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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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2 mixed numbers between 3 and 4 that have a product between 9 and 10
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3 0
3 years ago
-1.2= y/2.4 -1.7<br> Solve for y
evablogger [386]

{\huge{\boxed{\sf{Question}}

-1.2= y\div2.4 -1.7

Solve for y

{\huge{\boxed{\sf{Answer\:with\:explanation }}}

let's put our equation first

-1.2= y\div2.4 -1.7

Flip the equation

y\div2.4-1.7=-1.2

Now follow the rule of BOMDAS/PEMDAS

{\huge{\boxed{\sf{BOMDAS }}}

  • Brackets
  • Of multiplication
  • Division
  • Addition
  • Subtraction

{\huge{\boxed{\sf{PEMDAS}}}

  • Parenthesis
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

_________________________

{\huge{\boxed{\sf{Solve\:the\:equation}}}

_________________________

y\div2.4-1.7=-1.2

{\underline{simplify}}

0.416667y-1.7=-1.2

add 1.7 to both sides

0.416667y=0.5

Divide both sides by 0.416667

y=1.2

{\huge{\boxed{\sf{Answer}}}

y would equal 1.2

4 0
2 years ago
There are 2 questions pls answer fast
Furkat [3]

Answer:

Q1: B. UHWXUQV

Q2: None of these answers equal 12 so I'll just tell you the answers for all of them in case you mistyped.

a. 66

b. 82

c. 120

d. 109

Im assuming you meant 120. If so, your answer is c.

5 0
2 years ago
Which of these describes the equation –18x + 9y = –416?
Minchanka [31]

Answer:

We conclude the equation is linear because it can be rewritten in the form y = mx + b.

Hence, option D is correct.

Step-by-step explanation:

The slope-intercept form of the line or linear equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

<u>Important Tip:</u>

The graph of a linear equation is always a straight line.

Convert the given equation in the slope-intercept form

18x + 9y = -416

subtract 18x from both sides

18x+9y-18x = - 18x-416

simplify

9y = -18x - 416

divide both sides by 9

y=-2x-\frac{416}{9}

Now, comparing the equation y=-2x-\frac{416}{9} with a slop-intercept form of linear equation

  • The slope m = -2
  • The y-intercept b = -416/9

Therefore, we conclude the equation is linear because it can be rewritten in the form y = mx + b.

From the attached graph, is also clear that the graph of the equation y=-2x-\frac{416}{9} is a straight line.

Hence, option D is correct.

3 0
2 years ago
Read 2 more answers
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