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hichkok12 [17]
3 years ago
7

Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod d.

Mathematics
1 answer:
masya89 [10]3 years ago
6 0
From the rules of modular arithmetic, (A+B)mod C= (A)modC +(B)modC

So,  (m + dk) mod d =  (m) mod d+<span> (dk) mod d

clearly </span>(dk) mod d = 0, as one of the things (dk) mod d represents, is the remainder of dk, when divided by d, which is clearly 0.


Thus

(m + dk) mod d =  (m) mod d+ (dk) mod d= (m) mod d+ 0=(m) mod d


(m + dk) mod d =(m) mod d
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R + 3 1/2 = -4 2/3
alexandr402 [8]

Answer:

R = -8 1/6

Step-by-step explanation:

We'll solve the given equation for R.

Subtract 3 1/2 from both sides of the equation, to isolate R:

           R +  3 1/2  -  3 1/2 = -4 2/3  - 3 1/2, or

            R = -4 2/3 - 3 1/2

The LCD here is 6, which is the product of 3 and 2.  Converting the fractions to denominator 6, we get:

              R = -4 4/6 - 3 3/6, or

               R = -7 - 7/6, or R = -7 - 1 1/6, or -8 1/6

3 0
3 years ago
PLEASE HELP ASAPPP !! Instructions: State what additional information is required in order to know that the triangles are congru
Svetllana [295]
<h3>Answer: angle T = angle W</h3>

Explanation:

We are given the sides are congruent due to the tickmarks. Specifically

TU = WV (single tickmarks)

TV = WX (double tickmarks)

So we just need the "A" of "SAS". The A is between the two S letters, so the angle is between the two sides. For triangle TUV, the angle T is between the two sides with the tickmarks. Similarly, angle W is between the tickmarked sides of triangle WVX.

If we know that angle T = angle W, then we have enough information to use SAS.

5 0
4 years ago
Shelly can cut a lawn with a riding mower in 22 hours less time than it takes william to cut the lawn with a push mower. if they
umka2103 [35]
Let n be the amount of time it takes william to cut the lawn. Then Shelly takes
n-2 hours. So:
1/n+1/n-2=1/3
3(n-2)+3n=n²-2n
6n-6=n²-2n
n²-8n+6=0
Using the quadratic formula, we get a positive value of 7.1623 hrs as the amount of time william takes working alone, and 5.1623 as the amount  of time Shelly takes working alone
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7 0
3 years ago
If f(x)=2x+5, then what is f(3)?
FromTheMoon [43]

Answer:

\Large \boxed{f(3)=11}

Step-by-step explanation:

f(x)=2x+5

For f(3), the input for the function f(x) is 3.

Let x (input) = 3.

f(3)=2(3)+5 \\\\ f(3)=6+5 \\\\ f(3)=11

7 0
3 years ago
Read 2 more answers
54 thousands 6 hundreds 12 tens – 15 thousands 8 hundreds 26 tens = ________(1 Point)
Afina-wow [57]

Answer:

38,660

Step-by-step explanation:

54 thousands 6 hundreds 12 tens – 15 thousands 8 hundreds 26 tens

54 thousands = 54000

6 hundreds = 600

12 ten = 12*10 = 120

54 thousands 6 hundreds 12 tens = 54000+600+120 = 54720

15 thousands = 15000

8 hundreds = 800

26 tens = 26*10 = 260

15 thousands 8 hundreds 26 tens = 15000+800+260 = 16060

Thus,

54 thousands 6 hundreds 12 tens – 15 thousands 8 hundreds 26 tens

= 54720- 16060 = 38,660 (Answer)

3 0
3 years ago
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