8.3 + 2.7 Adding and Subtracting Decimals

FIFTY POINTS - It took 4 hours for a biker to travel from one city to another going at a certain speed. On the return trip, the

Crazy boy [7]

Answer:

Either 200 km or 160 km.

Step-by-step explanation:

Distance = speed × time

Let x = the biker's normal speed

Then

(1) d = 4x

For the return trip,

Time = distance/speed

(2) 4.5 = 100/x + (d -100)/(x - 10)

4.5x = 100/x + (4x -100)/(x - 10) Substituted (1) into (2)

4.5x = 100 + x(4x -100)/(x - 10) Multiplied each side by x

4.5x(x - 10) = 100(x - 10) + x(4x -100) Multiplied each side by (x - 10)

4.5x² - 45x = 100x - 1000 + 4x² -100x Removed parentheses

4.5x² - 45x = -1000 + 4x² Cancelled terms

0.5x² - 45x = -1000 Subtracted 4x² from each side

0.5x² - 45x +1000 = 0 Added 1000 to each side

x² - 90x +2000 = 0 Multiplied each side by 2

(x - 50)(x - 40) = 0 Factored the quadratic

x - 50 = 0 x - 40 = 0 Applied zero product theorem

x = 50 x = 40

Substitute in (1)

d = 4 × 50 = 200 km; d = 4 × 40 = 160 km

The distance between the two cities is either 200 km or 160 km.

Check:

x = 50 x = 40

4.5 = 100/50 + (200 - 100)/(50 - 10) 4.5 = 100/40 + (160 - 100)/(40 - 10)

4.5 = 2 + 100/40 4.5 = 2.5 + 60 /30

4.5 = 2 + 2.5 4.5 = 2.5 + 2

4.5 = 4.5 4.5 = 4.5

OK

8 0

3 years ago

Dr. Huey told Bob to drink 4 gallons of water everyday. After 7 days, how many gallons of water did Bob drink? (1 gallon = 3.79

love history [14]

Answer:

He should have drunk 28 gallons in 7 days

Step-by-step explanation:

This is pretty simple, so let's assume he drank 4 galloiljs of water a day. 4 gallons a day x 7 days

4*7

that is 28

8 0

3 years ago

Joseph has a collection of stickers. When the stickers are aranged in piles of 3, there are 2 stickers left over. When the stick

Elodia [21]

Answer:

2 stickers will be left over

Step-by-step explanation:

To answer the question, all you need to do is figure out at what value of stickers would the remaining stickers be equal to 2 if the piles are made up of either 3 to a set or 4 to a set. To do this, we need to figure out the size of the whole set of stickers.

Lets assume that the total number of stickers is 14. Lets test the 2 given conditions. If we divide it in piles of 3 then we will have a pile of 12 stickers (4 piles of 3 stickers each) with 2 stickers remaining.

Lets test the second condition. If we divide it in piles of 4, we will again have 12 stickers (3 piles of 4 stickers each) with 2 stickers remaining.

Now that both conditions have been satisfied, all we have to do is see how many stickers are left if we make a pile of 12 stickers. In this case, we will have just one pile of 12 stickers and, again, we will be left with 2 stickers.

Therefore, the answer is 2 stickers

6 0

3 years ago

Can someone please help me

Butoxors [25]

Answer:

1a. 58/99

1b. 53/90

1c. 29/50

Step-by-step explanation:

let's start with the easiest one

1.(c)

0.58 = 58/100 = 29/50

that is the simplest possible form, as 29 is a prime number and not a factor of 50.

1.(a)

0.585858585858... = 58×0.0101010101010101...

now, we know that 1/"double digit" (like 1/22) mostly produces a repeating pattern with a period length of 2 after the decimal point.

and we find

1/99 = 0.01010101010101...

so, our solution is

58 × 1/99 = 58/99

that is the simplest possible form, as 58 and 99 do not share any factors.

1.(b)

0.5888888888888... = 0.5 + 0.0888888888888... =

= 0.5 + 8×0.01111111111111... = 0.5 + 8×1/10 × 0.1111111111...

we know how to create 0.11111111111... :

1/9 = 0.111111111111111...

so, our solution is

0.5 + 8 × 1/10 × 1/9 = 0.5 + 8/90 = 5/10 + 8/90 =

= 45/90 + 8/90 = 53/90

this is the simplest possible form, as 53 is already a prime number and not a factor of 90.

8 0

2 years ago

Which conclusion can be made?

Pachacha [2.7K]

Step by step equation
Answer-

4 0

3 years ago