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The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ

Trigonometric identities are equations which contain the trigonometric ratios.

Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.

So, we proceed as follows

Since cot²θ + 1 = 1/tan²θ + 1     (since cot²θ = 1/tan²θ)

Now taking the L.C.M, we have that

1/tan²θ + 1 = (1 + tan²θ)/tan²θ

We know that the trigonometric identity 1 + tan²θ = sec²θ

So, substituting this into the equation, we have that

(1 + tan²θ)/tan²θ =  sec²θ/tan²θ

Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that

sec²θ/tan²θ = cot²θsec²θ

So, cot²θ + 1 = cot²θsec²θ

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Therefore, the interval (0, 1) must be countless and infinite. Since the interval (0, 1) is as large as R, R is also infinite.

Interval:

In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing (0, 1), and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).

Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.

Open Interval:

Open intervals do not include endpoints and are indicated by parentheses.  For example, (0, 1) means greater than 0 and less than 1. This is (0, 1) = {x | 0 This interval can also be expressed as ]0, 1[ . Please refer to the following.

Closed Interval:

A closed interval is an interval that contains all boundary points and is indicated by square brackets. For example, [0, 1] means greater than or equal to 0 and less than or equal to 1.

Half- Open Interval:

A half-open interval contains only one of its endpoints and is represented by a combination of open and closed interval notation. Example: (0, 1) means greater than 0 and less than or equal to 1, [0, 1) means greater than or equal to 0 and less than 1.

Complete Question:

II. Identify the following terms described in each item. Quantitative & Quaeritated. It can be separated into different categories that are distinguished by some nonnumeric characteristics. 2. It consists of numbers representing counts or measurements. Quantitative Quantitative 3. The result from either a finite number of possible values or countable number of possible values as 0, or 1, or 2, and so on 4. The result from infinitely many possible values that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions 5. It is characterized by data that consist of names, labels, or categories only. 6. It involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. 7. It involves meaningful amounts of differences between data. It has no true zero point or absolute zero. 8. It contains all the properties of the interval level but has true zero point or absolute zero. 9. It is a complete collection of all elements to be studied. 10. It is a branch of Mathematics that deals with the collection, organization presentation, analysis, and interpretation of data.​

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7x and 7x2 are NOT like terms.

Terms with identical variables (like x or y) and any exponents (like the 2 in x2). Similar phrases can be combined. Similar or like terms are those that only differ in numerical coefficient but have the same literal coefficients raised to the same powers. Related terms are those that have the same exponent applied to similar variables. Dissimilar or unlike terms are those that do not have the same literal coefficients raised to the same powers. Only the numerical coefficients can change in terms similar to those of algebra.

However, because to the various exponents, 7x and 7x2 are NOT similar expressions.

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The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3, 1/5 is a fraction.

We have,

Let the fraction be a/b.

2/5 < a/b < 2/3

Now,

a/b

= (2/3 + 2/5) / 2

= (10 + 6) / 30

= 16/30

= 8/15

= 0.533

Thus,

The fraction is 8/15.

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[tex] \longmapsto \: 7x + 5x + 2x = 35820 \\ \\ x = \frac{35840}{14} = 2560[/tex] length equals to 7 into 2560 = 1792

The outcome for the event "at least two tails" is HTT. Option B

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

HHH → All heads

HHT → Two heads + one tail

HTH → Two heads + one tail

HTT → Two tails + one head

THH → One tail + two heads

THT → Two tails + one head

TTH → Two tails + one head

TTT → All tails

Therefore, At least two tails means → Sample space outcome with two tails Or all tails

Therefore, from the given options HTT is having two tails. Option B is the correct option.

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The factors for the Polynomial are (x+1) and (x+2).

According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

Given:

f(x) = 2x³ + 9x² + 13x + 6

Now, first (x+1) =0

x= -1

put x= -1 in f(x) as

f(-1) = 2(-1) + 9(1) + 13(-1) + 6

      = -2 + 9 - 13 + 6

      = 0

So, (x+1) is factor of f(x).

Now, second (x-1)= 0

x= 1

put x= 1 in f(x) as

f(1) = 2(1) + 9(1) + 13(1) + 6

      = 2 + 9 + 13 + 6

      = 31

So, (x-1) is not a factor of f(x).

Now, second (x+2)= 0

x= -2

put x= -2 in f(x) as

f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6

      = -16 + 36 - 26 + 6

      = 0

So, (x+2) is factor of f(x).

Now, second (x-2)= 0

x= 2

put x= 2 in f(x) as

f(1) = 2(2)³ + 9(2)² + 13(2) + 6

      = 16 + 36 + 26 + 6

      = 84

So, (x-2) is not a factor of f(x).

Now, second (x+3)= 0

x= -3

put x= -3 in f(x) as

f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6

      = -54 + 81 - 39 + 6

      = -6

So, (x+3) is not a factor of f(x).

Now, second (x-3)= 0

x= 3

put x= 3 in f(x) as

f(1) = 2(3)³ + 9(3)² + 13(3) + 6

      = 54 + 81 + 39 + 6

      = 180

So, (x-3) is not a factor of f(x).

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The equation of the line perpendicular to x - 4y = 7 can be written as:

y = 4*x + b

Where b could be any real number.

Two lines are perpendicular if the product between the slopes of the lines is equal to -1.

Where a general line in the slope-intercept form is written as:

y  =a*x +b

And the given line is:

x - 4y = 7

Writing this in the slope-intercept form we will get:

-4y = -x - 7

y = (-1/4)*x + 7/4

So the slope is -1/4, then the slope of our line must be such that:

a*(-1/4) = -1

a = -4*-1 = 4

a =4

So the line perpendicular to the given one is:

y = 4*x + b

Where b can be any real number.

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Answer:

7

Step-by-step explanation:

As we want to find the whole number, and to do so we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

21/3 = 7

Answer: The answer is C

Step-by-step explanation: i took the test and got it right

Answer:

[tex]x = -7\\x = -3[/tex]

Step-by-step explanation:

The steps are in the image attached to this response.

Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.

An expression is made up of a number, a variable, or a combination of both, along with certain operation symbols. Two expressions that make up an equation are separated by an equal sign. Example of a Word 8, 3, and the result is 11.

Here,

Given :  the numbers 4. 3, -1. 07, and -2. 971

Using the above given numbers we can construct

an expression which contain both

addition and subtract

thus ,

In order to form we use + sign and - sign

We get,

-1.07+(-2.917)-4.3=-8.287

Therefore , the solution of the given problem of expression comes out to be -1.07+(-2.917)-4.3=-8.287.

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Answer:

y = -1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 0, and the y-intercept is located at (0,-1), so the equation is

y = -1

Answer:

y = -1

Step-by-step explanation:

The coeficient of x^3+y^4 in the algebraic expression is the number 2

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

2x^3+ 2y^4

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.

2 is the coefficient of x^3+y^4

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Answer:

Step-by-step explanation:

(f.g)(x)=[tex]-3*(-3x)^{2}+3=-27x^{2}+3[/tex]

If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25  and cost for riding m miles is $[tex]3.50+0.75m[/tex]   .

The pickup charge that taxi service charges is = $3.50  ;

the additional charge for per miles driven is = $0.75  ;

we have to find the cost for riding 5 miles ;

So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;

substituting the values , the total cost equation becomes ;

[tex]Total Cost = 3.50 + 0.75\times5[/tex]

= [tex]3.50+3.75[/tex]

= 7.25

So , the cost for 5 miles is = $7.25  ;

to find cost for driving "m" miles ,we substitute the number of miles = m;

[tex]Total Cost = 3.50+0.75\times m[/tex]

= [tex]3.50+0.75m[/tex]

Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .

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The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent

What is probability ?

Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

X ∼ Geom(p) and Y ∼ Geom(r) are independent.

P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})

=∑1≤k<n,n∈NP(X=k,Y=n)

=∑n=1∞∑k=1n−1P(X=k)P(Y=n)

=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1

=pq∑n=1∞(1−q)n−11−(1−p)n−1p

=q∑n=1∞(1−q)n−1(1−(1−p)n−1)

=1−q / ∑n=1∞[(1−q)(1−p)]n−1

=1−q / 1−(1−p)(1−q)

=1−(1−p)(1−q)−q / 1−(1−p)(1−q)

=p(1−q) / p+q−pq.

Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent.

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Answer:

9.1

Step-by-step explanation:

For the first one, I just multiplied 4.55 and 0.5 by 2 somthey are proportional. Or divide distance by time!

Hello there!

Answer:

y = ± 13

Step-by-step explanation:

[tex]y {}^{2} - 58 = 25 \times 4 + 11 \\ y {}^{2} - 58 = 100 + 11 \\ y {}^{2} - 58 = 111 \\ y {}^{2} - 58 - 111 = 111 - 111 \\ y {}^{2} - 169 = 0 \\ (y + 13)(y - 13) = 0 \\ y = - 13 \: \: \: and \: \: \: y = 13[/tex]

The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.

The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.

Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.

Given that ΔAED ≈ΔBEC & AC = BD.

as  ΔAED ≈ΔBEC, AD = BC     .................(1)

Now in  ΔABD and ΔBAC,

     AD = BC        

(corresponding sides of similar triangles) [from (1)]

     AB = AB        

(common side)

     AC = BD      

   (given)

∴     ΔABD ≈ΔBAC  (By SSS criteria)    

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The formula for an isosceles triangle is A = (1/2) * b * h, where b is the base, h is the height, and A is the area.

The formula for an isosceles triangle is A = (1/2) * b * h. This formula is used to calculate the area of an isosceles triangle. To use the formula, you need to know the base, b, and the height, h, of the triangle. The base is the length of any one of the two equal sides of the isosceles triangle, and the height is the distance from the base to the opposite vertex. Once you have these measurements, you can plug them into the formula to calculate the area of the triangle. The formula multiplies the base, b, by the height, h, and then divides the product by two. This will give you the area of the triangle, A.

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Answer:

thats by step overr.ic. yttt. .

There are several types of angles, including: acute angles, right angles, obtuse angles, straight angles, reflex angles, complementary angles, supplementary angles, adjacent angles, linear pair, vertically opposite angles, alternate interior angles, alternate exterior angles, and corresponding angles.

Acute angles: angles measuring less than 90 degrees.

Right angles: angles measuring exactly 90 degrees.

Obtuse angles: angles measuring greater than 90 degrees but less than 180 degrees.

Straight angles: angles measuring exactly 180 degrees.

Reflex angles: angles measuring greater than 180 degrees but less than 360 degrees.

Complementary angles: two angles that add up to 90 degrees.

Supplementary angles: two angles that add up to 180 degrees.

Adjacent angles: two angles that share a common vertex and a common side but no common interior points.

Linear pair: two angles that add up to 180 degrees and share a common side.

Vertically opposite angles: two angles formed by two intersecting lines that are opposite to each other.

Alternate interior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and inside the parallel lines.

Alternate exterior angles: two angles formed by two intersecting lines that are on opposite sides of the transversal and outside the parallel lines.

Corresponding angles: two angles formed by two intersecting lines that are in the same relative position.

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The X-intercept is the point where the line crosses the x-axis. This happens where the Y is equals to zero.

The point slope form of a line is an equation of the line that takes on the form y - y1 = m(x - x1). In this equation, m is the slope of the line, and (x1, y1) is a point on the line. The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. This always happens at the point where y is equal to 0. Therefore, we find the x-intercept of a line in point-slope form by plugging y = 0 into the equation and then solving for x. The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. It is said to be as the x-coordinate of a point where a line, curve, or surface intersects the x-axis.

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Answer:

The (1/4) slope is the prive per ticket.  The y intercept is the money in the cash box before any tickets were sold.

Step-by-step explanation:

Let y be the money and x the numbers of tickets sold, as requested.  We are told that the equation for this situation is:

   y = (1/4)x + 8

Let's assume the money is in units of dollars.  The slope of (1/4) would mean that each carnival game ticket cost $(1/4), or 25 cents.  The y-intercept is the value of y when x=0, which means zero tickets have been sold.  That means that the cash box had $8 before any sales were made.  [perhaps to use for making change].

Answer:

7.14%

Step-by-step explanation:

Any comparison with the increase or decrease in price has to be compared to the ORIGINAL price. (at the beginning of the month.)

The price increased from $3.50 to $3.75, an increase of $0.25

To find what percent it is use:[tex]\frac{change}{original}[/tex]×100%

[tex]\frac{0.25}{3.50}[/tex]×100%

Answer:

7.1428571% increase

7  1/7 % increase

Step-by-step explanation:

To find the percent increase ( we know this is an increase since the amount went up), take the new amount and subtract the original amount

3.75 - 3.50 = .25

Divide by the original amount

.25 / 3.50

.071428571

Multiply by 100 %

7.1428571%

7 1/7 %

Answer:

Obtuse and isosceles

Step-by-step explanation:

obtuse because an angle is more than 90* and isosceles because two sides are equal.

Hope this helps!

Equivalent fractions are those that, despite their visual differences, reflect the same value. we consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

If the denominators differ, similar fractions with a common denominator must be used. This requires figuring out the LCM of the two denominators. To be used as a denominator in fractions with various denominators, rename the fractions with a similar denominator.

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