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2 years ago

Find the value of x.A. 4B. 5C. 6D. 9

Mathematics

1 answer:

lubasha [3.4K]2 years ago

7 0

Answer:

C. 6

Step-by-step explanation:

You can try the answers to see which satisfies the Pythagorean theorem:

A. 4² +7² = 16+49 ≠ 117

B. 5² +8² = 25 +64 ≠ 117

C. 6² +9² = 36 +81 = 117 . . . . this (C) is the correct choice

and, for completeness, ...

D. 9² +12² = 81 +144 ≠ 117

_____

<em>Working out</em>

You can also actually work the problem. The Pythagorean theorem tells you ...

x² + (x+3)² = (√117)²

2x² +6x +9 = 117

2x² +6x = 108 . . . . subtract 9

x² +3x = 54 . . . . . . divide by 2

x(x +3) = 54 . . . . . . factor

Now, you can compare to your memorized times tables, where you find 6×9 = 54, so you know that x=6.

In case times tables are a challenge, you can continue to complete the square:

x² +3x +1.5² = 54 +1.5²

(x +1.5)² = 56.25 = 7.5² . . . . write as squares

x = 7.5 -1.5 = 6 . . . . . . . . . . . square root, subtract 1.5

The value of x is 6.

_____

The other solution to the quadratic equation is x=-9, but negative segment lengths make no sense. We acknowledge, then ignore, that extraneous solution.

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Six fifths of what number is 60?

Crazy boy [7]

<h3>Hey Buddy,</h3>

<h3>Answer :-</h3>

Answer is 72 .

<h3><u>Explanation :-</u></h3>

$\frac{6}{5} \: of \: what \: number \: is \: 60 \:$

You probably , Know that the number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well .

• Any number can be converted to fraction if you use 1 as the denominator:

$\frac{60}{1}$

• So now that we've converted 60 into a fraction, to work out the answer, we put the fraction 6/5 side by side with our new fraction, 60/1 so that we can multiply those two fractions.

• convert the whole number to a fraction and then multiply the numerators and denominators.

$\frac{6 \times 60}{5 \times 1} = \frac{360}{5}$

• Our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.

• You can use our handy GCF calculator to work this out yourself if you want to. We already did that , And the GCF of 360 and 5 is 5.

• We can now divide both the new numerator and the denominator by 5 to simplify this fraction down to its lowest terms.

$\frac{360}{5} = 72$

$\frac{5}{5} = 1$

• When we put that together, we can see that our complete answer is :-

$\frac{72}{1}$

<h3> Hence ,the complete and simplified answer to the question what is 6/5 of 60 is :- 72 .</h3>

<h3>Hope this helps you...!</h3>

<h3>#Carry on learning#</h3>

<h3>I hope you can understand !! </h3>

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2 years ago

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Dmitry_Shevchenko [17]

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Solution: -Inf < x < Inf

Interval Notation: (-Inf, Inf)

Inf = Infinity (Replace "Inf" with the infinity symbol)

"-" = Negative sign

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Step-by-step explanation:

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