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2 years ago

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A subway train makes six stops of equal length during its 21 km run. The train is actually moving for 20 minutes of the trip. At

most how long can the train remain at each station if the average speed for the trip, including stops, is to be at least 36 km/hr?
$\frac{d}{t} = r$

1 answer:

photoshop1234 [79]2 years ago

3 0

Answer:

The subway train can stop for a maximum of 2.5 minutes on each stop.

Step-by-step explanation:

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How many solutions does the system of equations below have?

soldier1979 [14.2K]

Answer:

One solution

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

$\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }$

Simplify

$x = \dfrac{ 53 }{ 30 }$

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

$\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Now\:lets\:solve\:for\:"y"\:then}$

$y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}$

$y = \dfrac{ -5 \times 53 }{ 30 } +8$

$\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }$

$y = \dfrac{ -265 }{ 30 } +8$

$\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }$

$y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8$

$\mathrm{Simplify}$

$y = - \dfrac{ 53 }{ 6 } +8$

$\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53 }{ 6 }}$

$\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}$

$\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}$

$\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}$

$y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }$

$\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}$

$y = \dfrac{ -53+48 }{ 6 }$

$\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}$

$y = - \dfrac{ 5 }{ 6 }$

$\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53 }{ 30 }, - \dfrac{ 5 }{ 6 })}$

So there is only one solution to the equation.

5 0

1 year ago

Seven friends each bought a movie ticket for $14.95, popcorn for $6.99, and a drink for $2.25. How much did the friends spend in

VLD [36.1K]

Answer:

$169.33

Step-by-step explanation:

Each of the friends spent ...

$14.95 +6.99 +2.25 = $24.19

The seven friends together spent ...

7($24.19) = $169.33

5 0

1 year ago

Dad is 4 times as old as his son Jim. In 10 years, dads age will be 20 years mare than twice jims age. How old is Jim?

luda_lava [24]

10 is the answer I’m AssuminG

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2 years ago

Read 2 more answers

Please answer this correctly

Mrrafil [7]

Gary swam the fewest laps.
Hope this helps!

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2 years ago

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4 3/4 X 4 1/7 what is it please help

Y_Kistochka [10]

first you turn the fractions into inproper fractions by multiplying the whole number by the denomonator and adding the numerator

4×4=16

16+3=19

19/4

4×7=28

28+1=29

29/7

keep the denomonators the same. now that you've converted them into inproper fractions you can multiply them

19/4 × 29/7=551/28

there is no way to simplify this answer so this is the final answer

7 0

2 years ago