write [tex]sec^{2} x=\frac{1}{cos^2x}[/tex] in two equivalent forms.

To solve complex fractions there are two methods -

1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.

2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.

A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.

There are two ways to solve a complex fraction -

method 1 : Take an example - (1/3-1/4)/(1/8+1/2)

step1; If necessary, combine the denominator and numerator into a single fraction.

Add the numerator -

=1/3-1/4

=(4-3)/12

=1/12

Add the denominator -

=1/8+1/2

=(1+4)/8

=5/8

Combine back to form a complex fraction -

=(1/12)/(5/8)

Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.

Step 3: Simplify the rational expression if necessary.

=(1/12)×(8/5)

=8/60

=2/15

Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]

Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.

(x^2-25)=(x+5)(x-5)

The denominator of the denominator’s fraction  has the following factor -

(x-5)

Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -

(x+5)(x-5)

By multiplying the LCD by the numerator and denominator -

=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]

=(2x+1)/(2x+1)(2x-1)(x+5)

Step 2 - Simplify the rational expression if necessary.

=(2x+1)/(2x+1)(2x-1)(x+5)

=1/(2x-1)(x+5)

Therefore, there are two methods to solve complex fractions.

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The additive inverse of 2 9 is -2 9. This means that if you add -2 9 to 2 9, the result will be zero. This is because any number plus its opposite will equal zero.

2 9 + (-2 9) = 0

20 + (-20) = 0

The additive inverse of a number is the opposite of that number. This means that the inverse of 2 9 would be -2 9. When you add a number and its inverse together, the result is always zero. This is because any number plus its opposite will equal zero. For example, if we take 2 9 and add it to its inverse -2 9, the result will be 0. This is because 20 + (-20) = 0. The same concept can be applied to other numbers as well. For instance, if we take 3 4 and add it to its inverse -3 4, the result will be 0 because 34 + (-34) = 0. This shows that the additive inverse of a number is the opposite of that number, and when a number and its inverse are added together, the result is always zero.

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No, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side for a triangle to be formed.

In order to determine whether 7 cm, 8 cm, and 11 cm can form a triangle, we must first consider the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side in order for a triangle to be formed. Therefore, in order for 7 cm, 8 cm, and 11 cm to form a triangle, the sum of any two sides must be greater than 11 cm. Since

7 cm + 8 cm = 15 cm,

which is less than 11 cm, 7 cm, 8 cm, and 11 cm cannot form a triangle.

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Answer:

No

Step-by-step explanation:

3+6 is 9 which is greater than 7 so no it can not be a triangle

Answer:

For three lengths to form a triangle, the sum of two of the sides has to be more than the length of the third line. 3,6,8 or 3,6,7 will form triangles.

Step-by-step explanation:

A table can be read from top to bottom or left to right. When reading a table across a row, you should read the data from left to right.

In mathematics, a sequence is a list of items that is in a particular order (or events). It has members and is comparable to a set (also called elements, or terms). The amount of ordered elements determines how long the sequence is (potentially infinite). The four basic types of sequences that you should be knowledgeable about are arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. A number sequence is a collection of integers connected by a pattern. If you understand the rule, you can determine the subsequent numbers in the sequence. In this case, there is a 6 difference between each number. As a result, the rule for this sequence is to add 6 each time.

given

A table can be read from top to bottom or left to right. When reading a table across a row, you should read the data from left to right.

There are four black animals in total in the Cats and Dogs Table (2 + 2 = 4). The numbers in the row directly to the right of the term "Black" are those, as you can see.

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So the total area of the South China Sea and the Arctic Ocean is 2.10286 x 107 km2

To find the total area of the South China Sea and the Arctic Ocean, you would add their individual areas together.

The formula for finding the total area is:

Total Area = Area of South China Sea + Area of Arctic Ocean

By applying this formula we get:

Total Area = 6.963 × 106 km2 + 1.4056 × 107 km2

Total Area = 2.10286 x 107 km2

So the total area of the South China Sea and the Arctic Ocean is 2.10286 x 107 km2. The final answer is correct and has correct number of significant digits as per the given figures.

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The required rent is divided by the family as  $456,  $456, and $574.56.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Total rent = $ 1475
The total area of the place =  12× 10 + 10×11.2 + 12 × 12.6 = 383.2 units

Now,
Rent per square units = 1475/ 383.2 = $3.8
Now,
rent of bedroom with measure 12 by 10 = 12 × 10 × 3.8 = $456
rent of bedroom with measure 10 by 11.2 = 10 × 11.2 × 3.8 =  $456
rent of bedroom with measure 12 by 12.6 = 12 × 12.6 × 3.8 = $574.56

Thus, the required rent is divided by the family as  $456,  $456, and $574.56.

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The exponential function is y = 1200(1.04)^t and the investment amount after 16 years is $2247.58.

What is exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Jayden invests $1,200 in a savings account. Each year, the value increases by 4%.

Let t = time in years

Let y = amount of money invested in savings account

Start with $1200 and each year add 4% interest to the amount in the bank.

1st year: Interest = 1200 × (0.04) = $48

This is added to the previous amount -

= $1200 + $1200 × (0.04)

= $1200 (1+0.04)

= $1200 (1.04)

= $1248

2nd year: Previous amount + interest on the previous amount

= $1248 (1+0.06)

= $1248 (1.06)

= $1297.92

So, the exponential formula becomes -

y = 1200(1.04)^t

Now, to find the value of investment after 16 years, substitute t = 16.

y = 1200(1.04)^t

y = 1200(1.04)^16

y = 1200(1.87298125)

y =$2247.58

Therefore, the value of investment after 16 years is $2247.58.

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Answer: B -3

Step-by-step explanation

-3/4 my teacher would say rise over run, run means x axes and rise is y axes to get 2 to 8 you need 6 if you times -3/4 by 2 you would get -6/8 6 is x +2 from (5,2) you would get 8 so (m,8) then -8 +5 is -3 creating (-3,8)

Answer:

-24 + 3f

3f - 24.

3(-8 + f)

Step-by-step explanation:

-3/4( 32 - 4f)

= -3/4 * 32 - 3/4 * -4f

= -3*8 + 3f

= -24 + 3f.

= 3f - 24

= 3(-8 + f)

Answer:

Step-by-step explanation:

translate

6 Need to increase the number of workers.

Now, According to the question:

A building company used 24 worker to prepare a building site.

The site measured 30 acre and the work was completed in 10 day.

The company is asked to prepare another site measured 45 acre.

This work has to be completed in 15 days.

To find the least amount of worker the company should employs for this work.

=> 30 ÷ 10 = 3 Daily worked of 24 workers.

=>3 ÷ 24 = 1/8 Daily worked of 1 worker.

=> 45 ÷ 12 = 15/4 The amount of work that the project needs to complete each day

=> 15/4 ÷ 1/8 = 30 Number of workers needed.

=> 30 - 24 =  6 Need to increase the number of workers.

Hence, 6 Need to increase the number of workers.

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Answer:

x = price of shirt = $10

y = price of cap = $2

Step-by-step explanation:

x = price of shirt

y = price of cap

(1)  x+y = 12

(2)  2x+3y = 26

x = 12-y  substitute this into equation 2

2(12-y) + 3y = 26

24 - 2y + 3y = 26

y = 26-24 = 2  substitute this into equation 1

x+2 = 12

x = 12-2 = 10

Answer:

x = price of shirt = $10y = price of cap = $2

Answer:

Step-by-step explanation:

The answer is 28 ft

Step-by-step explanation:

[tex] \frac{ \cot(x) - 1 }{ \cot(x) + 1} \\ \cot(x) = \frac{1}{ \tan(x) } \\ (\frac{1}{ \tan(x) } - 1) \div ( \frac{1}{ \tan(x) + 1} ) \\ multiply \: though \: by \: \tan(x) \\ \tan(x) \times ( \frac{1}{ \tan(x) } - 1 ) \div \tan(x) \times ( \frac{1}{ \tan(x) } + 1) \\ = 1 - \tan(x) \div 1 + \tan(x) \\ \frac{ \cot(x) - 1}{ \cot(x) + 1 } = \frac{1 - \tan(x) }{1 + \tan(x) } [/tex]

Answer:

A. 106

Step-by-step explanation:

Use the correct order of operations.

(8 + 2)² + (6 − 4) × 3 =

= 10² + 2 × 3

= 100 + 6

= 106

The area of one circle is 48 in² if the butcher paper is 24 inches long.

The area of a two-dimensional figure is the total area it takes up. It is the quantity, in other words, that counts the number of unit squares that cover the surface of a closed figure.

Square units—commonly expressed as square inches, square feet, etc.—are the accepted unit of area.

Given that:

3 congruent circles are perfectly fitted in the rectangular banner of length 24 inches,

⇒ diameter of each circle =  length of rectangular banner/3

⇒ d =  24/3

⇒ d =  8

⇒ r =  8/2

⇒ r =  4

Area of circle, A = π r²

A = 3× 4 × 4        (used pi as 3 as instructed in the question)

A = 48 in²

Thus, the area of one circle is 48 in² if the butcher paper is 24 inches long.

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Answer :

17+44 = 61

10+51= 61

The equation of variation is xy = 96. The value of y when x = 18 is 16/3 and the value of x when y = 8 is 12.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

y inversely varies as x.

That means, y ∝ 1/x.

So, y = kx, where k constant of variation.

Then, x × y = k

When y = 16, x = 6.

k = 6 × 16 = 96

So, the equation of variation is xy = 96.

When x = 18,

18y = 96

⇒ y = 96/18

⇒ y = 16/3

When y = 3.2,

3.2(30) = 96

When y = 8

8x = 96

⇒ x = 12

Therefore, the values are  y = 16/3 and  x = 12.

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Answer: -24x+18y

Step-by-step explanation:

6(-4x+3y)

=6*(-4x)+6*(3y)

=-24x+18y

Answer:

6(-4x + 3y)

Step-by-step explanation:

-24x + 18y

6(-4x + 3y)

Your response should be the first point on your graph because x = 0 on the y-axis.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices.

that a line's equation is y = mx + b, where m is its slope and b is its y-intercept. Your initial point should be at -2 on the y-axis to start. Go up 1 and over 2 for your next point because your slope is 1/2 (rise/run). Continue along like this, and your points will become clear.

The x values you have can also be plugged in to determine your y-values. Your first point is that y = 1/2(2) - 2 = 1 - 2 = -1. (2,-1). This ought should appear on your graph as well.

Your response should be the first point on your graph because x = 0 on the y-axis.

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Therefore , the solution of the given problem of table comes out to be  15 to 20 table are given as follows :  14,28,42,56,70,84,98,112,126 and 140

A statistical list is a collection of numbers that shows the outcomes of a computation with numerous inputs. Data is made up of descriptions and numbers and is arranged in rows and columns. The table and indeed the pattern of 10 are easily recalled. In numerical order, the numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, then 20. Value mapping is used to show how multiple data pieces are related to one another. Any science class can benefit from including the values table.

Here,

Given :

=> 13,26,39,52,65,78,91,104,117 and 130

=> 14,28,42,56,70,84,98,112,126 and 140

=> 15,30,45,60,75,90,105,120,135 and 150

Therefore , the solution of the given problem of tables comes out to be  13 to 15 table are given as follows :  14,28,42,56,70,84,98,112,126 and 140

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Percent of land planted with wheat  is 50% of total land.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

a farmer planted

320 acres of one variety of wheat

160 acres of a second variety of wheat.

He also planted 40 acres of milo,

and he has 440 acres that will lie fallow

Total land farmer has = 320 + 160 + 40 + 440 = 960 acres

Land planted with wheat = 320 + 160 = 480 acres

Percentage of land with wheat

= (land planted with wheat/ total land)× 100

= 480/960 × 100

= 0.5 × 100

= 50%

Hence, 50% of total land is planted with wheat.

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Answer:

Step-by-step explanation:

One 1/12 is equal to 1/12, so you do not need to add any other fractions of 1/12 to get 1/12.

1/12 + 0 = 1/12

You can think of it in another way, if you want to add a certain number of fractions to obtain 1, you just need to add 12 of 1/12s to get 1, not one.

Answer:

The sum of the exterior angles is 360.  360/14 = 25.7 would be the measure of one exterior angle.

The sum of the interior angles is 1260.  1260/14 = 154.3 would be the measure of on interior angle.

Step-by-step explanation:

(n-2)180

n  is the number of sides

(14-2)180

12(180) 1260

This is the sum of the interior angles of the polygon.  

1260/14 = 154.3  Is the measure of one angle.

Answer:

x=-4/5, y=-6/5. (-4/5, -6/5).

Step-by-step explanation:

y-1/4x=-1

y-2=4x

--------------

y=4x+2

4x+2-1/4x=-1

4x-1/4x=-1-2

16/4x-1/4x=-3

15/4x=-3

x=-3/(15/4)

x=(-3/1)(4/15)

x=-12/15=-4/5

y-2=4(-4/5)

y-2=-16/5

y=-16/5+2

y=-16/5+10/5

y=-6/5

For the given data, ∅ is the given angle in standard position, terminal side passes through (21, -20) then the exact value of cot ∅= ( - √41/ 20 ) in simplest radical form.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( 21, -20 )

( 21, -20) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = 21

Altitude = -20

Using Pythagoras theorem,

Hypotenuse² = (21)² + (-20)²

⇒ Hypotenuse = √41

Cot ∅    = - √41/20 ( simplest radical form )

Then the exact value of

Cot ∅  = ( - √41/ 20 )  in simplest radical form.

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The equation of the line is y = -3x + 16

The general equation of a line is expressed as;

y = mx + c

Given that;

From the diagram shown, the coordinates of the line is expressed as;

(3, 7) and (2.5, 3)

The intercept. c = -3

Substitute the values

7 = -3(3) + c

expand the bracket

7 = -9 + c

collect like terms

c = 7 + 9

c = 16

The equation of the line is then given as;

y = -3x + 16

Hence, the equation is y = -3x + 16

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In AutoCAD, you can change the UCS icon from 3D to 2D by following these steps:

AutoCAD is a commercial computer-aided design and drafting software application.

Alternatively, you can also change the UCS icon to 2D by typing "UCSICON" in the command line, then pressing the F6 key. This will toggle the UCS icon between 2D and 3D.

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