IM GIVING BRAINIEST TO THE FIRST CORRECT ANSWER !!! HURRY.

<img src="https://tex.z-dn.net/?f=%20log_%7B2%7D%283x%20%2B%204%29%20%20-%207%20log_%7B4%7D%7Bx%7D%5E%7B2%7D%20%20%2B%20%20log_%

olga2289 [7]

First of all, we need all logarithms to have the same base. So, we use the formula

$\log_a(b)=\dfrac{\log_c(b)}{\log_c(a)}$

To change the second term as follows:

$\log_4(x^2)=\dfrac{\log_2(x^2)}{\log_2(4)}=\dfrac{\log_2(x^2)}{2}$

Finally, using the property

$\log(a^b)=b\log(a)$

we have

$\dfrac{\log_2(x^2)}{2}=\log_2(x)$

So, the equation becomes

$\log_2(3x+4)-7\log_2(x)+\log_2(x)=2 \iff \log_2(3x+4)-6\log_2(x)=2$

We can now use the formula

$\log(a)-\log(b)=\log\left(\dfrac{a}{b}\right)$

to write the equation as

$\log_2(3x+4)-6\log_2(x)=2 \iff \log_2(3x+4)-\log_2(x^6)=2 \iff \log_2\left(\dfrac{3x+4}{x^6}\right)=2$

Now consider both sides as exponents of 2:

$\dfrac{3x+4}{x^6}=4 \iff 4x^6-3x-4=0$

This equation has no "nice" solution, so I guess the problem is as simplifies as it can be

5 0

3 years ago

The equation of a circle is x^2+y^2-2x +6y-6=0. Find the center and radius of the circle by completing the square.you must inclu

zavuch27 [327]

Answer:

The center of the circle is at;

$(1,-3)$

The radius of the circle is;

$r=4$

Explanation:

Given the equation of circle;

$x^2+y^2-2x+6y-6=0$

we want to re-write it in the form;

$(x-h)^2+(y-k)^2=r^2$

where;

$\begin{gathered} (h,k)\text{ is the center of the circle} \\ r\text{ is the radius} \end{gathered}$

Applying Completing the square method;

$\begin{gathered} x^2+y^2-2x+6y-6=0 \\ x^2-2x+1+y^2+6y+9=6+1+9 \\ (x-1)^2+(y+3)^2=16 \\ (x-1)^2+(y+3)^2=4^2 \end{gathered}$

comparing the derived equation to the general form we have;

$\begin{gathered} h=1 \\ k=-3 \\ r=4 \end{gathered}$

Therefore;

The center of the circle is at;

$(1,-3)$

The radius of the circle is;

$r=4$

6 0

1 year ago

Help me with this one please

Drupady [299]

Step-by-step explanation:

1cm = 16 km

Distance between York and London = 23.1 cm

<em>Now the real distance between </em><em>York </em><em>and </em><em>London </em><em>=</em><em> </em><em>2</em><em>3</em><em>.</em><em>1</em><em> </em><em>*</em><em> </em><em>1</em><em>6</em>

6 0

3 years ago

Question 1

olya-2409 [2.1K]

Answers:

Step-by-step explanation:

To solve this, we plug in the given values for x, 1, 2, and 3.

<h2>Scenario 1. What is y when x is 1?</h2>

y = 3x + 4

y = 3(1) + 4

y = 3 + 4

y = 7

<h2>Scenario 2: What is y when x is 2?</h2>

y = 3x + 4

y = 3(2) + 4

y = 6 + 4

y = 10

<h2>Scenario 3: What is y when x is 3?</h2>

y = 3x + 4

y = 3(3) + 4

y = 9 + 4

y = 13

Interesting pattern: y appears to be 3 times x

In other words: as x increases by 1, y will increase by 3. The slope of this line is y/x or 3/1 or simply, 3.

7 0

3 years ago

A local agricultural cooperative claims that 55% of about 60,000 adults in a country believe that gardening should be part of th

insens350 [35]

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.0409 = 4.09% probability that, from a simple random sample of 300 adults in the county, less than 50% would say they believe that gardening should be part of the school curriculum.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample proportions for a proportion p in a sample of size n has $\mu = p, s = \sqrt{\frac{p(1 - p)}{n}}$

In this problem:

The proportion is of 55%, hence $p = 0.55$

The sample has 300 adults, hence $n = 300$

Then, the <u>mean and the standard error</u> are given by:

$\mu = p = 0.55$

$s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.55(0.45)}{300}} = 0.0287$

The probability is the <u>p-value of Z when X = 0.5,</u> hence:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.5 - 0.55}{0.0287}$

$Z = -1.74$

$Z = -1.74$ has a p-value of 0.0409.

0.0409 = 4.09% probability that, from a simple random sample of 300 adults in the county, less than 50% would say they believe that gardening should be part of the school curriculum.

A similar problem is given at brainly.com/question/25800303

8 0

3 years ago