All categories

3 years ago

Evaluate log1∕6 36. please help

1 answer:

4 0

$\log_{\tfrac 16} 36 \\\\\\=\dfrac{\ln 36}{ \ln \left(\tfrac 16\right)}\\\\\\=\dfrac{ \ln 6^2}{\ln (6^{-1})}\\\\\\=\dfrac{2 \ln 6}{-1 \ln 6}\\\\= - 2$

You might be interested in

The ordered pairs (−4,−3)

lilavasa [31]

The equations and inequality expresses the relationship between the variables.

The correct responses are;

First part; The rule that represent the function is; y = 0.5·x - 1

Second part; the correct option is the inequality; 2·n - 6 ≥ 35

Third part; $\displaystyle \underline{b = \frac{- a\cdot x^2 - c}{x}}$

Fourth part; Table 4

Fifth part; $\displaystyle \underline{y < -\frac{1}{2} \cdot x - 4}$

Sixth part; 75·w + 55 ≤ 400

Reasons:

First part;

The difference between y-values following a change in 2 units of the x-value is a constant, and is equal to 1;

The rate of change of the function, m, is therefore;

$\displaystyle m = \frac{2 - 1}{6 - 4} = \frac{1}{2} = 0.5$

The slope and intercept form of the equation of the function is therefore;

y - 3 = 0.5·(x - 8) = 0.5·x - 4

y = 0.5·x - 4 + 3 = 0.5·x - 1

The rule that represent the function is; y = 0.5·x - 1

Second part;

2·n represent twice the number

The difference between twice the number and 6 = 2·n - 6

At least 35 = ≥ 35

Therefore, the inequality is; 2·n - 6 ≥ 35

Third part;

The given quadratic equation is; a·x² + b·x + c = 0

Therefore;

$\displaystyle \underline{b = \frac{-c - a\cdot x^2}{x}}$

Fourth part;

The best correct option is table 4, given that the table is as follows;

$\begin{tabular}{|c|cc|}In&&Out\\Not clear&&\\9&&17\\10&&19\end{array}\right]$

Fifth part;

The y-intercept of the graph is -0.5

The slope is -4 ÷ 8 = -0.5

Therefore, the equation is; y = -0.5·x - 4

The shaded area is the area lower than the y-values, with broken lines (indicating < relationship) which gives, the correct inequality as follows;

$\displaystyle \underline{y < -\frac{1}{2} \cdot x - 4}$

Sixth part;

The amount Jordan part-time job pays = $75

The amount he has already saved = $55

The cost of the iPhone = $400

Let w represent the number of weeks Jordan works, at his part-time job to purchase the iPhone, we have;

75·w + 55 ≤ 400

Learn more about writing equations and inequalities here:

brainly.com/question/14321394

3 0

2 years ago

A circle with radius of 5 cm sits inside a 11 cm * 11 cm rectangle.

Nadusha1986 [10]

Answer:

42.43 $cm^{2}$

Step-by-step explanation:

Given:

A circle with a radius of 5 cm sits inside a 11 cm x 11 cm rectangle.

Question asked:

What is the area of the shaded region as shown in the figure ?

Solution:

First of all calculate area of circle and then area of rectangle:-

$Area\ of\ cirle=\pi r^{2}$

$=\frac{22}{7} \times5\times5\\ \\ =\frac{550}{7}\\ \\=78.571\ cm^{2}\\$

As here length an width both are 11 cm, we can say that this is a square.

$Area\ of\ square=(Side)^{2}$

$=11\times11=121\ cm^{2}$

Now, area of shaded region = Area of square - Area of circle

= 121 - 78.571 = 42.429 $cm^{2}$

Therefore, the area of the shaded region will be 42.43 $cm^{2}$

Download docx

5 0

3 years ago

Find the range of the dataset 8,11,5,22,9,18,5,20

lakkis [162]

Answer: 17

Step-by-step explanation: The range of a data set is the difference between the largest and smallest numbers

In this data set, the largest number is 22 and the smallest number is 5 so the range of the data set will simply be 22 - 5 or 17.

So the range of this data set is 17.

3 0

4 years ago

Read 2 more answers

Find the x-intercept of the line graphed by the equation x - 7y = 7. (0, 14) (7, 0) (14, 0) (0, 7)

Nastasia [14]

X－7y＝7
To find the x-intercept, substitute y＝0
x－7×0＝7
x－0＝7
x＝7
∴ the x-intercept of the line is (7,0)

7 0

3 years ago

a beekeeper estimates that his bee population will triple each year. Currently he has 150 bees. Write a function to represent th

Soloha48 [4]

Answer:

Exponential functions!

Step-by-step explanation:

I think what you are dealing with is an exponential function!

So, to solve this, we need to first understand the main form of an exponential function:

$f(x)=a*b^{x}$

Where a is the number we start off with, and b is the constant thing(forgot what it was called).

Now, 150 is our starting number, so it is a, and b is our constant at which the initial term is multiplied, which is 3!

Also, defining variables:

Let f(x)= # of Bees

Let x= # of years

Thus, here is our equation:

$f(x)=150*3^{x}$

So, that's it!

Now, some of my answers have been recently deleted because they violated community guidelines for recommending something that shall not be named, so if you do really need help on the subject, look online! It is the largest source of information humanity has created! (also I cannot explain Exponential Functions in a single paragraph)

Stay Safe!

4 0

3 years ago