Choose the equation that represents a line that passes through points (−3, 2) and (2, 1).
5x + y = −13
5x − y = 17
x − 5y = −13
x + 5y = 7

Answer:

The true statements are:

m∠ 3 + m∠ 4 = 180° ⇒ 1st

m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd

m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd

Step-by-step explanation:

* Look to the attached diagram to answer the question

# m∠ 3 + m∠ 4 = 180°

∵ ∠ 3 and ∠ 4 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠ 3 + m∠ 4 = 180° ⇒ true

# m∠ 2 + m∠ 4 + m∠ 6 = 180°

∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle

∵ The sum of the measures of interior angles of any Δ is 180°

∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ true

# m∠ 2 + m∠ 4 = m∠ 5

∵ In any Δ, the measure of the exterior angle at one vertex of the

  triangle equals the sum of the measures of the opposite interior

  angles of this vertex

∵ ∠ 5 is the exterior angle of the vertex of ∠ 6

∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6

∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ true

# m∠1 + m∠2 = 90°

∵ ∠ 1 and ∠ 2 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠1 + m∠2 = 90° ⇒ Not true

# m∠4 + m∠6 = m∠2

∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle

∵ There is no given about their measures

∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is

  equal to the measure of ∠ 2

∴ m∠4 + m∠6 = m∠2 ⇒ Not true

# m∠2 + m∠6 = m∠5

∵ ∠ 5 is the exterior angle at the vertex of ∠ 6

∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ Not true

Answer: A,B,C. OR 1,2,3

Step-by-step explanation:

Answer:

So any number in the following set is a solution:

[tex](-\infty,-4) \cup (1,\infty)[/tex]

given the inequality to solve was:

[tex]x^2+3x-4>0[/tex]

Step-by-step explanation:

The left hand side is a quadratic while the right hand side is 0.

Since this is a quadratic>0, I'm going to factor the quadratic if possible and then solve that quadratic=0 for x.

That is I'm going to solve:

[tex]x^2+3x-4=0[/tex]

Since a=1, I get to ask what multiplies to be c (-4) and add up to be b(3).

Those numbers are 4 and -1.

So the factored form for the equation is:

[tex](x+4)(x-1)=0[/tex]

Setting both factors equal to 0 since 0*anything=0:

x+4=0            and              x-1=0

 -4   -4                                 +1   +1

---------------------------------------------------

x=-4              and                   x=1

Ok so if this wasn't a quadratic I would make a number line and choose numbers to plug into the quadratic to see which intervals would give me positive results.  I say positive due to the >0 part.

However since I know about the shapes of quadratics, I'm going to use that.

The quadratic function [tex]f(x)=x^2+3x-4[/tex] has x-intercepts (-4,0) and (1,0) and is open up.

I determine that it was opened up because the leading coefficient is 1 which is positive.

Now the left tail and right tail is what is above the x-axis so the solution set is:

[tex](-\infty,-4) \cup (1,\infty)[/tex]

Answer:

-6 and 5

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The interquartile range is a measure of the difference between the upper quartile and the lower quartile.

The first step is to organise the data in ascending order, that is

10, 12, 13, 15, 17, 18, 21

Next find the median which is the middle value of the data.

10, 12, 13, 15, 17, 18, 21

                 ↑ ← the median = 15

Now find the upper and lower quartiles which are the middle values of the data to the right and left of the median.

10, 12, 13, 15, 17, 18, 21

      ↑                    ↑

upper quartile = 18 and lower quartile = 12

interquartile range = 18 - 12 = 6

Interquartile range of the given data set is 6.

Interquartile is the difference between upper quartile and lower quartile

Lower quartile is the median of the lower half of the data set.

Upper quartile is the median of the upper half of the data set.

Given data set 13, 17, 18, 15, 12, 21, 10

Arranging the data set in ascending order we get 10, 12, 13, 15, 17, 18, 21

Number of values in the data set is n = 7

Lower quartile is given by [tex]Q_{1} =\frac{n+1}{4} =\frac{7+1}{4} =\frac{8}{2} =2^{nd} \ value[/tex]

Therefore, the lower quartile is [tex]Q_{1} =12[/tex]

Upper quartile is given by [tex]Q_{3}=\frac{3}{4} (n+1)=\frac{3}{4} (7+1)=\frac{3}{4}(8)=6^{th} \ value[/tex]

Therefore, the upper quartile is [tex]Q_{1} =18[/tex]

Therefore, the inter quartile is given by [tex]Q_{3}-Q_{1} =18-12=6[/tex]

Interquartile range of the given data set is 6.

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The answer is 6, reaosn is because 6/8 is not simplified, so if we divide both sides by 2 (the numerator and the denominator), we can get a simplified fraction, which is 3/4. Steps: 6/8, 6 divided by 2/8 divided by 2, 3/4.

Hope this helped!

Nate

A fraction is a way to describe a part of a whole. The missing number that will make this fraction equal is 6.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The missing number in the given fraction can be found as shown below,

3/4 = ?/8

? = 8 × (3/4)

? = 6

Hence, the missing number that will make this fraction equal is 6.

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Answer:

y = - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, - 6) and (x₂, y₂ ) = (4, 3)

m = [tex]\frac{3+6}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3

y = 3x + c ← is the partial equation

To find c substitute any of the 2 points into the partial equation

Using (4, 3), then

3 = 12 + c ⇒ c = 3 - 12 = - 9, hence

y- intercept c = - 9 ⇒ (0, - 9 )

Answer:

=-9 (the first choice)

Step-by-step explanation:

To find the y-intercept we must first find the equation of the line in the form y=mx + c where m is the gradient and c is the y- intercept.

m=Δy/Δx

=(3--6)/(4-1)

=9/3

=3

Let us write the equation using any of the given points, say (4,3)

(y-3)/(x-4)=3

y-3=3(x-4)

y-3=3x-12

y=3x-12+3

y=3x-9

Using the format y=mx+c, the y-intercept is -9

Answer:

LARGEST ANGLE= 96 DEGREES

Step-by-step explanation:

MEASURE OF LARGEST ANGLE= 3A

SMALLEST ANGLE= A

THIRD ANGLE= 20+A

3A+A+20+A=180(SUM OF INTERIOR ANGLES OF TRAINGLE IS 180 DEGREES)

TRANSPOSE 20 TO RHS.

5A=180-20=160

A=160/5

=32

MEASURE OF SMALLEST ANGLE=32

LARGEST ANGLE=3A=3*32=96 DEGREES

THIRD ANGLE=32+20=52 DEGREES

Answer:

The largest angle has a measure of 96 degrees.

Step-by-step explanation:

In order to solve this problem, we have to know the fact that the sumatory of the internal angles of any triangle is 180 degrees.

With this statement in mind, and looking at the image, we can say:

180 = A + B + C (eq. 1)

Before continue any further, let's affirmt that B is the smallest angle.

Now the enunciate says "One angle in a triangle has a measure that is three times as large as the smallest angle"; This can be express as:

A = 3B (eq. 2)

The other enunciate is "The measure of the third angle is 20 degrees more than that of the smallest angle" This can be express as:

C = B + 20 (eq. 3)

Now, replacing equations 2 and 3 into 1:

(eq. 1) 180 = 3B + B + B + 20

And clearing B:

B = 32.

By knowing B, we can clear A and C from equations 2 and 3 respectively:

(eq. 2) A = 3B,  so A= 96

(eq. 3) C = B + 20, so C =52

Answer:

Part 1) The greater unit rate of the two functions is the linear function of the table

Part 2) The greater y intercept of the two functions is the linear equation of the graph

Step-by-step explanation:

we know that

The rate of a linear function is equal to the slope

step 1

Find the slope of the linear equation in the table

we have

(0,5) and (5,15)

The slope is equal to

[tex]m=(15-5)/(5-0)=10/5[/tex]

To find the unit rate divide by 5 both numerator and denominator

[tex]m=2/1=2[/tex]

step 2

Find the slope of the linear equation of the graph

we have

(-4,0) and (0,6)

The slope is equal to

[tex]m=(6-0)/(0+4)=6/4=3/2[/tex]

To find the unit rate divide by 2 both numerator and denominator

[tex]m=1.5/1=1.5[/tex]

Compare the unit rate of the two linear equations

2 > 1.5

therefore

The greater unit rate of the two functions is the linear function of the table

step 3

Find the y-intercepts of the linear equations

Remember that the y-intercept is the value of y when the value of x is equal to zero

Linear equation of the table

Observing the table

For x=0, y=5

therefore

The y-intercept of the linear equation of the table is the point (0,5)

Linear equation of the graph

Observing the graph

For x=0, y=6

therefore

The y-intercept of the linear equation of the table is the point (0,6)

Compare the y-intercept both functions

6 > 5

therefore

The greater y intercept of the two functions is the linear equation of the graph

Answer:

the greater unit rate is 2 and the greater y intercept is 6

Step-by-step explanation:

Answer:

224 square centimeters

Step-by-step explanation:

If you slice this rectangular prism parallel to the face BFCG, you will get another cross section that is a rectangle with base 32 cm and height 7 cm.

We know area of rectangle = base * height

Thus, the area of the cross section is 7 * 32 = 224 square centimeters.

Answer:

The answer for K12 is 216

NOT 224 i got it wrong on the test

Have a great day guys! You can do it!

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

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

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

[tex]y=3x+5[/tex]

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

[tex]y=2(x+3)\\y=2x+6\\-2x+y=6[/tex]

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

[tex]-2x+y=6\\2x-y=-6[/tex]

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

[tex]y=3x+5\\-3x+y=5\\3x-y=-5[/tex]

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.

Answer:

A 40, 80, 160

Step-by-step explanation:

Given:

2.5, 5, 10, 20, ...

geometric sequence has a constant ratio r and is given by

an=a1r(r)^(n-1)

where

an=nth term

r=common ratio

n=number of term

a1=first term

In given series:

a1=2.5

r= a(n+1)/an

r=5/2.5

r=2

Now computing next term a5

a5=a1(r)^(n-1)

   = 2.5(2)^(4)

   = 40

a6=a1(r)^(n-1)

   = 2.5(2)^(5)

   =80

a7=a1(r)^(n-1)

   = 2.5(2)^(6)

   =160

So the sequence now is 2.5, 5, 10, 20,40, 80, 160!

[tex]

f(x)=-x^2+6x-1 \\

g(x)=3x^2-4x-1 \\

f(x)+g(x)=-x^2+6x-1+3x^2-4x-1=\boxed{2x^2+2x-2}

[/tex]

The answer is A.

Hope this helps.

r3t40

Answer:

41 units

Step-by-step explanation:

In this question, you should remember that the diagonal  drawn will represent the longest side of the triangle that will be formed .This is to say the triangle will have the two shorter sides (the length and width) and the longest side (diagonal).

Apply the Pythagorean relationship where

The formula to apply here will be

[tex]a^2+b^2=c^2\\\\\\a=9,b=40,c=?\\\\\\9^2+40^2=c^2\\\\\\81+1600=c^2\\\\\\c^2=1681\\\\\\c=\sqrt{1681} =41units[/tex]

Answer:

Diagonal = 41 units

Step-by-step explanation:

It is given that,a rectangle has a width of 9 units and a length of 40 units.

To find the diagonal of rectangle

We know that rectangle can be considered as combination of two right triangles.

Here length of right triangle = 40 units and height = 9 units

Hypotenuse = diagonal of rectangle.

Hypotenuse² = Length² + height

 = 40² + 9²

 = 1600 + 81

 = 1681

Hypotenuse = √1681 = 41

Therefore diagonal of rectangle = 41 units

Answer:

a. A parallelogram

Step-by-step explanation:

A trapezoid is a four-sided flat shape with a pair of parallel sides.

A parallelogram has two pairs of parallel sides.

b. can apply to a trapezoid. A polygon has three or more sides.

c. can apply to a trapezoid. A quadrilateral has four sides.

d. can apply to a trapezoid. A shape with four angles is also a quadrilateral.

The term that does not describe a trapezoid is A. a parallelogram.

The term that does not describe a trapezoid is A. a parallelogram. A trapezoid is indeed a polygon, which by definition is a plane figure with at least three straight sides and angles. Also, a trapezoid is a type of quadrilateral or quadrangle, meaning it has four sides. However, unlike a parallelogram, a trapezoid only has one pair of parallel sides, while a parallelogram has two pairs of parallel sides. The distinct characteristic of a parallelogram is that its opposite sides are not only parallel but also equal in length, which does not apply to a trapezoid.

Answer:

A) the longest side

B) the smallest angle

Step-by-step explanation:

Relationship of sides to interior angles in a triangle

In a triangle:    

Recall that in a scalene triangle, all the sides have different lengths and all the interior angles have different measures. In such a triangle, the shortest side is always opposite the smallest angle. Similarly, the longest side is opposite the largest angle.

So,

A) the longest side

B) the smallest angle

Answer:  the longest side

the smallest angle

Step-by-step explanation: the largest is longest

the smallest is shortest

Answer:

Step-by-step explanation:

The formula of a volume of a square pyramid:

[tex]V=\dfrac{1}{3}s^2H[/tex]

s - base length

H - height

We have the volume V = 32 ft³ and the base length s = 4 ft.

Substitute and solve for H:

[tex]\dfrac{1}{3}(4^2)H=32\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}(16)H=(3)(32)\\\\16H=96\qquad\text{divdie both sides by 16}\\\\H=\dfrac{96}{16}\\\\H=8\ ft[/tex]

Answer:

x = 44

Step-by-step explanation:

Adjacent angles in a parallelogram add up to 180 degrees.

180 = 3x + 6 + 42

132 = 3x

x = 44

Please mark for Brainliest!!  :D Thanks!

For any questions, please comment below and I'll respond ASAP! :)

Answer:

Step-by-step explanation:

In each parallelogram angles at one side add up to 180°.

Therefore we have the equation:

[tex](3x+6)+42=180[/tex]

[tex]3x+(6+42)=180[/tex]

[tex]3x+48=180[/tex]     subtract 48 from both sides

[tex]3x=132[/tex]          divide both sides by 3

[tex]x=44[/tex]

Answer:

red, red, red, red, red, red, green, red, red, yellow

A. red, red, red, red, red, red, green, red, red, yellow

Frequency state to the number of times an event and the value occurs. A frequency table is a table that lists items or shows the number of times the items occur. We represent a frequency by the English alphabet ‘f’.

From the frequency table, there are 8 red lights, 1 green light and 1 yellow light for a total of 10 lights.

In option A, there are 8 red lights, 1 green light and 1 yellow light, with 10 total lights.  This is the correct option.

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Answer:

[tex]\large\boxed{C.\ y=\dfrac{1}{2}x-5}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff\ m_1m_2=-1\to m_2=\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]

Parallel line have the same slope.

Therefore a line parallel to the line [tex]y=\dfrac{1}{2}x+1[/tex] has equation

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

Answer:

It is F

Step-by-step explanation:

if you plug in the y and x values that should get you the answer

Answer:

F.

Step-by-step explanation:

Answer:

3/6=1/2 so one half

Step-by-step explanation:

3/6 × 10 =30/60=3/6=1/2

Answer:

Average number of even number outcomes =5

Step-by-step explanation:

Probability = number of possible outcome / sample space

A fair die has sides labeled 1,2,3,4,5,6.

Therefore sample space = 6

Odd numbers = 1,3,5

Possible outcome of odd numbers = 3

Even numbers = 2,4,6

Possible outcome of even numbers = 3

Probability of even numbers = possible outcome of even numbers / sample space

Probability of even numbers = 3/6 = 1/2.

If the die is rolled 10times

Total number of outcome = 10

Average number of even number outcomes = probability of even numbers * total number of outcome

= 1/2 x 10

= 5

Average number of even number outcomes =5

Answer:

15 cm, 15 cm, and 19 cm

Step-by-step explanation:

Isosceles Triangle is a type of triangle in which two of the three sides are equal in length. The perimeter is 49 cm. Therefore, in this question, since the sides are unknown, we can assume that:

Length of the longer side = x cm.

Length of the other sides = y cm.

The relationship between x and y is given by:

x = (2y - 11) cm (because it is mentioned that the longest side is 11 cm less than twice as long as the other sides).

Perimeter of a triangle = sum of all sides.

Since its an isosceles triangle, therefore:

Perimeter of the triangle = x + 2y.

Substituting the values in the perimeter formula gives:

Perimeter of the triangle = 2y - 11 + 2y.

49 = 4y - 11.

4y = 60.

y = 15 cm.

Substituting y = 15 in the equation x = 2y - 11 gives x = 2(15) - 11 = 19 cm.

So in the ascending order, the lengths are 15 cm, 15 cm, and 19 cm!!!

Final answer:

To solve for the lengths of the sides of the isosceles triangle, we create an equation based on the given perimeter and the relationship between the sides. After simplifying, we find that each of the equal sides is 15 cm and the longest side is 19 cm. Thus, the sides in ascending order are 15 cm, 15 cm, 19 cm.

Explanation:

The question involves finding the lengths of the sides of an isosceles triangle given the perimeter and a relationship between its sides. Let the length of the two equal sides be x cm. According to the problem, the longest side would be 2x - 11 cm. The perimeter of the triangle is the sum of the lengths of all sides, which is given as 49 cm.

Now we set up the equation:

x + x + (2x - 11) = 49

Combining like terms, we get:

4x - 11 = 49

Adding 11 to both sides of the equation, we get:

4x = 60

Dividing both sides by 4, we find:

x = 15

The lengths of the two equal sides are each 15 cm, and the longest side is:

2(15) - 11 = 30 - 11 = 19 cm

So, the lengths of the sides in ascending order are: 15 cm, 15 cm, 19 cm

Answer:

A= 706.85m^2

Step-by-step explanation:

A= 4• Pi•r^2

= 4•Pi•15^2

=2827.43/4

=706.8575m^2

For this case we have that by definition, the area of a circular sector is given by:

[tex]A = \frac {a * r ^ 2} {2}[/tex]

Where:

r: It's the radio

a: It is the angle of the sector

We have to:

a = 90 degrees

[tex]90\ degrees = \frac {\pi} {2}[/tex]

Then, replacing:

[tex]A = \frac {\frac {\pi} {2} * 15 ^ 2} {2} = \frac {225 \pi} {4}[/tex]

Answer:

Option A

Answer:

9/10p

Step-by-step explanation:

1/2p+ 2/5 p

Get a common denominator of 10

1/2 p *5/5 = 5/10 p

2/5p *2/2 = 4/10 p

1/2p * 2/5 p

5/10p * 4/10 p

9/10p

Midpoint has form of,

[tex]M(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

We can insert the data,

[tex]M(\dfrac{4+3}{2},\dfrac{-1+2}{2})[/tex]

Which simplifies to,

[tex]\boxed{M(3.5, 0.5)}[/tex]

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\==============================[/tex]

[tex]\text{We have the equation:}\ y=5x-4\to m_1=5.\\\\\text{Therefore}\ m_2=5.\\\\\text{We have the equation:}\ y=5x+b.\\\\\text{Put the coordinates of the given point (3, 4) to the equation:}\\\\4=5(3)+b\\\\4=15+b\qquad\text{subtract 15 from both sides}\\\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=5x-11[/tex]

Answer:

1/110

Step-by-step explanation:

Her chance of originally grabbing a pink marker is 1/11. Her chance of grabbing a blue marker after the pink marker is taken out is 1/10. When you multiply 1/11 by 1/10, you get a 1/110 chance of getting the colored markers in this series

Answer:

The probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]

Step-by-step explanation:

Hello, this is a great question and one that many people struggle with in school. Hopefully I can help you understand it more clearly. Kelly has 11 markers in total within her backpack and needs to randomly pick out the pink marker. since there is only 1 that would mean her probability of picking out the pink marker is 1/11 .

Now there are 10 markers inside the backpack and she needs to randomly pick out the blue marker. since there is only 1 blue marker that would mean her probability of picking that one out is 1/10.

So now we have the following probabilities

Now if we want to find the probability of her getting the pink marker and the blue marker one after another we would need to multiply both fractions together

[tex]\frac{1}{11} * \frac{1}{10} = \frac{1}{110}[/tex]

So the probability of her picking both out in a sequence would be [tex]\frac{1}{110}[/tex]

Multiply 8 and 75% together

75/100 divide by 5

15/20 divide by 5

15/20=3/4

8*3/4

Cross out 8 and 4 , divide by 4

2*3= 6

Answer is 6- C.

Answer:

C. 6.

Step-by-step explanation:

We multiply the number of solo acts by the percent that were singers

8 * 75%

8 * .75

6

Answer:

3q = 36

q = 12

Step-by-step explanation:

Just work out the steps and compare to the choices

√(3q) = 6

[√(3q)]² = 6²

3q = 36  (Answer)

q = 36/3 = 12 (Answer)

A=36 and B=12 is the required steps for the equation √3q=6 given that 3q=A and q=B. This can be obtained by finding the remaining steps for finding q.

Given that √3q=6

              (√3q)²=6²

                   3q = 6×6 = 36 ⇒ A = 36 (squaring both sides)

                     q = 36/3 = 12 ⇒ B = 12 (divide both sides by 3)

Hence A=36 and B=12 is the required steps for the equation √3q=6 given that 3q=A and q=B.

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Answer:

x  , reciprocal= 1/x  

x+2(1/x)=27/5  

x+2/x=27/5  

x^2+2=27/5*x  

x^2-27/5*x+2=0  

(x-5)(x-2/5)=0  

x=5, 2/5