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mamaluj [8]
3 years ago
9

Solving Rational equations. LCD method. Show work. Image attached.

Mathematics
1 answer:
posledela3 years ago
4 0

(k-2)(k-6)=k^2-2k-6k+12=k^2-8k+12

So in order to get all the fractions to have a common denominator, we need to multiply \dfrac k{k-2} by \dfrac{k-6}{k-6}, and \dfrac1{k-6} by \dfrac{k-2}{k-2}:

\dfrac k{k-2}\cdot\dfrac{k-6}{k-6}=\dfrac{k(k-6)}{(k-2)(k-6)}=\dfrac{k^2-6k}{k^2-8k+12}

\dfrac1{k-6}\cdot\dfrac{k-2}{k-2}=\dfrac{k-2}{(k-2)(k-6)}=\dfrac{k-2}{k^2-8k+12}

Now,

\dfrac4{k^2-8k+12}=\dfrac{(k^2-6k)+(k-2)}{k^2-8k+12}

As long as k\neq2 and k\neq6 (which we can't have because otherwise k^2-8k+12=0), we can cancel k^2-8k+12 in the denominators on both sides:

4=(k^2-6k)+(k-2)

4=k^2-5k-2

0=k^2-5k-6

We can factorize the right side:

0=(k-6)(k+1)

which tells us that k=6 and k=-1 are solutions.

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Compare the numbers. Use >, =, or <
lesya692 [45]

Answer:

746.982 > 746.963

68.098 < 68.987

589.987 = 589.987

Step-by-step explanation:

4 0
3 years ago
An analysis of the decay of 10 grams of an unstable element over time was completed and is displayed in the computer output.
Lady bird [3.3K]

The equation of the least-squared regression line is: In(Element) = 2.305 - 0.101(Time).

<h3>What is a regression line?</h3>

A regression line displays the connection between scattered data points in any set. It shows the relation between the dependent y variable and independent x variables when there is a linear pattern.

According to the given problem,

From the table we can see,

ln(Element) is the dependent variable and Time is the independent variable.

The constant = 2.305,

Time = -0.101

Hence, we can conclude, our least squared regression line will be

In (Element) = 2.305 - 0.101 (Time).

Learn more about regression line here: brainly.com/question/7656407

#SPJ2

6 0
2 years ago
13(6x – 5) – x = 13 – 2(x + 1)
Murrr4er [49]

Answer:

x = 76/79

Hope this helped

7 0
3 years ago
Read 2 more answers
What is the value for x
Sloan [31]
Because this is a right angle triangle, we can use the Pythagorean theorem to find the missing leg.

The Pythagorean theorem is this: a^{2} + b^{2} = c^{2}

The Pythagorean theorem tells us if you square both the legs then add them up together, you will get the length of the hypotenuse squared.

We know one leg is 24 and the hypotenuse is 26. Plug them into the equation.

24^2 + b^2 = 26^2

Solve for b.

24^2 + b^2 = 26^2
576 + b^2 = 26^2
576 + b^2 = 676
b^2 = 100

Take the square root of both sides.

b = 10

So, the other leg of the triangle is 10 units long.
8 0
3 years ago
Read 2 more answers
Plumber A charges $60 an hour. Plumber B charges $40 to visit your home plus $55 for each hour. For how many hours will the tota
GuDViN [60]

Answer:

8 hours

$480

Step-by-step explanation:

Let us assume the hours be x

There should be two equations

For Plumber A = 60x

For Plumber B = 40 + 55x

Now in order to considered the cost to be the same we equate these two equations

60x = 40 + 55x

5x = 40

x = 8 hours

Now the total cost for plumber A is

= 480

And, the total cost for plumber B is

= 40 + 55(8)

= 480

hence, the total cost is $480

6 0
2 years ago
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