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
Troyanec [42]
3 years ago
12

Two problems here I need solved! I need every step, so please have that with your answers!!

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
7 0
QUESTION 1

We want to solve,

\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}

We factor the denominator of the fraction on the right hand side to get,

\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-4x - 2x+8}.

This implies
\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x(x-4) - 2(x - 4)}.

\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{(x-4)(x - 2)}

We multiply through by LCM of
(x-4)(x - 2)

(x - 2) + x(x-4) = 2

We expand to get,

x - 2 + {x}^{2} - 4x= 2

We group like terms and equate everything to zero,

{x}^{2} + x - 4x - 2 - 2 = 0

We split the middle term,

{x}^{2} + - 3x - 4 = 0

We factor to get,

{x}^{2} + x - 4x- 4 = 0

x(x + 1) - 4(x + 1) = 0

(x + 1)(x - 4) = 0

x + 1 = 0 \: or \: x - 4 = 0

x = - 1 \: or \: x = 4

But
x = 4
is not in the domain of the given equation.

It is an extraneous solution.

\therefore \: x = - 1
is the only solution.

QUESTION 2

\sqrt{x+11} -x=-1

We add x to both sides,

\sqrt{x+11} =x-1

We square both sides,

x + 11 = (x - 1)^{2}

We expand to get,

x + 11 = {x}^{2} - 2x + 1

This implies,

{x}^{2} - 3x - 10 = 0

We solve this quadratic equation by factorization,

{x}^{2} - 5x + 2x - 10 = 0

x(x - 5) + 2(x - 5) = 0

(x + 2)(x - 5) = 0

x + 2 = 0 \: or \: x - 5 = 0

x = - 2 \: or \: x = 5

But
x = - 2
is an extraneous solution

\therefore \: x = 5
You might be interested in
Is j+j+j+j and j with the power of four equivalent
riadik2000 [5.3K]

Answer:

The joule (/ dʒ aʊ l, dʒ uː l / jawl, jool; symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of the force's motion through a distance of one metre (1 newton metre or N⋅m). It is also the energy dissipated as heat when an electric ...

Step-by-step explanation:

3 0
3 years ago
Please help i’m blanking lol
tangare [24]

Answer:

The answer is the graph D

Step-by-step explanation:

The inequation states that:

abs(x) >3.

By definition, the absolute value | x | is the distance of x from zero. In this case: | x | > 3 The solution is going to be all the points that are greater than three units away from zero.

For that reason the solution is -3>x>3. That is to say, all values greater than 3 or less than -3 are solutions.

5 0
3 years ago
Read 2 more answers
The population p (in millions) of Italy from 1990 through 2008 can be approximated by the model p=56.8e^o.oo15t , where t repres
dimulka [17.4K]

As we already have the model that describes the change of the population in Italy in terms of the years that have elapsed, we only have to replace the conditions that are requested in that equation.

Therefore to find the population of Italy in the year 2000 (t = 10 years)  substitute t = 10 in the equation and have:

p = 56.8e^{0.0015*10}\\

p=57.6584 million people

To find the population of Italy in 2008 (t = 18 years)

substitute t = 18 in the equation and have:

p=56.8e ^{0.0015*18}\\

p=58.3545 million people


To predict the population in Italy for 2015 and 2020 with this model, we substitute in the equation t = 25 and t = 30

t = 25

p=56.8e^{0.0015*25}

p=58.9704 million people


 t = 30

p=56.8e^{0.0015*30}

p=59.4144 million people

8 0
3 years ago
Use PMT equals StartFraction Upper P (StartFraction r Over n EndFraction )Over [1 minus (1 plus StartFraction r Over n EndFracti
Zigmanuir [339]

Answer:

I think it’s best to ask your teacher

Step-by-step explanation:

Sorry I needed the points

8 0
3 years ago
What is the slope of the line represented by the equation y=x/4-€
sveticcg [70]
Y = x/4 - <span>€

y = (1/4)x - </span><span>€
</span><span>
y = 0.25x - </span>€   comparing to y = mx + c

m = slope = 0.25 or (1/4)
5 0
3 years ago
Other questions:
  • Answer as much as possible
    8·1 answer
  • What is 7 29/80 as a mixed number with a decimal
    12·1 answer
  • You are choosing a book from your friend’s book collection. You can choose 1 of 6 science fiction books, 1 of 2 mystery books, o
    7·2 answers
  • What does the 2 represent in 12.789
    6·2 answers
  • How to a measure of angle A
    12·1 answer
  • If the radius of a circle is 5.75 mm, what is the diameter?
    7·2 answers
  • Sumone help me plz lol
    10·2 answers
  • Write AB−⇀− with A(−7,5) and B(−3,−7) in component form.
    7·1 answer
  • What is the value of one divided by zero?
    13·2 answers
  • For the past 15 months, Frank recorded the cost of his monthly home heating bill and the corresponding average monthly temperatu
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!