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4 years ago

Prove that if d|m and d|n, then d|(m+n)

1 answer:

5 0

$d\mid m$ means to say there is some $k_1$ such that $m=dk_1$ . Similarly, $d\mid n$ is equivalent to saying there exists $k_2[/te]x such that [tex]n=dk_2$ .

Now, $m+n=dk_1+dk_2=d(k_1+k_2)=dk_3$ , i.e. there is some $k_3$ such that $m+n$ is a multiple of $d$ , i.e. $d\mid(m+n)$ .

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3 How can you use mental math to find 14x3/4

Tamiku [17]

Turn 14 into a fraction which would be 14/1

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4 years ago

Name the mathematical property for an equation

kirza4 [7]

Answer:

There are four basic properties of numbers: commutative, associative, distributive, and identity.

I hope this helped :)

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4 years ago

Question 131 ptsIt takes a team of 8 workers 2 hours and 15 minutes to clean 12 apartments. Howmany apartments can the tearsclea

Amanda [17]

$48\:apartments\:in\:9\:hours$

1) In this problem, the first thing to do is to enlist the categories:

workers time to clean # apartments

8 2h15 12

8 9 x

2) Note that the number of cleaners is the same. So, we can pick the ratios that fall under the category time and #apartments

We need to convert that 2h 15 into decimal form before setting the ratios:

$2h15\:2+\frac{15}{60}=2.25$

3) Now, we can set the ratios and solve for x:

$\begin{gathered} \frac{2.25}{9}=\frac{12}{x} \\ 2.25x=12\cdot9 \\ \frac{2.25x}{2.25}=\frac{108}{2.25} \\ x=48 \end{gathered}$

Thus, the answer is 48

5 0

1 year ago

The steps below show the incomplete solution to find the value of x for the equation

monitta

The next step is most likely to add 3 to both sides, so that 3 cancels out, and 15 turns into 18.

The answer is: Step 4: 3x = 18
(I don't know if you want me to continue or not, but I will) ;)

Then divide by 3 on both sides so that 3 cancels out and 18 turns into 6, and you have the value of x.

Step 5: x = 6

You can check your answer by replacing x with 6.

5 · 6 - 2 · 6 - 3 = -2 + 17
15 = 15

Hope this helped! If you have anymore questions or don't understand, please comment or DM me. :)

5 0

3 years ago

the sum of any n consecutive integers is always equal to 100 less than the sum of the next n consecutive integers. Find n.

Salsk061 [2.6K]

When we have a given number k, the consecutive number to k will be (k + 1), the next consecutive will be (k + 2), and so on.

With this, we can find that the value of n is 100.

So here we have n consecutive numbers, let's assume we start with the number k, then the sum will be:

k + (k + 1) + ... + (k + n - 1)

Now we know that this is 100 less than the sum of the next n consecutive numbers.

For the next n consecutive numbers we need to start at k + 1, then we get:

(k + 1) + (k + 2) + ... + (k + n - 1) + (k + n)

If we take the difference we will get:

((k + 1) + (k + 2) + ... + (k + n - 1) + (k + n)) - (k + (k + 1) + ... + (k + n - 1)) = 100

As you can see, there are a lot of terms that are in both parentheses, then when we do that difference a lot of them cancel out.

So we will et:

((k + 1) + (k + 2) + ... + (k + n - 1) + (k + n)) - (k + (k + 1) + ... + (k + n - 1))

= (k + n) - k = k + n - k = n

And we knew that this difference must be equal to 100, then we have:

n = 100

We just found the value of n.

If you want to learn more, you can read:

brainly.com/question/1767889

3 0

3 years ago