1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Katena32 [7]
3 years ago
5

What is the solution set of the equation, and why?

%7B4%7D%7Bx%7D" id="TexFormula1" title="\frac{x-11}{x+4}= 2-\frac{4}{x}" alt="\frac{x-11}{x+4}= 2-\frac{4}{x}" align="absmiddle" class="latex-formula">
A. {-8, 2}
B. {-16, 1}
C. {-1, 16}
Mathematics
2 answers:
Ne4ueva [31]3 years ago
5 0

Domain:\\x+4\neq0\ \wedge\ x\neq0\\\\\boxed{D:x\neq-4\ \wedge\ x\neq0}\\------------------------\\\\\dfrac{x-11}{x+4}=2-\dfrac{4}{x}\\\\\dfrac{x-11}{x+4}=\dfrac{2x}{x}-\dfrac{4}{x}\\\\\dfrac{x-11}{x+4}=\dfrac{2x-4}{x}\qquad\text{cross multiply}\\\\(x+4)(2x-4)=x(x-11)\qquad\text{use distributive property}\\\\(x)(2x)+(x)(-4)+(4)(2x)+(4)(-4)=(x)(x)+(x)(-11)\\\\2x^2-4x+8x-16=x^2-11x\\\\2x^2+(-4x+8x)-16=x^2-11x\\\\2x^2+4x-16=x^2-11x\qquad\text{subtract}\ x^2\ \text{from both sides}

x^2+4x-16=-11x\qquad\text{add}\ 11x\ \text{to both sides}\\\\x^2+15x-16=0\\\\x^2+16x-x-16=0\\\\x(x+16)-1(x+16)=0\\\\(x+16)(x-1)=0\iff x+16=0\ \vee\ x-1=0\\\\\boxed{x=-16\in D\ \vee\ x=1\in D}\\\\Answer:\ B.\ \{-16,\ 1\}

mart [117]3 years ago
3 0

Answer:

B.) {-16,1}

Step-by-step explanation:

First let us combine like terms so let us move the -4/x to the right side:

\frac{x-11}{x+4}=2-\frac{4}{x}

\frac{x-11}{x+4} +\frac{4}{x}=2

Let us find a common denominator for the left side by using : \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd} and so:

\frac{x(x-11)+4(x+4)}{x(x+4)} = 2\\ \\\frac{x^2-11x+4x+16}{x^2+4x}=2\\

Now lets get rid of that fraction by multiplying both sides by x^2+4x and we obtain:

x^2-7x+16=2(x^2+4x)\\\\x^2-7x+16=2x^2+8x

I'm going to move everything on the left side to the right by: -(x^2-7x+16) and so:

0=2x^2+8x-x^2+7x-16\\\\0=x^2+15x-16

Now let's factor.  We can factor by multiplying outer coefficients, so 1 x -16 = -16.  Now let's list all the factors of 16:  1×16,8×2,4×4.  From these factors try to find two that if you add or subtract them they will return the middle term of 15.  So, 16 - 1  = 15.  Therefore,

0=x^2+15x-16\\\\0=x^2+16x-x-16\\\\0=x(x+16)-(x+16)\\0=(x-1)(x+16)

Now lets solve for both cases:

Case 1:

x-1=0

x=1

Case 2:

x+16=0

x=-16

and so your solutions are:

x={1,-16} or x={-16,1}



You might be interested in
Estimate the solution of the system of equations. Write the answer as an ordered pair.
AysviL [449]
(1,2.5) would be the solution to the system of equations
8 0
3 years ago
Which table(s) show x and y in DIRECT PROPORTION
Nataly [62]

Answer:

B and C only show direct proportion

3 0
3 years ago
Read 2 more answers
What is the unit price for a piece of cheese if 1.24 pounds costs $11.25?
Luba_88 [7]

Answer:

$9.07 per pound

Step-by-step explanation:

Take the total cost and divide by the number of pounds

$11.25/ 1.24

$9.072580645 per pound

Rounding to the nearest cent

$9.07 per pound

7 0
3 years ago
If U = {x: X € N, 1 < × < 15)
Inessa05 [86]

Answer:

Step-by-step explanation:

Given:

U = {x: X € N, 1 < × < 15) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A = {2,4,6,8,10,12,14}

B = {3,6,9,12,15}

C = {5,10,15}

(a) Verify A(BnB)=(AUB)(AUB)

A U (B n B)

=  {2,4,6,8,10,12,14} U (  {3,6,9,12,15} n  {3,6,9,12,15} )

=  {2,4,6,8,10,12,14} U {3,6,9,12,15}

=  {2,3,4,6,8,9,10,12,14,15}

( A U B) n (A U B)

= {2,3,4,6,8,9,10,12,14,15} n {2,3,4,6,8,9,10,12,14,15}

= {2,3,4,6,8,9,10,12,14,15}

Therefore

A U (B n B)  =  ( A U B) n (A U B)

verifies

(b) Verify An(BUC)=(AnB)u(AnC)

A n ( B U C)

=  {2,4,6,8,10,12,14} n ( {3,6,9,12,15} U {5,10,15} )

=  {2,4,6,8,10,12,14} n {3,5,6,9,10,12,15}

= {6,10,12}

( A n B ) U ( A n C )

= ( {2,4,6,8,10,12,14} n {3,6,9,12,15} ) U ( {2,4,6,8,10,12,14} n {5,10,15} )

= {6,12} U {10}

= {6,10,12}

Therefore

A n ( B U C) = ( A n B ) U ( A n C )

verifies

(c) Verify AU(BUC)=(AUB)U(AUC)​

AU(BUC)

=  {2,4,6,8,10,12,14}U{3,6,9,12,15}U{5,10,15}

= {2,3,4,5,6,8,9,10,12,14,15}

(AUB)U(AUC)​

=  ({2,4,6,8,10,12,14}{3,6,9,12,15})U({2,4,6,8,10,12,14}U{5,10,15})

= {2,3,4,6,8,9,10,12,14,15}U{2,4,5,6,8,10,12,14,15}

= {2,3,4,5,6,8,9,10,12,14,15}

Therefore

AU(BUC)=(AUB)U(AUC)​

verifies

5 0
3 years ago
Which choice is equivalent to the product below for acceptable values of x
victus00 [196]

the answer would be A.

7x × X gives you 7x^2

7x × 2 gives you 14 X

so the answer is the square root of 7x^2 + 14 X

5 0
3 years ago
Read 2 more answers
Other questions:
  • Pedro sells wooden children's furniture at a crafts market.He charges $65 for a chair.The materials for a chair cost $45 and the
    10·1 answer
  • The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.Wha
    8·1 answer
  • I don’t quite understand this
    5·1 answer
  • The answer please..:.....
    12·1 answer
  • 6. Find the inverse of the function f(x)= 2x - 4 and show explain each step used to find the inverse.
    15·2 answers
  • Find the midpoint M of the line segment joining the points S = (8,-5) and T = (-2, 3).
    8·1 answer
  • Write the first trigonometric function in terms of the second for theta in the given quadrant:
    8·2 answers
  • What would be the answer ?? how do I interpret the remainder in this situation ?
    6·1 answer
  • Y is directly proportional to x. If y=15 when x=3,find y when x=30<br><br><br><br><br>Pls help​
    8·1 answer
  • How much money do we have, after interest, if we put $2500 into an account that compounds annually one) at a rate of 2.1% over 3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!