Answers please ASAP !!!!

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 16 miles per hou

Verizon [17]

We'll use variables to represent the speeds of the eastbound and westbound trains.

x will represent the speed of the eastbound train.
y will represent the speed of the westbound train.

The eastbound train is 16 mph faster than the westbound train. An equation can be made from this:

$x - y = 16$

Subtraction is used, because it represents the difference in distances between the two trains if they travel the same direction.

After 4 hours, the trains are 800 miles apart. An equation can be made from this:

$4x + 4y = 800$

Addition is used, because the trains are heading in opposite directions, which means their distances from the starting point are added together.

Set the two equations up vertically:

$x - y = 16$
$4x + 4y = 800$

We will use elimination to solve for x.

Multiply the entire first equation by 4 so that the coefficients for y will be opposite numbers:

$(x - y = 16) \times 4 = 4x - 4y = 64$

$4x - 4y = 64$
$4x + 4y = 800$

Combine the two equations together to cancel out y:

$8x = 864$

Divide both sides by 8 to get x by itself:

$x = 108$

The speed of the eastbound train is 108 mph.

5 0

3 years ago

Factorise: 5(2^n)+2^n+2

marin [14]

Answer:

2 ( n + 2 ) ( n + 1 2 )

Step-by-step explanation:

coefficient of the first term:

2 = 2 × 1

coefficient of the last term:

2 = 2 × 1

coefficient of the middle term (using only the factors above):

5 = 2 × 2 + 1 × 1

2 n 2 + 5 n + 2 = ( 2 n + 1 ) ( n + 2 )

Alternative method:

Treat the given expression as a quadratic set equal to zero, with the form

a n 2 + b n + c

and use the quadratic formula

− b ± √ b 2 − 4 a c 2 a

This will given solutions

n = − 2 and n = − 1 2

for a factoring

2 ( n + 2 ) ( n + 1 2 )

Hope this helped

3 0

2 years ago

A gust of wind forces a rock to fall off a cliff that's 20 feet high. This is represented by the function h(t) = –16t2 + 20, whe

Helga [31]

Answer: C.) 1.12 seconds

Step-by-step explanation:

Hi, to answer this question we have to substitute h=0 (when the rock hits the ground the height above it is 0) in the equation given:

h (t) = –16t2 + 20

Solving for t (time)

0= –16t2 + 20

16t2=20

t2=20/16

t=√1.25 =1.12 seconds (option C)

Feel free to ask for more if needed or if you did not understand something.

8 0

2 years ago

Dimensional Analysis

Firlakuza [10]

Answer:

$5.058 USD/gal
$60.70 USD to fill the tank

Step-by-step explanation:

You want to know the cost per gallon of gas and the cost for 12 gallons of gas when the cost per liter is $1.31 CDN and the exchange rate is $1.02 USD per CAD.

<h3>Cost per gallon</h3>

The conversion between liters and gallons is ...

1 US gallon = 3.785411784 liters (exactly)

Then the cost conversion is ...

$\dfrac{\$1.31\text{ CAD}}{1\text{ L}}\times\dfrac{3.785411784\text{ L}}{1\text{ gal}}\times\dfrac{\$1.02\text{ USD}}{\$1.00\text{ CAD}}\approx\boxed{\$5.058\text{ USD/gal}}$

The cost per gallon in terms of US dollars is about $5.06.

The cost for 12 gallons will be ...

(12 gal)×($5.058 /gal) ≈ $60.70

It will cost you $60.70 to fill your 12 gallon tank.

__

<em>Additional comment</em>

The price of gas is routinely specified to tenths of a cent, both in the US and in Canada. As of today, the cost of gas in Canada has declined to $1.864 CAD/liter. At today's exchange rate of about $0.77 USD per CAD, the equivalent price is $5.406 USD/gal.

8 0

1 year ago

Pouvez vous maider pour la questuon deux merci

Vanyuwa [196]

quelle est ta question?

6 0

2 years ago