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2 years ago

Explain how you know whether 1/15 is equal a terminating decimal or

Mathematics

1 answer:

Ulleksa [173]2 years ago

3 0

The lame answer is that you put it into a calcuator and see.

The more formal way you know is if, when the fraction is reduced, the denominator's only prime factors are 2s or 5s. If that's the case, the fraction will terminate. If you have any prime factor other than 2 or 5, it will repeat.

But knowing that "2 or 5 prime factor" idea would have to be something specifically taught in your class (or a prerequisite class).

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A collection of coins consists of nickels, dimes, and quarters. There are three fewer quarters than nickels and six more dimes t

weeeeeb [17]

Answer:

You have 15 dimes. You have 9 quarters. You have 12 nickels

Step-by-step explanation:

lets set some variables:

let "n" = the number of nickels

let "d" = the number of dimes

let "q" = the number of quarters

So, the total amount of money you have should be: $4.35 = 0.25q + 0.10d + 0.05n

Now let's look at the relationships between the coins:

"There are three fewer quarters than nickels": n - 3 = q

"six more dimes than quarters": q + 6 = d

So now you have three equations with three variables, all you need to do is solve.

$\left \{ {{4.35 = 0.25q + 0.10d + 0.05n} \atop {n - 3 = q}} \atop {q + 6 = d}}\right.$

first, you can substitute "n-3" for "q" (according to the 2nd equation) in the 1st and 3rd equation, you get:

$\left \{ {{4.35=0.25(n-3)+0.10d+0.05n} \atop {(n-3)+6=d}} \right.$

You now only have two equations and two variables.

Simplify:

$\left \{ {{4.35=0.25n-0.75+0.10d+0.05n} \atop {n+3=d}} \right.$

$\left \{ {{4.35=0.30n-0.75+0.10d} \atop {n+3=d}} \right.$

Now substitute "n+3" for "d" (according to the 2nd equation) in the 1st equation:

4.35=0.30n-0.75+0.10(n+3)

simplify:

4.35=0.30n-0.75+0.10n+0.30

4.35=0.40n-0.45

4.35+0.45=0.40n

4.80=0.40n

n=12

You have 12 nickels. Now sub "n" back into your equations to find the number of dimes and quarters:

n - 3 = q

12 - 3 = q

q = 9

You have 9 quarters.

q + 6 = d

9 + 6 = d

d = 15

You have 15 dimes.

3 0

3 years ago

Han is cycling at a speed of -8 miles per hour; if he starts at the same zero point, what will his position be after 45 minutes?

baherus [9]

Answer:

-6mph

Step-by-step explanation:

45 is 3/4hour so -8 times 3/4= -24/4=-6mph

7 0

3 years ago

A) Work out the value of 213 + (29)2

Alina [70]

a) 2^13 / 2^18

b) 216

6 0

2 years ago

In New York State's Quick Draw lottery, players choose between one and ten numbers that range from 1 1 to 80 . 80. A total of 20

amid [387]

Answer:

Step-by-step explanation:

7 0

3 years ago

Kenny wrote the equation for a linear relationship shown below

Ilia_Sergeevich [38]

Y would equal -17! Good luck!

4 0

2 years ago

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