2log 6- log 12 + log 16​

The sine , cosine and tangent of an acute angle can be find by using:

Acute Angle:

Acute angles are defined as angles less than 90 degrees, i.e. angles between 0° and 90°. Examples include 60°, 30°, 45°. A triangle with all interior angles less than 90° is called an acute triangle. For example, an equilateral triangle is an acute triangle because its interior angles are 60°.

Sine of an Acute Angle :

The sine of an angle in a right triangle is the ratio of the opposite side of the angle to the hypotenuse. The sine function is the important periodic function in trigonometry, with period 2π. To understand the derivation of sin x, consider the unit circle centered at the origin of the coordinate plane. On the boundary (perimeter) of this circle the variable point P moves. Note that P is in the first quadrant and OP makes an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis.

Cosine:

Cosine or cos x is the trigonometric periodic function. Imagine a unit circle centered at the origin of the coordinate plane. The variable point P moves on the circumference of this circle. From the figure, we can see that P is in the first quadrant and OP forms an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis. A triangle is therefore formed by connecting the points O, P, and Q as shown. where OQ is the base and PQ is the height of the triangle.

Tangent:

The tangent function is one of the six most important trigonometric functions, commonly written as tan x. It is the ratio of the opposite side to the adjacent side of the angle considered in a right triangle. There are various trigonometric identities and formulas related to the tangent function that can be derived using various formulas. The period expression for the tangent function f(x) = a tan (bx) is given by Period = π/|b|. The tangent function tan x is periodic, with period π/1 = π (because b = 1 for tan x).

So the formula for tan x is:

tan x = sin x/cos x

tan x = opposite side/adjacent side

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The domain and range of the logarithmic function is given by:

Domain= [ 0 , ∞ ) and Range = { y ∈ R }.

As given in the question,

Let y = logₐ x be the given logarithmic function.

Logarithmic function is defined for all the positive values.

Domain of the logarithmic function is given by x∈ R , x > 0.

Range of the logarithmic function is inverse of the domain of the exponential function.

x = e^y

Here y is set of all the real numbers.

Range of logarithmic function is set of all the real numbers.

Therefore, domain of the logarithmic function is set of all real number greater than zero and range of the logarithmic function is the set of all the real numbers.

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The perimeter of the sign is 22 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangular school banner has a length of 21 inches and a perimeter of 66 inches.

Let the perimeter of the sign for the length of 7 inches of the banner = x

So, By definition of proportion, we get;

⇒ 21 / 66 = 7 / x

Solve for x;

⇒ x = 7 × 66 / 21

⇒ x = 22

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To know whether Elena is correct or not, you need to find out the height of each stack of file folder.

Assume that all 200 files have the same height.

Let the height of each file folder be m inches.

So, by unitary method the height of each file folder would be,

m = Total height of stack / Number of file folders

here, the total height of stack = 5.125 inches

And the number of file folders = 200

So, m = 5.125 / 200

m = 0.0256 inches

But Elena guesses that each file folder is 0. 035 inches thick.

This means, Elena is wrong as the answer Elena gave is too large than the actual answer.

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The figure also has a line symmetry for the vertical line x is  5, and a line symmetry for the horizontal line y is 5 .Therefore the figure has both symmetry

A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it creates a symmetrical split in the figure and the separated pieces look like mirror reflections of one another, we also refer to this line as the axis of symmetry or the mirror line.

An imaginary line that splits a line or shape into two identical parts is called the axis or line of symmetry. The symmetry axis of a parabola will be required of you at higher level mathematics. This u-shaped line on the graph is a parabola.

B) The transformation that maps the figure unto itself are therefore;

1) Rotating the figure 180° about the point (5, 5) which is the center of the figure

2) The figure reflected across the line x = 5 and the figure reflected across the line y = 5

The complete question is : Determine if the figure below has rotational symmetry, line symmetry or both and

describe the transformation that mas the figure onto itself. BE SPECIFIC. You must

name the center of rotation and degree of rotation if it has rotational symmetry or lines of reflection if it has line symmetry

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A log 10 transformation is a mathematical operation that is used to change the scale of a variable in a data set. The log 10 transformation is applied to the variable by taking the base-10 logarithm of each value in the data set. The result of this operation is a new variable that is on a different scale than the original variable.

The log 10 transformation is commonly used in statistics and data analysis to normalize data that is on a large scale, such as data that spans several orders of magnitude. By applying the log 10 transformation, the data is transformed into a more manageable scale that is easier to work with and analyze.

The log 10 transformation can also be used to stabilize the variance of a variable, this is particularly useful when the data is positively skewed. The log 10 transformation can also be useful for data that has a multiplicative relationship, for example, population growth or stock prices.

It is important to note that the log 10 transformation can only be applied to data that is positive and greater than zero because the logarithm of zero or a negative number is not defined.

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Answer:

D)  5

Step-by-step explanation:

1,2,2,3,3,3,4,5,6,6,7,7,7,8,9

there are 15 data values so the 8th one is the median

Answer:

30

Step-by-step explanation:

Step 1: Find the area of the whole figure

The whole figure is a rectangle with a width of 4cm and a length of 12cm

The area of a rectangle can simply be calculated by multiplying the width by the length

So area = 4 * 12 which = 48

So the area of the whole figure is 48cm²

Step 2: Find the area of the non shaded area

The non shaded area forms a triangle with a base length of 9cm and a height of 4cm

The area of a triangle can be calculated using this formula

[tex]A=\frac{bh}{2}[/tex] where b = base length and h = height

That being said we plug in the values into the formula

[tex]A=\frac{9*4}{2} \\9*4=36\\\frac{36}{2} =18[/tex]

Hence the area of the non shaded region is 18cm²

Final step: Our last step is to subtract the area of the non shaded region by the area of the whole figure

so the answer = 48 - 18 which equals 30

Hence the area of the shaded region is 30 square centimeters.

Answer:144

Step-by-step explanation:

LM = √(8² + 6²) = √(64 + 36) = √100 = 10 yd

Area = 2 × (1/2) × 6 × 8 = 48 yd²

Answer:

Step-by-step explanation:

The simple explanation is that the hypotenuse and sides of a right triangle are always shorter than one another. Therefore, any side's to any hypotenuse's ratio will never be greater than 1. The figure is no longer a triangle when the angle is 0 or 90 degrees because one of the sides vanishes and the other side lines up with the hypotenuse. For this reason, sin and cosine have values of 0 or 1 in these extreme situations.

Answer:

1000

Step-by-step explanation:

it is much that's why period

Answer:

32.9% i think

Step-by-step explanation:

Answer: 1.55

Step-by-step explanation:

The possible values of x for the given triangle ABC are 0.75<x<8.

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Given that, m∠A < m∠B < m∠C.

a) From triangle ABC,

BC<AC<AB

2x+3<6x<5x+8

Now, 2x+3<6x

Subtract 2x on both the sides of an inequality, we get

3<4x

Divide 4 on both the sides of an inequality, we get

0.75<x

Here, 6x<5x+8

Subtract 5x on both the sides of an inequality, we get

x<8

So, possible values of x are 0.75<x<8

b) From triangle ABC,

BC<AC<AB

3x+1<4x+8<7x+2

Now, 3x+1<4x+8

Subtract 3x on both the sides of an inequality, we get

1<x+8

Subtract 8 on both the sides of an inequality, we get

-7<x

Here, 4x+8<7x+2

Subtract 4x on both the sides of an inequality, we get

8<3x+2

Subtract 2 on both the sides of an inequality, we get

6<3x

Divide 3 on both the sides of an inequality, we get

2<x

So, possible values of x are -7<x<2

Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.

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Answer: 12.96

Step-by-step explanation: you should multiply 12 * 0.08 = 0.96

then just add 0.96 + 12 = 12.96

Answer:

53

Step-by-step explanation:

Aim :

We have to convert them into improper fractions as they are into mixed fractions. So let's start..!!

Solution :

1) [tex] \bf{ 1\dfrac{5}{8} }[/tex]

Multiply 8 into 1 and add 5 into it,

[tex]: \: \implies \: \sf{ \dfrac{8 \times 1 \: + \: 5}{8}} \\ \\ : \: \implies \: \sf{ \dfrac{8 \: + \: 5}{8}} \\ \\ : \: \implies \: \red{\sf{ \dfrac{13}{8}}}[/tex]

_______________________________________

2) [tex] \bf{ 4\dfrac{2}{5} }[/tex]

Multiply 4 into 5 and add 2 into it.

[tex]: \: \implies \: \sf{ \dfrac{4\times 5 \: + \: 2}{5}} \\ \\ : \: \implies \: \sf{ \dfrac{20 \: + \: 2}{5}} \\ \\ : \: \implies \: \red{\sf{ \dfrac{22}{5}}}[/tex]

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3) [tex] \bf{ 2\dfrac{6}{8} }[/tex]

Multiply 8 into 2 and add 6 into it after multiplying.

[tex]: \: \implies \: \sf{ \dfrac{2 \times 8 \: + \: 6}{8}} \\ \\ : \: \implies \: \sf{ \dfrac{16 \: + \: 6}{8}} \\ \\ : \: \implies \: \red{\sf{ \dfrac{22}{8}}}[/tex]

Answer:

I believe it is 240 ft

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

7-6x+3x

You have to replace x for a 5.

7-6(5)+3(5)

After this you would multiple all of it.

7-30+15

Then add

7+15=22

-30+22=-8

Answer:

[tex] \sf \: 7 - 6x + 3x = - 8[/tex]

Step-by-step explanation:

Now we have to,

→ find the value of expression.

The expression is,

→ 7 - 6x + 3x

→ using (x = 5)

Let's solve the expression,

→ 7 - 6x + 3x

→ 7 - 6(5) + 3(5)

→ 7 - 30 + 15

→ 7 - 15

→ -8 => final answer

Hence, the answer is -8.

The x-intercept of the graph of y = x² - 4x + 4 is x = 2.

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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Answer:

70

Step-by-step explanation:

First, put the values they gave you in order from least to greatest.

52 62, 72, 77

In order for the median to be 72, it has to be in the middle of the data set. Since there are 2 values on the left of 72, there must be 2 values on the right. The data set is also in order from least to greatest, so we know that the last value has to be over 72. Because it is placed to the right of 72. The only value of the options that isn't greater than 72 is 70.

The unlikely temperature of the fifith day is 70.

The The median of an observation is the number that is in the middle of a set of numbers arranged in ascending or descending order.

The median temperature is 72. So, it has to lie in the middle of the observation. Let the temperature of the fifth day be represented with x. The unknown temperature has to be greater than 72 because there are already two numbers less than 72.

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Answer:

the hl theorem that says that if a leg and a hypotenuse of a right triangle are congruent to a leg and a hypotenuse of another right triangle, the two triangle are congruent

Step-by-step explanation:

Answer:

B. 10

Step-by-step explanation:

The first choice has 2 options: square or circle

The second choice has 5 options: orange, blue, yellow, red, or green.

2 x 5 = 10 total outcomes

Answer:

62%

Step-by-step explanation:

First, you got the formulate: 1-27%-11%

Second, calculate the difference: 0.73-0.11

Third, the sum is 0.62

Then you multiply 0.62 ×100\100

Write a single fraction: 0.62×100\100

Calculate the product or quotient: 62\100

100% to a percentage: 62%

That is your answer 62%

Answer:

The sample is large enough, representative of the entire population, and chosen randomly so the conclusion is valid.

The conclusion that 75% of the students in your school have visited an art museum is valid.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given that,

Total number of students in the art club being surveyed = 36

Number of students who visited art museum = 27

Number of students who does not visited art museum = 9

Percentage of students who visited art museum = (27 / 36) × 100

                                                                                 = (3/4) × 100

                                                                                 = 0.75 × 100

                                                                                 = 75%

Hence the conclusion that 75% of the students in your school have visited an art museum is valid.

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Answer:

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1

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2

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3

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4

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