of 54.50

The total cost would be

54.50 + 2.72

that would equal

57.22

How do you do an area model of 15 times 11

Answers

Make a rectangle, one set of parallel sides should be longer than the other, then, make the length (long side) 15, and the width (short side) 11. label them, and in order to find the area, multiply the length, by the width (15 x 11)

Which input value produces the same output value for
the two functions?
O x=-12
O x=9
O x=-6
Ox=-3

Answers

Answer:

-6

Step-by-step explanation:

Took test

At x = -6, both functions have the same output of 3.

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, We get;

f(x) = 2/3x + 7

when x = -12;            

     = 2/3(-12) + 7                                      

     = -8 + 7                                            

     = -1                                                    

g(x) = 2x + 15....

when x = -12

= 2(-12) + 15

= -24 + 15

= - 9

When x = -9;                      

f(x) = 2/3(-9) + 7                              g(x) = 2(-9) + 15

     = -6 + 7                                             = -18 + 15

     = 1                                                     = -3

When x = -6;

f(x) = 2/3(-6) + 7                             g(x) = 2(-6) + 15

     = -4 + 7                                            = -12 + 15

     = 3                                                   = 3

Thus, At x = -6, both functions have the same output of 3.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

e - i = 5
e + 3i = 9
e value =
i value =
What is the answer

Answers

Answer:

e value = 6

i value = 1

Step-by-step explanation:

The system of equation are;

e - i = 5...(1)

e + 3·i = 9...(2)

Making e the subject of equations (1) and substituting the value of e equation (2) gives;

From equation (1), e - i = 5, we have, e = 5 + i

Substituting the value of e in equation (2), e + 3·i = 9 gives;

e + 3·i = (5 + i) + 3·i = 5 + 4·i = 9

4·i = 9 - 5 = 4

i = 4/4 = 1

i = 1

From e = 5 + i, we have;

e = 5 + i = 5 + 1 = 6

e = 6

Therefore;

e value = 6

i value = 1

Please give an answer this question is worth 20 points on my test

Find the equation for each line.

Answers

Line l: y=4
Line n:y=x-4
Line p: x=-4
Line m: y=4-2x

Hope this helped!

for the equation 2x² -11x+9=0 solve for x using AC method , completing the square, and the quadratic formula
help please

Answers

Answer:

x=1, 4.5

Step-by-step explanation:

-(-11)plus/minus square root of (-11)^2-4(2)(9) divided by 2 times 2

Triangle ABC has an altitude AH that lies in the exterior of the triangle which of the following could be true about this figure

Answers

Answer:

In triangle ABC, angle B is obtuse.

Step-by-step explanation:

The type of triangle is obtuse, angle A and C are acute, angle B is obtuse.

Complete the inequality with >, <, or =.

72 _____ 34

Answers

Answer:

>

Step-by-step explanation:

which ever the arrow is opening up to, is the greater number bro

Larissa plans to bake at most 10 loaves of bread. She makes x loaves of banana bread that sell for $1.25 each and y loaves of nut bread that sell for $1.50 each. She hopes to make at least $24 in sales. Write and graph a system of inequalities for this situation. What does the graph show?

Answers

Answer:

1) The system of inequalities are;

x × 1.25 + y × 1.5 ≥ 24

x + y ≤ 10

Please find attached the required graph of the two inequalities ,created with Microsoft Excel

2) The graph of inequality shows that Larissa cannot to make less than 10 loafs of bread and sell them for over $24 at the given prices of each loaf of bread

Step-by-step explanation:

1) The maximum number of loaves Larissa plans to make = 10

The price at which she sells each of x loaves of banana bread = $1.25

The price at which she sells each of y loaves of nut bread = $1.50

The total amount she hopes to make = $24

The system of inequalities are;

x × 1.25 + y × 1.5 ≥ 24

x + y ≤ 10

Making y the subject of both inequalities gives;

For the first inequality, we have,

y ≥ 24/1.5 - 1.25/1.5·x which gives;

y ≥ 16 - 5/6·x

For the second inequality, we have,

y ≤ 10 - x

Please find attached the required graph of the two inequalities

2) From the attached graph of inequality, created with Microsoft Excel, it shows that it is not possible for Larissa to make less than 10 loafs of bread and at the same time sell them for over $24 if the price of each banana bread is $1.25 and the price of each nut bread is $1.50.

please help. problem involving magic squares

Answers

Step-by-step explanation:

First, let us find the magic sum in each row/column/diagonal.

Sum of numbers from 1 to 9 = 45.

45 divide by 3 rows = 15 each row.

The magic sum is 15.

For the diagonals, we have:

8 + 5 + x = Magic sum = 15,

6 + 5 + y = Magic sum = 15.

Therefore x = 2 and y = 4.

In one game of basketball Henry scored 24 points.
How many points would Henry score if he played 3 games of
basketball?

Answers

Answer:

72

Step-by-step explanation:

24 x 3 = 72 just like the problem.

i need to find the points for a graph asap by finding the asymptote!!!

Answers

Answer:

y=0

Step-by-step explanation:

Exponential functions, always have a horizontal asymptote. A function of the form f(x) = a (b^x) + c always has a horizontal asymptote at y = c. In this case the function is

[tex]y=3^{x+2} \\\\We\ can\ rewrite\ it\ like\\\\\y=3^x.3^2\\y=9(3^x)[/tex]

so it doesn't have a +c which means the horizontal asymptote is y = c = 0

y = 0 is the horizontal asymptote

Tanisha has 16 books she wants to read. She reads One Fourth of them. How many books has Tanisha read?

Answers

Answer:

Im guessing she reads 64 of the book

16 divided by 1/4 = 64

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The main criticism of the Articles of Confederation was that they failed toA. provide adequate powers for the central governmentB. prevent the development of military ruleC. allow for the admission of new statesD. limit the powers of the president5. In the 1780s, the national government under the Articles of Confederation established its authority in the Northwest Territory byA. settling the border dispute with MexicoB. rejecting Native American Indian claims of sovereigntyC. extending the nations border to the Rocky MountainsD. providing a system for the formation of new states6. A principal reason for calling the Constitutional Convention of 1787 was toA. strengthen the central governmentB. increase the power of the statesC. weaken the system of checks and balancesD. settle land disputes with Canada7. 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