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
assume that when adults with smartphones are randomly selected, 44% use them in meetings or classes. If 10 adult smartphones use
tensa zangetsu [6.8K]

Solution: The given random experiment follows Binomial distribution with n=10,p=0.44

Let X be the number of adults who use their smartphones in meetings or classes.

Therefore, we have to find:

P(X

We know the binomial model is:

P(X=x)=\binom{n}{x} p^{x} (1-p)^{n-x}

\therefore P(X

                       =\binom{10}{0}0.44^{0}(1-0.44)^{12-0}+\binom{10}{1}0.44^{1}(1-0.44)^{10-1}+\binom{10}{2}0.44^{2}(1-0.44)^{10-2}

                       =1 \times 1 \times 0.0030 + 10 \times 0.44 \times 0.0054 + 45 \times 0.1936 \times 0.009672

                       =0.0030+0.0238+0.0843

                       =0.1111

Therefore, the probability that fewer than 3 of them is 0.1111

7 0
3 years ago
Spiral Review A chili cook-off has adult tickets a and child tickets C. A group of visitors buys 3 adult tickets and 2 child tic
dem82 [27]

Equation 1 would be: 3a+2C

Equation 2 would be: 5a+3C

3 0
3 years ago
Please can anyone help me with this I tried to do it and I got it wrong.
MatroZZZ [7]

Answer:

how do I not know it not a vires?

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
If the moon is approximately 3.63*10/8 meters from earth <br>what is 3.63*10/8 in standard Notation
disa [49]
Move the decimal to the right 8 places
8 0
3 years ago
Read 2 more answers
What is the answer to this
LekaFEV [45]
4 \dfrac{3}{5} \times \dfrac{5}{12} =

= \dfrac{23}{5} \times \dfrac{5}{12}

You changed the mixed numeral into a fraction correctly.
Now you need to multiply the fractions.
Multiply the numerators together, and multiply the denominators together.

= \dfrac{23 \times 5}{5 \times 12}

Now we could multiply out the numerator and denominator, and then we'd need to reduce the fraction, but before we multiply, we see there is a factor of 5 both in the numerator and in the denominator, so we can reduce before we multiply.

= \dfrac{23 \times 5}{12 \times 5}

= \dfrac{23}{12}

= 1 \dfrac{11}{12}
6 0
3 years ago
Other questions:
  • If each dozen cookies needs 3/4 of a bag of flour to make how many bags of flour does Grandma need to buy if she's making 10 doz
    10·1 answer
  • 9 is 12% of what number ???
    14·2 answers
  • Line m passes through (4, 7) and (8, 2). Line n is parallel to line m. What is the slope
    8·1 answer
  • A television sports commentator wants to estimate the proportion of Americans who follow professional football. What sample size
    9·1 answer
  • Find the area of the triangle
    12·1 answer
  • TODAY ONLY: Towels are 30% off at the Towel Emporium. If our total before discount was $99.30, what is the price we will pay?
    15·1 answer
  • Isabella saved $13,000 and bought a car that cost $11,675. The insurance for the car will cost $650 per year.
    10·2 answers
  • Let f(x) = x2 − 3x − 7. Find f(−3).
    14·2 answers
  • Which one of the following would prove that two triangles are congruenta
    13·1 answer
  • $6500 were divided equally among a certain number of persons. Had there been 15 more persons, each would got $30 less. Find the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!