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
Nikolay [14]
1 year ago
10

hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

shows me every step thank you

Mathematics
1 answer:
Mariulka [41]1 year ago
6 0

Given:

The equation is,

2\log _3x-\log _3(x-2)=2

Explanation:

Simplify the equation by using logarthimic property.

\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{      \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}

Simplify further.

\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}

Solve the quadratic equation for x.

\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

\begin{gathered} x-6=0 \\ x=6 \end{gathered}

For (x - 3) = 0,

\begin{gathered} x-3=0 \\ x=3 \end{gathered}

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

You might be interested in
Slope of (-20,9) (14,9)
skelet666 [1.2K]
Y2-y1/x2-x1 is slope so

9-9/14-(-20) so you get 0/34 which means there is no slope since they have the same y (the equation would be y=0x+9 therefore y=9)
Which makes sense since the equation is a straight line
3 0
3 years ago
Classify the following as discrete or continuous random variables.
Elena-2011 [213]

Answer:

A discrete variable is a variable that can only take some selected given values from a given set, like x ∈ {x₁, x₂, ..., xₙ}

While a continuous variable can take any value in the range, like x ∈ {x₁, xₙ}.

1)  The weight of bags of apples, with 10 apples in each bag.

Here the weight depends on the number of apples in the bag, and we can have only whole numbers of apples in the bag, so this is clearly a discrete variable.

2) The number of times required for a modem to dial an internet provider before connecting.

Same as before, here we can have only a whole number of attempts, so this set is discrete.

3) Out of 10 times connecting to an internet provider, the average number of attempts necessary before connecting.

Here we will have an average of 10 integer numbers:

M = \frac{x_1 + x_2 + ... + x_{10}}{10}

so here we have a kinda dense set of possible values, so we can think of this as a continuous variable.

4)  A pair of dice is rolled, and the sum to appear on the dice is recorded.

Here the possible values are whole numbers again, so we can not have values like 3.5, so again, this is a discrete variable.

8 0
3 years ago
The front row in a movie theater has 23 seats. If you were asked to sit in the seat that occupied the median position, in which
Scorpion4ik [409]

Answer:

You would have to sit in the 12th seat. (12)

Step-by-step explanation:

The median is the middle number in a sorted, ascending or descending, list of numbers.

3 0
3 years ago
Simplify: (-2)(-3)+(4)(-8)<br><br>Simplify: (3)(-6)-18​
koban [17]

Answer:

4

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
As inflation increases, it causes the money you earn today to have _____. less value in the future more purchasing power in the
Anika [276]

Answer:

This answer is A

Step-by-step explanation:

your welcome, im fast to answer

5 0
3 years ago
Read 2 more answers
Other questions:
  • A marketing consultant was in the process of studying the perceptions of married couples concerning their weekly food expenditur
    7·1 answer
  • 57.42
    13·1 answer
  • *Use the Area formula
    9·1 answer
  • I will give BRAINLIEST for questions 3 and 4
    7·1 answer
  • PLEASEE CHOOSE ONE ANSWER :) <br>A, B, C or D
    10·1 answer
  • Why was one trinomial jealous of the other trinomial?
    11·1 answer
  • 1. f(x) = x^3– 4x^2 – 7x + 10
    6·1 answer
  • Please help with geometry homework
    6·1 answer
  • PLZ HELP <br>fill in the blanks ​
    13·2 answers
  • List all the 3-digit odd numbers that can be created by rearranging these number tiles.<br> 7 3 4
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!