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igor_vitrenko [27]
3 years ago
9

Prove that the product of any three consecutive numbers is even.

Mathematics
1 answer:
mestny [16]3 years ago
4 0

Answer:

The product of three consecutive numbers is essentially the product of an odd number and an even number.

The product of an odd number and an even number is always even.

Explanation:

Consecutive numbers follow a pattern - they alternate between odd and even. (Any number sequence goes: ... odd, even, odd, even, odd ...)

With three consecutive numbers, there are two combinations:

1. odd, even, odd

2. even, odd, even

Remember these rules:

The product of two odd numbers is always odd.

The product of two even numbers is always even.

***The product of an odd number and an even number is always even.

Simplify the equations of consecutive numbers with the rules.

odd X even X odd

= even X (odd)(odd)

= even X odd

= even

even X odd X even

= odd X (even)(even)

= odd X even

= even

***Why this rule works:

In any multiplication statement, the multiplication sign means "groups of".

For example, 5 times 3 = 5 groups of 3.

An even number means, like if a number was represented by number of people, everyone would have a partner.

odd X even means "odd# groups of even # people".

Within each group, everyone already has a partner. It does not matter how many groups there are.  Therefore it's an even number.

even X odd means "even# groups of odd # people".

In this model, there is a leftover person in each of the groups. These people find a partner from another group. Since there are an even number of groups, there is an even number of leftover people. Then they all find a partner. Therefore it's an even number.

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PLEASE HELP ME WITH THIS ONE QUESTION
gavmur [86]

Given:

n=4 and r=3.

To find:

The combinations without repetition are possible if n=4 and r=3.

Solution:

Combination of selecting r item from total n items is:

^nC_r=\dfrac{n!}{r!(n-r)!}

We have n=4 and r=3. By using the above formula, we get

^4C_3=\dfrac{4!}{3!(4-3)!}

^4C_3=\dfrac{4\times 3!}{3!1!}

^4C_3=4

Therefore, the correct option is D.

5 0
3 years ago
X=7 -2x+10<br> What does this equal?
mote1985 [20]

Step-by-step explanation:

Since X is given to you (in this case, it’s 7), all you have to do is plug it into the equation.

1. -2(7) + 10

When a variable or a number is directly outside a number, it means you should multiply the two numbers, no matter what.

Now that we know this: -2 * 7 = (-14) When a negative is multiplied by a positive, it turns out negative.

2. (-14) + 10: Let’s say (for instance), that I owe 14 dollars to a friend. If I pay 10 of it, how much do I owe my friend? It would be -4 because you’re still in debt, and haven’t payed your friend all of her 14 dollars back.

3. You should come up with an answer of (-4) because of all of the steps given.

If something doesn’t make sense, please make a note of it and tell me. Otherwise, have a splendid day.

6 0
2 years ago
Read 2 more answers
In the picture below, what is the value of x?
lana [24]

Answer: 9

Step-by-step explanation:Because you have to loom at the answer

5 0
2 years ago
The road that leads to the beach is 3 miles long. What is the length in kilometers?
Airida [17]

1) Let's convert it to kilometers, using for that a Rule of three

1 mile ---------- 1.600 km

3 -----------------x

2) Multiplying it crossed

3*1.600=1x

4800=x

x = 48

4 0
1 year ago
- The four-digit number 1210 has an interesting property.
vampirchik [111]

Answer:

ABCDEFG = 3211000

Step-by-step explanation:

A counts the number of zeroes, and there are 3 zeroes (E, F, G), so A = 3.B counts the number of ones, and there are 2 ones (C, D), so B = 2.C counts the number of twos, and there is 1 two (B), so C = 1.D counts the number of threes, and there is 1 three (A), so D = 1.There is no four, five, six in, so E, F, G are all zeroes.

5 0
2 years ago
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