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Kaylis [27]
3 years ago
11

(arb)4 = 81r24 where a and b are positive integers. Work out a and b.

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
8 0

Step-by-step explanation:

(arb)4 = 81r24

a4r4b = 81r24

a4  = 81

a = 4√81

a = 3

r4b = r24

4b = 24

b = 6

any more help just ask :)

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charle [14.2K]
1 and 3 i just did the math tell me if i’m wrong
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3 years ago
A pet store sells goldfish and hermit crabs,
Elis [28]

Answer:

Cost = \$28

Step-by-step explanation:

Given

Represent Goldfish with g and hermit crabs with h.

The first statement, we have:

7g + 3h = 26

The second statement, we have:

4g + 5h = 28

Required

Determine the selling price of 6 goldfish and 4 hermit crabs

The equations are:

7g + 3h = 26 --- (1)

4g + 5h = 28 --- (2)

Make g the subject in (2)

4g + 5h = 28

4g = 28 - 5h

Divide both sides by 4

g = \frac{1}{4}(28 - 5h)

Substitute \frac{1}{4}(28 - 5h) for g in (1)

7g + 3h = 26

7(\frac{1}{4}(28 - 5h)) + 3h = 26

\frac{7}{4}(28 - 5h) + 3h = 26

Multiply through by 4

4 * \frac{7}{4}(28 - 5h) + 4*3h = 26*4

7(28 - 5h) + 4*3h = 26*4

Open bracket

196 - 35h + 12h = 104

196 -23h = 104

Collect Like Terms

-23h = 104-196

-23h = -92

Make h the subject

h = \frac{-92}{-23}

h = \frac{92}{23}

h = 4

Substitute 4 for h in g = \frac{1}{4}(28 - 5h)

g = \frac{1}{4}(28 - 5*4)

g = \frac{1}{4}(28 - 20)

g = \frac{1}{4}(8)

g = 2

This implies that:

1 goldfish = $2

1 hermit crab = $4

The cost of 6 goldfish and 4 hermit crabs is:

Cost = 6g + 4h

Cost = 6*\$2 + 4*\$4

Cost = \$12 + \$16

Cost = \$28

5 0
3 years ago
How many different arrangements can be made with the letter of the word 'M O R O C C O'?
valentinak56 [21]
Since the order matters, it's a permutation of 7 letters, but mind you in 
MOROCCO. you have 3 O's and 2 C's, Hence the arrangements are:

⁷P₇ /(3!2!) = 7!/(3!2!) = 5040/(3!2!) = 420 arrangements 
8 0
3 years ago
Find the largest positive integer that will divide 542, 436, 398 leaving reminders 7, 11, 15 respectively
saveliy_v [14]

Answer:

17

Step-by-step explanation:

Here in this question for finding the numbers that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively we have to first subtract the remainder of the following. By this step we find the highest common factor of the numbers.

And then the required number is the HCF of the following numbers that are formed when the remainder are subtracted from them.

Clearly, the required number is the HCF of the numbers 398−7=391,436−11=425, and, 542−15=527

We will find the HCF of 391, 425 and 527 by prime factorization method.

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Hence, HCF of 391, 4250 and 527 is 17 because the greatest common factor from all the numbers is 17 only.

So we can say that the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.

Note: - whenever we face such a type of question the key concept for solving this question is whenever in the question it is asking about the largest number it divides. You should always think about the highest common factor i.e. HCF. we have to subtract remainder because you have to find a factor that means it should be perfectly divisible so to make divisible we subtract remainder. because remainder is the extra number so on subtracting remainder it becomes divisible.

8 0
3 years ago
Based on the information in the diagram, what is the length of side b?
Keith_Richards [23]

Answer:

29

Step-by-step explanation:

7 0
3 years ago
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