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2 years ago

The sum of a number and its reciprocal is 2whole number 1 over 6. Find that number

Mathematics

1 answer:

notsponge [240]2 years ago

6 0

Answer:

2/3 or 3/2

Step-by-step explanation:

Let x represent the number. The given relation is ...

x +1/x = 2 1/6

x^2 +1 = (13/6)x

6x^2 -13x +6 = 0 . . . . . subtract the right side and multiply by 6

(6x -9)(6x -4)/6 = 0 . . . . factor

(2x -3)(3x -2) = 0 . . . . . . simplify a bit

x = 3/2 or 2/3 . . . . . . . . values of x that make the factors zero

The number is 2/3 or its reciprocal, 3/2.

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What two numbers can add to 4 but multiple to -12

olasank [31]

Answer:

<em>Numbers: 6 and -2</em>

Step-by-step explanation:

<u>Equations</u>

This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.

However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:

$x+y=4\qquad\qquad [1]$

$x.y=-12\qquad\qquad [2]$

Solving [1] for y:

$y=4-x$

Substituting in [2]

$x(4-x)=-12$

Operating:

$4x-x^2=-12$

Rearranging:

$x^2-4x-12=0$

Solving with the quadratic formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

With a=1, b=-4, c=-12:

$\displaystyle x=\frac{-(-4)\pm \sqrt{(-4)^2-4(1)(-12)}}{2(1)}$

$\displaystyle x=\frac{4\pm \sqrt{16+48}}{2}$

$\displaystyle x=\frac{4\pm 8}{2}$

The solutions are:

$\displaystyle x=\frac{4+ 8}{2}=6$

$\displaystyle x=\frac{4- 8}{2}=-2$

This confirms the preliminary results.

Numbers: 6 and -2

7 0

3 years ago

I have 20 movies 85% are action how many are action

Alona [7]

20*0.85
17
17 are action movies

8 0

3 years ago

Read 2 more answers

it was recently estimated that domestic vehicles out numberforegin vehicles by about six to five. if there are 2673 vehicles in

klio [65]

The question is an example of a ratio problem. This implies that

$\begin{gathered} \text{Domestic vehicles ratio=6} \\ \text{Foreign vehicles ratio=5} \\ Sum\text{ of vehicles ratio =5+6=11} \end{gathered}$

Therefore, le the number of domestic vehicles be x. We can say that;

$\begin{gathered} \frac{6}{11}=\frac{x}{2673} \\ 11x=16038 \\ x=\frac{16038}{11} \\ x=1458 \end{gathered}$

Answer: 1458

7 0

1 year ago

How many tens are in 700?

scoray [572]

Answer:

Step-by-step explanation:

700 / 10 = 70

5 0

3 years ago

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Emoji were first introduced on Japanese mobile phones in the year 1997.

Alenkinab [10]

Answer:

1997 > y

Step-by-step explanation:

5 0

2 years ago

The sum of a number and its reciprocal is 2whole number 1 over 6. Find that number​

The sum of a number and its reciprocal is 2whole number 1 over 6. Find that number