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blondinia [14]
3 years ago
6

If x is divided by 5 the remainder is 4. If why is divided by 5 the remainder is 1. What is the remainder when x+y is divided by

5
Mathematics
1 answer:
Naddik [55]3 years ago
8 0

Answer:

0

Step-by-step explanation:

We are given the following:

\frac{x}{5}=q_1+\frac{4}{5}      (equ. 1)

\frac{y}{5}=q_2+\frac{1}{5}      (equ. 2)

We are asked:

\frac{x+y}{5}=q_3+\frac{r}{5}  (equ. 3) , what is r?

The q_i's represent the quotients you get.

r is the remainder of dividing x+y by 5.

We know that r is a number in {0,1,2,3,4}.

x=5q_1+4 (I got this by multiplying both sides of equ 1. by 5.)

y=5q_2+1 (I got this by multiplying both sides of equ 2. by 5.)

Let's add these equations together:

x+y=(5q_1+5q_2)+(4+1)

Factoring the 5 out for the q_i's part and simplify 4+1 gives:

x+y=5(q_1+q_2)+5

So 5 can't be the remainder of dividing something by 5 but see that we can factor this right hand expression more as:

x+y=5(q_1+q_2+1)

So q_3=q_1+q_2+1 while there is no remainder (the remainder is 0).

Let's do an example if you are not convinced at this point that the remainder will be 0.

So choose x=9 since 9/5 gives a remainder of 4.

And choose y=16 since 16/5 gives a remainder of 1.

x+y=9+16=25 and 25/5 gives a remainder of 0.

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Answer:

The length and width of the parking lot is 78 meters and 114 meters respectively.

Step-by-step explanation:

Given;

Perimeter of the parking lot = 384\ m

Solution,

Let the width of the parking lot be x.

Then, according to question length = (x-36).

The perimeter of a rectangle is sum of all the sides of rectangle. Which is given by an expression;

perimeter=2\times(length+width)

Now substituting the values, we get;

384=2\times(x-36+x)\\\frac{384}{2}=(2x-36)\\192=2x-36\\192+36=2x\\2x=228\\x=\frac{228}{2}= 114

Width = 114\ m

Length = x-36=114-36=78\ m

Hence the length and width of the parking lot is 78 meters and 114 meters respectively.

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A sweater priced at $34.99 is on sale for 25% off. Find the cost with 7.5% sales tax.
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Step-by-step explanation:

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3 years ago
Solve for the hypotenuse in the right triangle shown.​
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Square root of 34

Step-by-step explanation:

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Question 696338: Please I need help solving an algebra: solving proportions
CHARITY Karthik spent $35 of his allowance and gave $5 to a charity. If the number of dollars he spends is proportional to the number of dollars he gives to charitt, how much of much of a $100-allowance will he give to a charity?
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Answer by stanbon(74715) About Me (Show Source):
You can put this solution on YOUR website!
Karthik spent $35 of his allowance and gave $5 to a charity. If the number of dollars he spends is proportional to the number of dollars he gives to charitt, how much of a $100-allowance will he give to a charity?
-----
x/100 = 5/35
----
6 0
3 years ago
Solve for b .<br><br> + b = -1<br> b =
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Answer:

b = -1

Step-by-step explanation:

Solve for b means, write in the form of b =...

Given

+ b = - 1 and this is the same as b = - 1.

That is because the plus sign has no real meaning here, so you can ignore it as if it was not there at all.

It so turns out you now have the answer!

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