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timama [110]
3 years ago
15

Please Help Me, Take Your Time.

Mathematics
1 answer:
Doss [256]3 years ago
7 0
<h3>Given</h3>

72 blue, 42 red beads

beads are used to make identical necklaces

<h3>Find</h3>

(a) the greatest number of necklaces that can be made

(b) the number of each color bead in each necklace

<h3>Solution</h3>

You can write and factor the equation

... necklaces = 72 blue + 42 red

... necklaces = 6(12 blue + 7 red)

where 6 is the greatest common factor (GCF) of 72 and 42.

(a) You can make up to 6 identical necklaces. 6 is the largest common factor of 72 and 42. If you were to try to make more, they could not be identical.

(b) Each necklace can consist of 12 blue and 7 red beads. These are the numbers obtained when the total bead count is divided into 6 equal groups.

_____

There are several ways you can find the GCF of two numbers. For small numbers, it is generally feasible to use your knowledge of multiplication tables and factors to choose the largest common factor of two numbers. You can also use Euclid's algorithm, which is to repeatedly compute

... (largest number) modulo (smallest number)

until the result is zero. The final "smallest number" is the GCF.

Here, that looks like

... 72 mod 42 = 30

... 42 mod 30 = 12

... 30 mod 12 = 6

... 12 mod 6 = 0 . . . . . . . so 6 is the GCF

___

Of course, you know that

... 72 = 2³×3²

... 42 = 2×3×7

so, the largest set of common factors is 2×3 = 6.

___

Your graphing calculator may have a function for computing the greatest common divisor (GCD), too. The TI-84 does, for example.

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Bingel [31]

Answer:

  n = 2

Step-by-step explanation:

In order for the ratio to have a value of 1, the sum of exponents in the numerator must equal the sum of exponents in the denominator:

  n + 7 = 9

  n = 9 -7 . . . . . . subtract 7 from both sides of the equation

  n = 2

___

Alternatively, you can simplify the given expression:

  \dfrac{9^n(9^7)}{9^9}=1=\dfrac{9^n}{9^2}

Hopefully, it is clear to you that the value of n must be 2 in order to make the numerator equal to the denominator.

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Step-by-step explanation:

The union of two sets is a set which contains all the elements of both the sets. thus DUE= {0,10,12,18,19}

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Step-by-step explanation:

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2 years ago
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Answer:

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Step-by-step explanation:

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Since the question doesn't ask or concern the future or present value of money, after depositing $132 you will totally (T) have:

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hope this helps
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