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3 years ago

Prove the divisibility of the following number using factoring! 7^6 +7^5 -7^4 by 11

1 answer:

5 0

X = 7^6 + 7^5 - 7^4
x = 7^4*7^2 + 7^4*7 - 7^4*1
x = 7^4*(7^2 + 7 - 1)
x = 7^4*(49 + 7 - 1)
x = 7^4*55
x = 55*7^4
x = 11*5*7^4
x = 11*y .... where y = 5*7^4 is an integer

Since x = 11*y, and y is an integer, this means x is a multiple of 11

So that proves 7^6 + 7^5 - 7^4 is divisible by 11

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3 letters without replacement 4 letters A B C D how many ways can this be done if the order of the choices matters

Veseljchak [2.6K]

Answer:

Since the order of choice matters, we will permute the values. a bit more explanation for this:

If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter

Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters

Since we have 3 slots:

___ ___ ___

Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now

So:

_4_ ___ ___

**Keep in mind that the 4 is the possible number of values this slot can have**

Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with 3 more alphabets

we can put any one of the 3 alphabets in this second slot, Hence:

_4_ _3_ ___

Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3

Therefore:

_4_ _3_ _2_

Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets

Total possible words = 4 * 3 * 2

Total possible words = 24

We could've used the formula for Permutation as well

8 0

3 years ago

506 students went on a field trip. Nine buses

vampirchik [111]

Answer:

53 students on each bus

Step-by-step explanation:

506-29=477 (take out the students that went by car)

477/9 = 53 (distribute 477 students evenly in 9 buses)

8 0

3 years ago

Read 2 more answers

1 inch corresponds to 4ft, what is 2 1/4 inches converted to feet

Roman55 [17]

Answer:

9 feet

Step-by-step explanation:

2 1/4 can be written as an improper fraction 9/4

we are given:

1 inch ----> corresponds to 4 feet

hence,

2 1/4 inch ---> corresponds to 4 feet x 2 1/4 = 4 x (9/4) = 9 feet

5 0

4 years ago

Can you answer this for me? asap

galben [10]

46+19+54= 119, so the answer is 119

8 0

3 years ago

Read 2 more answers

Simplify: (7x^2 − 8x − 4) + (−2x^2 + 3x + 5) + (5x^2 − 10x − 8)

kramer

Step 1. Simplify
7x^2 - 8x - 4 - 2x^2 + 3x + 5 + 5x^2 - 10x - 8
Step 2. Collect like terms
(7x^2 - 2x^2 + 5x^2) + (-8x + 3x - 10x) + (-4 + 5 - 8)
Step 3. Simplify

10x^2 - 15x - 7

5 0

3 years ago