Si la mitad del reciproco de un numero se suma al duplo del reciproco de otro, la suma es uno mas que el reciproco del primer numero. la diferencia de los reciprocos de los numeros es una decima.​

Answers

Answer 1

Answer:

Ambos números son [tex]-\frac{25}{8}[/tex] y [tex]\frac{50}{21}[/tex]

Step-by-step explanation:

La mitad de una cantidad es el resultado de partir en dos partes iguales dicha cantidad, siendo cada una de esas partes es la mitad de la cantidad inicial. Por lo que la mitad de un número se calcula dividiendo el número por 2.

El recíproco o inverso multiplicativo de un número x es el número que, cuando es multiplicado por x , da 1.  Es decir, el producto de un número y su recíproco es 1. Para obtener el recíproco de un número, sólo divide 1 por el número. Entonces el reciproco de un numero cualesquiera x es [tex]\frac{1}{x}[/tex].

El doble o duplo de un número se calcula multiplicando el número por 2.

La diferencia es el resultado de la resta o sustracción.

Entonces:

La mitad del reciproco de un numero: siendo el número x, entonces esto se expresa como [tex]\frac{1}{x}[/tex]÷2El duplo del reciproco de otro numero: siendo el número y, entonces podes expresar [tex]\frac{1}{y}[/tex]*2Uno más que el reciproco del primer numero: [tex]\frac{1}{x}+1[/tex]

Entonces:

[tex]\frac{1}{x}[/tex]÷2 + [tex]\frac{1}{y}[/tex]*2 = [tex]\frac{1}{x}+1[/tex] Ecuación (A)

Siendo la diferencia de los recíprocos de los números igual a una decima, entonces

[tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{10}[/tex] Ecuación (B)

Entonces, de la ecuación (B) se obtiene:

[tex]\frac{1}{y}=\frac{1}{10}-\frac{1}{x}[/tex] Ecuación (C)

Reemplazando en la ecuación (A):

[tex]\frac{1}{x}[/tex]÷2 +( [tex]\frac{1}{10}-\frac{1}{x}[/tex])*2 = [tex]\frac{1}{x}+1[/tex]

Resolviendo:

[tex]\frac{1}{x}[/tex]÷2 + [tex]\frac{1}{10}*2-\frac{1}{x}*2[/tex] = [tex]\frac{1}{x}+1[/tex]

[tex]\frac{1}{x}[/tex]*[tex]\frac{1}{2}[/tex] - [tex]\frac{1}{x}*2[/tex] - [tex]\frac{1}{x}[/tex]= 1- [tex]\frac{1}{10} *2[/tex]

[tex]-\frac{5}{2}*\frac{1}{x}=\frac{4}{5}[/tex]

[tex]\frac{1}{x} =\frac{4}{5}[/tex] ÷ [tex](-\frac{5}{2})[/tex]

[tex]\frac{1}{x} =-\frac{8}{25}[/tex]

[tex]x=-\frac{25}{8}[/tex]

Entonces, reemplazando en ecuación (C)

[tex]\frac{1}{y}=\frac{1}{10}-\frac{1}{-\frac{25}{8} }[/tex]

[tex]\frac{1}{y}=\frac{1}{10}+\frac{8}{25}[/tex]

[tex]\frac{1}{y}=\frac{21}{50}[/tex]

[tex]y=\frac{50}{21}[/tex]

Entonces, ambos números son [tex]-\frac{25}{8}[/tex] y [tex]\frac{50}{21}[/tex]

Answer 2

Usando un sistema de ecuaciones, se encuentra que  los números son: [tex]-\frac{1}{4}, -2[/tex]

Un número es llamado de x, el otro de y.Los recíprocos son: [tex]\frac{1}{x}, \frac{1}{y}[/tex]

Si la mitad del reciproco de un numero se suma al duplo del reciproco de otro, la suma es uno mas que el reciproco del primer numero, o sea:

[tex]\frac{1}{2x} + \frac{2}{y} = 1 + \frac{1}{x}[/tex]

La diferencia de los reciprocos de los numeros es una decima, o sea:

[tex]\frac{1}{x} - \frac{1}{y} = 10[/tex]

[tex]\frac{y - x}{xy} = 10[/tex]

[tex]y - x = 10xy[/tex]

[tex]y = 10xy + x[/tex]

[tex]y = x(10 + y)[/tex]

[tex]x = \frac{y}{10 + y}[/tex]

Reemplazando en la primera ecuación:

[tex]\frac{1}{2x} + \frac{2}{y} = 1 + \frac{1}{x}[/tex]

[tex]\frac{10 + y}{2y} + \frac{2}{y} = 1 + \frac{10 + y}{y}[/tex]

[tex]\frac{10 + y + 4}{2y} = \frac{y + 10 + y}{y}[/tex]

[tex]\frac{14 + y}{2y} = \frac{2y + 10}{y}[/tex]

[tex]14y + y^2 = 4y^2 + 20y[/tex]

[tex]3y^2 + 6y = 0[/tex]

[tex]3y(y + 2) = 0[/tex]

[tex]y + 2 = 0[/tex]

[tex]y = -2[/tex]

[tex]x = \frac{y}{10 + y} = \frac{-2}{10 - 2} = -\frac{1}{4}[/tex]

Los números son: [tex]-\frac{1}{4}, -2[/tex]

Un problema similar es dado en https://brainly.com/question/24646137


Related Questions

b) Solve x + 5x – 14 = 0

Answers

5x+x=14
14/6= 2.3
x=2.3

Answer:

2 1/3

Step-by-step explanation:

Step 1:

x + 5x - 14 = 0      Equation

Step 2:

6x - 14 = 0      Combine Like Terms

Step 3:

6x = 14      Add 14 on both sides

Step 4:

x = 14 ÷ 6        Divide

Answer:

x =  2 1/3

Hope This Helps :)

Write an equation of the line passing through the point (8,-5) that is parallel to the line 2x – 6y=-3.
y = mx + b

Answers

Answer:

y=[tex]\frac{1}{3}\\[/tex]x - [tex]\frac{23}{3}[/tex]

Step-by-step explanation:

Ist put the first equation in y=mx+b form

2x-6y=-3

subtract 2x on both sides

2x-6y=-3

-2x    =-2x

-6y=-2x-3

then divide both sides by -6

-6y=-2x-3

-6

that gives y=[tex]\frac{1}{3}[/tex]x+[tex]\frac{1}{2}[/tex] for the original equation

Then plug in the point and slope in y=mx+b

Use the same slope since the lines are parallel

(-5)=([tex]\frac{1}{3}[/tex])(8)+b

-5=[tex]\frac{8}{3}[/tex]+b

then subtract 8/3 on both sides and that gives

-23/3 = b

then you can make the new equation using -23/3 for you b and 1/3 for your slop m

A deep sea diver descended from a rock that is 45 feet below

Answers

Diver descended 43 feet from the rock to the coral reef.
A deep sea diver descended from a rock that is 45 feet below sea level to a coral reef that is 88 feet below sea level.
To find : How far did the diver descend from the rock to the coral reef.
Solution : We have given
A deep sea diver descended below sea level = -45 feet .
A coral reef that is 88 feet below sea level = -88 feet.
Because we take the negative value below sea level( 0 ).
Difference = -45 - ( - 88)
Difference = -45 + 88 = 43
Diver descended 43 feet from the rock to the coral reef.
Therefore, Diver descended 43 feet from the rock to the coral reef.
If that is your question...

Salena needs to purchase 9 skirts for a new job. her friend, Jamie goes with her each of the skirts costs $41. Salena says that she can find the total cost by multiplying 9 and 4 and adding that to product of 9 and 1. Jamie disagrees and says that she needs to find the product of 9 and 40 and add that to the product of 9 and 1. Who is correct and why?

Answers

Answer:

Jamie is correct. This is because 41 is a combination of 40 and 1. Salena thinks that the 4 is just a 4, however, the 4 is in the tens place, so the 41 without the 1 is 40. The answer to this 41 times 9 is 369. Not 45.

Step-by-step explanation:

Each skirt is $41

Salena needs 9

(9*40) + (9*1)

360   +   9

    $369

In a study of the effect of aluminum intake on the mental development of infants, a group of 54infants who had been born prematurely were given a special aluminum depleted intravenous-feeding solution. At an adjusted age of 18 months,the neurologic development of the infants were measured using the Bayley Mental Development Index (BMDI), a unitless scale with higher scores indicating higher development. They had a sample mean BMDI of 97.4 and a sample standard deviation of 18.0.The (BMDI) is similar to an IQ score, with 100 being the average in the general population.

Assuming all relevant assumptions are met, carry out the appropriate testto determine if infants who receivedthealuminum depleted intravenous-feeding solution had a significantly differentaverage BMDI score thaninthe general population. Be sure to include all the stepsfor full credit.

Given:critical value= = 2.00

Answers

Answer:

The decision rule is  

  Fail to reject the null hypothesis

The conclusion is

   The no sufficient evidence to conclude  that the average  BMDI score is different from the general population

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  54

    The sample mean is  [tex]\= x  =  97.4[/tex]

    The standard deviation is  [tex]s = 18.0[/tex]

     The population mean is  [tex]\mu  =  100[/tex]

     The critical value  is  [tex]t_{critical } =  2.0[/tex]

Generally the test statistics is mathematically represented as  

       [tex]t =  \frac{\= x - \mu}{\frac{s}{\sqrt{n} } }[/tex]

=>    [tex]t =  \frac{ 97.4  - 100}{\frac{ 18}{\sqrt{54} } }[/tex]

=>    [tex]t =-1.062[/tex]

Comparing the obtained t statistics with the critical value we see that

   The  critical value is not within the region of rejection (i.e -1.062 to 1.062  )

Hence the decision rule is  

  Fail to reject the null hypothesis

The conclusion is

   The no sufficient evidence to conclude  that the average  BMDI score is different from the general population

3cm
3cm
8cm
13cm
in the diagram above, the curved part is a Semi-
Circle. Find the area of the shaded portion
and correct your answer to 3 significant
figure. ​

Answers

Answer:

can u attach the diagram

Step-by-step explanation:

Unit rate
Find each unit rate.
1. $140 for 18 ft2

Answers

Answer:

$17.50

Step-by-step explanation:

140 divided by 18 equals 17.50, the unit rate is dollars per foot.

Answer:

$7.78 : 1 ft²

Step-by-step explanation:

140 : 18

÷18  ÷18

7 7/9 : 1

    or

$7.78 : 1 ft²

What is this variable? 3/4a — 6 = 4+3a

Answers

The answer is
a= -40/9

which of the rolling values are solutions to the inequality , ILL MARK BRAINLIST !!!

Answers

Answer:

II and III

Step-by-step explanation:

I...

-9 - 5x > -1

-9 - 5(2) > -1

-9 - 10 > -1

-19 > -1

FALSE

II...

-9 - 5x > -1

-9 - 5(-5) > -1

-9 + 25 > -1

16 > -1

TRUE

III...

-9 - 5x > -1

-9 - 5(-10) > -1

-9 + 50 > -1

41 > -1

TRUE

Best of Luck!

Answer:

II. and III.

Step-by-step explanation:

-9 - 5x > -1

I. 2

-9 - 5(2) > -1

-9 - (10) > -1

-19 > -1

- 19 is not more than -1, thus I. is not an option

II. -5

-9 - 5(-5) > -1

-9 + 25 > -1

16 > -1

16 is more than -1, thus II. is an option

III. -10

-9 - 5(-10) > -1

-9 + 50 > -1

41 > -1

41 is more than -1, thus III. is an option

Determine the intercepts of the graph please be sure

Answers

X = (7,0) y= (0,2)


Hope this helps!!

Answer:

X= (_7, 0)

Y= (0, 2

Step-by-step explanation:

We meet again

Simplify the problem 4{28-[10+(3+1)×2]}

Answers

Answer:

= 40

Step-by-step explanation:

Calculate within the parentheses:

28 - [10 + (3 + 1) * 2]

= 10

Calculate within the parentheses:

[10 + (3 + 1) * 2]

= 18

Subtract (Left to right):

= 28 - 18

Simplify:

= 4 * 10

Simpliy:

= 40

i got 40

it’s a little less complicated that you think i’m not sure if this was the answer but i did it as i could remember.

Which graph represent proportional relationship?

Answers

Answer:

C

Step-by-step explanation:

Non proportional graphs are non-linear and don’t go (necessarily) through 0,0

Proportional graphs are linear and always (eventually) cross through with 0,0

I think the answer would be c:)

determine the range of the following graph:

Answers

Answer:

(-15)

Step-by-step explanation:

(-7) - 8 = (-15) (Range is the difference between Max and Min Value)

please follow me and mark as brainliest

There is 3 questions help asap

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The answer is A. C. D.

The expression 7(y-5)is equivalent to

Answers

7(y-5) = 7y-35

because 7(y) = 7y

and 7(-5) = -35

therefore 7y-35 is your answer

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divided the input by 3 to get the output

Answers

Answer: that will be 5

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

A number plus it’s opposite is ___ zero. always,sometimes,never

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Answer:

always

Step-by-step explanation:

Bro someone please help- i hate math -_-

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Answer:

I can't see the image can you re upload

Step-by-step explanation:

Answer:Well I think the answer is 1/2 for the top because with mixed fractions the denominator has to be bigger then the numerator....And the bottom one is 2 because you put the bottom number on top. Hope it's right and it helps.

Step-by-step explanation:

!!!!Please help!!!!Choose the answer that best represents the situation described below
Casey is taking pictures outdoors. She knows that the darker it is outside, the
stronger she needs to set her flash,
A. The amount of light outside is a function of the strength of flash
she needs
B. The strength of flash needed is a functlyn of the shutter speed of
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Answers

It is a ..............

Zenzizenzicube is an obsolete word that represents the square of the square of a cube. In​ symbols, zenzizenzicube is written as

(((x^3)^2))^2

Required:
a. Use the chain rule twice to find the derivative.
b. Use the properties of exponents to first simplify the​ expression, and then find the derivative.

Answers

Answer:

Step-by-step explanation:

Given the expression (((x^3)^2))^2

a) Differentiating the function with respect to x using chain rule.

Given y = (((x^3)^2))^2

Let u = (x³)²

y = u²; dy/du = 2u

Let p = x³; dp/dx = 3x²

u = p²; du/dp = 2p

Applying the chain rule formula:

dy/dx = dy/du • du/dp • dp/dx

substitute in the formula

dy/dx = 2u•2p•3x²

Since u = (x³)² and p = x³

dy/dx = 2(x³)²(2x³)(3x²)

dy/dx = 12x^6•x^5

dy/dx = 12x¹¹

b) Using property of exponent

y = (((x^3)^2))^2

y = (x^6)²

y = x¹²

dy/dx = 12x^12-1

dy/dx = 12x^11

Consider the function f(x) = 3.x2 + 7x + 2.
what is the value of the discriminat?

Answers

Answer:

The Discriminant is 25

Step-by-step explanation:

For this case, the discriminant will be given by

b ^ 2 - 4 * a * c

Where

b = 7

a = 3

c = 2

substituting

b ^ 2 - 4 * a * c = (7) ^ 2 - 4 * (3) * (2) = 25

Therefore the value of the discriminant is 25.

How many x-intercepts does this function have?

It has two intercepts with the x axis and can be found by equaling the function to zero. That is to say,

3x2 + 7x + 2 = 0

The results will be the interceptions with x.

What are the number of zeros for this function?

The number of zeros for this function is

two real number solutions

Because it is a quadratic function.

John and 3 friends are going out for pizza for lunch. They split one pizza and 4 large drinks. The pizza cost $13.50. They spend a total of $19.90. Find the cost of one large drink.

Answers

13.00 + 4X - 6.00 = 13.20

Combine the 13.00 - 6.00, getting 7.00

7.00 + 4X = 13.20

Subtract 7.00 from both sides:

7.00 + 4X = 13.20
-7.00 -7.00
------------------
4X = 6.00

Divide both sides by 4



X = $1.50

Matt and his dad are building a tree house. They buy enough flooring material to cover an area of 36 square feet. What are all possible dimensions of the floor?

Answers

Answer:

a square

Step-by-step explanation:

because the width would be 6 and the length would be also 6 .6x6 is 36



A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior
citizens. Create a function f (x) which models the amount, in dollars, a senior citizen would pay for 2 pounds
of bananas on Wednesday

Answers

Answer:

2

Step-by-step explanation:

f(x)= 0.90(0.59*2)

A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior citizens. We need to create a function f(x) which models the amount in dollars, a senior citizen would pay for 2 pounds

What is a simple Equation?

A mathematical equation which represents the relationship of two expressions on either side of the sign.

The 10% discount will make it so the senior citizens will pay 90% of the price.

90%=0.90

Also we need to know that 0.59*2 means how much money per pound the bananas cost.

So when you put it together, you should get f(x)=0.90(0.59*2)

The function f (x)=0.90(0.59*2) which models the amount, in dollars, a senior citizen would pay for 2 pounds of bananas on Wednesday

So the required function is f(x)=0.90(0.59*2)

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If an orthocenter lies inside of a triangle, then the triangle must be O isosceles. O acute. obtuse. o right​

Answers

If an orthocenter lies inside of a triangle, then the triangle must be acute.

Orthocenter of a triangle is the intersection of any two of three altitudes of a triangle. The third altitude usually pass through the point of the first two altitudes.

When the orthocenter lies inside a triangle, the angles formed by the intersection of the three altitudes is less than 90 degrees.An acute triangle is a type of triangle whose angles are less than 90 degrees.

Thus, If an orthocenter lies inside of a triangle, then the triangle must be acute.

Learn more about orthocenter here: https://brainly.com/question/6944944

Answer:D ( acute)

Step-by-step explanation:

edg

Marco has joined a bowling league, and is trying to raise his average to 140. On his last four games he scored 133, 130, 131, and 136. How much will he need to score on the next game to raise his mean to 140?

Answers

133 + 130 + 131 + 136 / 4 = 132.5
133 + 130 + 131 + 136 + 170 / 5 = 140

Noah is finding 3/4 of 8 find his mistake and correct it

Answers

you need to show his steps or else i cant find his mistake

Um 3/4 aka 75% of 8 is 6

1. Emma’s average in math increased from an 80 to an 84. By what percentage did her average increase?

Answers

Answer:

82

Step-by-step explanation:

find the square root of 625​

Answers

25 could I have brainliest plz !

Step-by-step explanation:

square root of 625 is 25

57. Designing a Patio Suppose that you wish to build a
rectangular cement patio that is to have a perimeter
of 80 feet. The length is to be 5 feet more than the
width.
(a) Find the dimensions of the patio.
(b) If the building code requires that the cement be
4 inches deep, how much cement do you have to
purchase?

Answers

Answer:

A. dimensions

Step-by-step explanation:

it's the first thing you will need to find out I beleave.

-A................................
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