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Sonja [21]
3 years ago
15

The numerator of a fraction is 5 more than the denominator. If 3 is added to both numerator and denominator the fractions become

s 2. What is the original fraction?
​
Mathematics
1 answer:
katen-ka-za [31]3 years ago
8 0

Answer:

Step-by-step explanation:

Given :-

The numerator of a fraction is 5 less than its denominator.

If 3 is added to the numerator and denominator both , the fraction becomes 4/5.

To Find :-

The Original Number

Solution :-

Let denominator of the fraction be = x

And then numerator be x – 5

Original fraction = (x – 5)/x

According to the Question,

⇒  (x – 5 + 3)/(x + 3) = 4/5

⇒ (x – 2)/(x + 3) = 4/5

⇒ 5(x – 2) = 4x + 12

(By cross multiplication)

⇒ 5x – 10 = 4x + 12

⇒ 5x - 4x = 12 + 10

⇒ x = 22

Original fraction = (x – 5)/x

Original fraction  = (22 – 5)/22

Original fraction = 17/22

Hence, the original number is 17/22.

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Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form. HELP PLEASE!!
Nataliya [291]

Answer:

  • Perimeter = 22*sqrt(2)
  • Area = 60.5 inches
  • D

Step-by-step explanation:

Remark

You need 2 facts.

  1. A square has 4 equal sides.
  2. It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

  • a^2 + a^2 = c^2
  • 2a^2 = c^2

Givens

  • c = 11

Solution

  • 2a^2 = 11^2
  • 2a^2 = 121                    Divide by 2
  • a^2 = 121/2                  Take the square root of both sides
  • sqrt(a^2) = sqr(121/2)    
  • a = 11/sqrt(2)                Rationalize the denominator
  • a = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]
  • a = 11 * sqrt(2) / 2

<em><u>Perimeter</u></em>

P = 4s

  • P = 4*11*sqrt(2)/2
  • P = 44*sqrt(2)/2
  • P = 22*sqrt(2)

You don't need the area. The answer is D

<em><u>Area</u></em>

  • Area = s^2
  • Area = (11*sqrt(2)/2 ) ^2
  • Area = 121 * 2 / 4
  • Area = 60.5


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Step-by-step explanation:

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