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3 years ago

PLZ HELP ME SCHOOL IS RIGHT AROUND THE CORNER

Mathematics

2 answers:

Jobisdone [24]3 years ago

5 0

Rice vinegar is 1.5 units out of 1.5 + 5 = 6.5 units of vinegar. So in 17 ounces of the mixture, the amount of rice vinegar will be

$\dfrac{1.5}{6.5} \cdot 17 = 3.923...$

Answer: 3.9 ounces of rice vinegar

AnnZ [28]3 years ago

3 0

Quantity of rice vinegar= one and half parts of total

Quantity of cide vinegar = 5 parts of total

ratio of rice vinegar : cide vinegar = 1.5 :5

total quantity = 17 ounces

$quantity of rice vinegar = \frac{1.5}{6.5} * 17$

Quantity of rice vinegar = 3.92 ounces

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2 years ago

Find the largest prime divisor of $15^6 - 7^6$<img src="https://tex.z-dn.net/?f=Find%20the%20largest%20prime%20divisor%20of%20%2

Novosadov [1.4K]

Answer:

Largest prime factor of the given expression is <em>379.</em>

Step-by-step explanation:

Given the expression:

$15^6 - 7^6$

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

$15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)$

Let us learn two formula:

$x^3+y^3 = (x+y)(x^2+y^2-xy)$

$x^3-y^3 = (x-y)(x^2+y^2+xy)$

Applying the above formula in the expression written above:

$(15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2$ ...... (1)

Similarly:

$(15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379$ ........ (2)

Multiplying the expressions from (1) and (2) to get the result:

$\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2$

So, largest prime factor of the given expression is <em>379.</em>

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