Perform the indicated operation.
3k+6/(k-2)+(2-k)= answers::: 3, -3,3k+6/k-2,3k+6/k+2


Answer 1


3 is the correct option.

Step-by-step explanation:

The given expression is:


Break the numerators:

3k/(k-2) + 6/(2-k)

Now Re-arrange the term (2-k) in the denominator as (-k+2)

3k/(k-2) + 6/(-k+2)

Now takeout -1 as a common factor from (-k+2)

3k/(k-2) + 6/-1(k-2)

Now  move a negative (-1)from the denominator of 6/-1(k-2) to the numerator

3k/(k-2) + -1*6/(k-2)

Now take the L.C.M of the denominator which is k-2 and solve the numerator

3k - 6/ (k-2)

Take 3 as a common factor from the numerator:


k-2 will be cancelled out by each other:

Thus the answer will be 3.

The correct option is 3....

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What kind of angle is formed by the tangent to a circle and a radius of that circle?


A tangent is always perpendicular to the radius at the point of tangency.

A right angle.

Answer: 90° which is a right angle

Step-by-step explanation:

The tangent to a circle is perpendicular to the radius at the point of tangency. The angle between a radius and tangent is 90°>


Witch statements about the reflections are true?check all that apply


More information is needed

The points at x equals=​_______ and xequals=​_______ are the inflection points on the normal curve


We know that the probability density function of a variable that is normally distributed is f(x) = 1/(σ√2π) * exp[1/2 (x – µ). Its inflection point is the point where f"(x) = 0.
Taking the first derivative, we get f'(x) = –(x–µ)/(σ³/√2π) exp[–(x–µ)²/(2σ²)] = –(x–µ) f(x)/σ².
The second derivative would be f"(x) = [ –(x–µ) f(x)/σ]' = –f(x)/σ² – (x–µ) f'(x)/σ² = –f(x)/σ² + (x-µ)² f(x)/σ⁴.
Setting this expression equal to zero, we get
–f(x)/σ² + (x-µ)² f(x)/σ⁴ = 0
Multiply both sides by σ⁴/f(x):
–σ² + (x-µ)² = 0
(x-µ)² = σ²
x-µ= + – σ
x = µ +– σ
So the answers are x = µ – σ and x = µ + σ.


Convert 86 degrees Fahrenheit to degrees celsius


86 degrees Fahrenheit is 30 degrees Celsius 

Kevin is buying water for his camping trip. He knows he needs at least 20 gallons of water for the trip. He already has five and a half gallons. The water comes in 32-fluid ounce (quarter-gallon) containers. What algebraic inequality represents this situation?



Step-by-step explanation:

Kevin already has five and a half gallons of water for the trip

He knows he needs at least 20 gallons of water for the trip.

The water comes in 32-fluid ounce (quarter-gallon) containers.

1 fluid ounce =0.0078125 gallons

32-fluid ounce

Let x be the number 32-fluid ounce (quarter-gallon) containers required  to have at least 20 gallons of water for the trip.

1 container contains 0.25 gallons of water

So, x container contains 0.25x gallons of water

So, Kelvin has total gallons of water =

Since we are given that He knows he needs at least 20 gallons of water for the trip.


Hence the algebraic inequality represents this situation is

Answer: One-fourth x + 5 and one-half greater-than-or-equal-to 20

Step-by-step explanation:


On a coordinate grid Ming's house is located 2 blocks to the right and 5 blocks up from (0,0). Joe house is located 3 blocks to the right and 2 blocks down from Ming's house. What ordered pair describes the location of joe house?



  (5, 3)

Step-by-step explanation:

Conventionally, the ordered pairs are (right, up). Then ...

Ming's = (0, 0) + (2, 5) = (2, 5)

Joe's = Ming's + (3, -2) = (2, 5) + (3, -2) = (2+3, 5-2)

Joe's = (5, 3)


( 5,3 )

Step-by-step explanation:

i am doing this test too


A Cat, sitting in the top of a tree, spots a dog and a Firefighter both on the flat ground below. From the cats point of view , the dog is 10 meters south from the base of the tree, at an angle of depression of 65 degrees, and the Firefighter is some distance east of the tree at an angle of depression of 50 degrees. How far is the Firefighter from the dog?


This is the concept of application of trigonometry;
The height of the tree will be given by:
tan theta=opposite/adjacent
adjacent= 10
tan 65=h/10
h=10 tan 65
h=21.45 m

The distance between the dog and the man is x;
the distance of the man to the tree is (x+10) m
this will be given by:
tan 50= 21.45/(10+x)
getting the reciprocal of the expression we get;
1/tan 50=(10+x)/21.45
cross multiplying the above expression we get;
21.45=(10+x)tan 50
We conclude that the distance of the Firefighter and the dog is x=7.875 m


15 meters

Step-by-step explanation:

Denote points: C - cat, B - base of the tree, D - dog, F - Firefighter.

Consider triangle CBD. This triangle is right triangle with right angle CBD and m∠BCD=65°, DB=10 m. Then

Consider right triangle CBF. In this triangle angle CBF is right angle and m∠CFB=50°, then

Consider right triangle BDF. In this triangle angle FBD is right and by the Pythagorean theorem,


To manufacture an automobile requires painting, drying, and polishing Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma Each Delta requires 9 hours for painting. 4 hours for drying, and 3 hours for polishing A Beta requires 13 hours for painting, 6 hours for drying, and 4 hours for polishing, and a Sigma requires 9 hours for painting, 4 hours for drying, and 1 hour for polishing If the company has 257 hours for painting,
116 hours for drying, and 59 hours for polishing per month, how many of each type of car are produced?



The company manufactures 5 Delta cars, 8 Beta cars and 12 Sigma cars.

Step-by-step explanation:

Let in the motor company x number of Delta cars, y number of Beta cars and z number of Sigma cars are manufactured.

So, from the condition given in the question we can write

9x + 13y + 9z = 257 ........ (1)

4x + 6y + 4z = 116 ........... (2) and  

3x + 4y + z = 59 ......... (3)

From equation (2) we get

9x + 13.5y + 9z = 261 ....... (4) {Multiplying with both sides}

Now, solving equations (1) and (4) we get

0.5y = 4

⇒ y = 8.

Now, from equation (2) putting the value of y we get,  

4x + 4z = 116 - 48 = 68

⇒x + z = 17 .......... (5)

Now, from equation (3) putting y = 8 we get,

3x + z = 59 - 32 = 27 ........ (6)

Hence, solving equations (5) and (6) we get, 17 - x = 27 - 3x

⇒ 2x = 10

⇒ x = 5  

So, z = 17 - x = 12

Therefore, the company manufactures 5 Delta cars, 8 Beta cars and 12 Sigma cars. (Answer)


(ab + 3)(ab - 3)
2262 +9
o alb2-6ab-9
o 2²2²-9



a^2b^2 - 3ab + 3ab - 9

a^2b^2 - 9

Step-by-step explanation:

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