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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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Activity 3
skad [1K]

Answer:

19 Lollipops per friend

Step-by-step explanation:

60-3=57\\\\57/3=19

3 0
2 years ago
Read 2 more answers
There are 132 counters in a bag. The ratio of green counters to purple
DedPeter [7]

9514 1404 393

Answer:

  77 purple counters

Step-by-step explanation:

There are a total of 5+7=12 ratio units, so each stands for 132/12 = 11 counters. The 7 ratio units representing the purple counters stand for ...

  11 × 7 = 77 purple counters

4 0
2 years ago
The population standard deviation of the numbers 3, 8, 12, 17, and 25 is 7.563 correct to 3 decimal places. what happens if each
user100 [1]
Let's figure this out as though we have no idea what the answer would be.

Step One
Find the new five numbers.
3*3, 8*3, 12*3, 17*3, 25*3
9 , 24 , 36, 51, 75

Step 2
Find the average
(9 + 24 + 36 + 51 + 75)/5 = 195/5 = 39

Step 3
Subtract the individual numbers from the average
(39 - 9) = 30
(39 -24) = 15
(39 - 36) = 3
(39 - 51) = - 12
(39 - 75) = -36

Step 4 
Square the results from Step 3
30^2 = 900
15^2 = 225
3^2 = 9
(-12)^2 = 144
(-36)^2 = 1296

Step 5
Take the average of the results from step 4
(900 + 225 + 9 + 144 + 1296)/5
2574 / 5 = 514.8

Step 6
Take the square root of the result from step 5
deviation = sqrt(514.8)
deviation = 22.689

Step seven 
Compare the two standard deviations.
s2/s1 = 22.689 / 7.563 = 3

Conclusion
If you are given 1 set of numbers to find a population standard deviation and you multiply each member by a, then the result will be a * the standard population deviation of the first set of numbers.

Note
Your calculator will do this as well, but you have to know how to enter the data into your calculator. That requires that you follow the directions carefully. 

7 0
3 years ago
Please help!!!! (don’t comment for free points, this isn’t the place)
Allushta [10]

tan 44 = h/ x

x = 15 ft * sin 26

so

h = x * tan 44

= (15 ft * sin 26) (tan 44 )

so the anser is D

hope this would help you

5 0
3 years ago
Read 2 more answers
Find the factors of<br>y2 + 2y - 35​
baherus [9]

Answer:

(y-5)(y+7)

Step-by-step explanation:

3 0
3 years ago
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