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3 years ago

What is the value of x? Enter your answer in the box. x =___

Mathematics

1 answer:

Zanzabum3 years ago

8 0

Answer:

x = 12

Step-by-step explanation:

The diagram shows an equilateral triangle (because all angles are congruent). All sides in equilateral triangle are congruent, so

$4x-10=5x-22=3x+2$

Solve the equation

$4x-10=5x-22\\ \\4x-10-4x=5x-22-4x\\ \\-10=x-22\\ \\-10+22=x-22+22\\ \\12=x$

Check this value:

$4x-10=4\cdot 12-10=48-10=38\ units \\ \\5x-22=5\cdot 12-22=60-22=38\ units\\ \\3x+2=3\cdot 12+2=36+2=38\ units$

Thus, $x=12$

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Can someone please give me a good explanation of how to work this out! 15 points for a good answer.

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Answer:

= 26,(6)

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Step-by-step explanation:

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3 years ago

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Simplify: 3√4 508/1331

olga2289 [7]

Answer:

The simplified form of ³√{4(508/1331)} is {1(7/11)}.

Step-by-step explanation:

Given that:

³√{4(508/1331)}

Let we first convert the mixed fraction to simplest fraction form.

= ³√{(1331*4+508)/1331}

= ³√{(5324 + 508)/1331}

= ³√(5832/1331)

Comparing the fraction with x√{(a/b)}, we get

a = 5832 , b = 1331 and x = 3

Using exponent rule x√{(a/b)} = {(x√a)/(x√b)}, we get

= {(³√5832)/(³√1331)}

Let now find the prime factorization of 5832 and 1331.

Prime factorization of 1331

11 | 1331

11 | 121

11 | 11

| 1.

Prime factorization of 1331 = 11 * 11 * 11

³√(1331)

= ³√(11 * 11 * 11)

= 11

⇛³√(1331) = 11

Now,

Prime factorization of 5832

2 | 5832

2 | 2916

2 | 1458

3 | 729

3 | 243

3 | 81

3 | 27

3 | 9

3 | 3

| 1.

Prime factorization of 5832 = 2*2*2 * 3*3*3 * 3*3*3

Hence, ³√(5832)

= ³√(2*2*2 * 3*3*3 * 3*3*3)

= 2 * 3 * 3

= 6 * 3

= 18

⇛³√(5832) = 18

Therefore,

{(³√5832)/(³√1331)}

= 18/11

= {1(7/11)

Answer: Hence, the simplified form of ³√{4(508/1331)} is {1(7/11)}.

Please let me know if you have any other questions.

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