Prove that:
(1 + Tan²A) Cos²A = 1​

Rational and Irrational numbers can described as the number that can be expressed as [tex]\frac{p}{q}[/tex] are rational and which cannot be expressed are called as Irrational Numbers .

The Rational Numbers are defined as a number that can be represented in the form of [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex].

We can also , say that the fraction where the denominator and the numerator are integers and the denominator is not equal to zero are called as Rational Numbers .

For Example : [tex]\frac{2}{3} , \frac{4}{9}[/tex] represents a rational numbers .

The Irrational Numbers are defined as a real number that cannot be expressed as a ratio of integers .

For Example : [tex]\sqrt{2} , \sqrt{5}[/tex] represents a Irrational number .

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Answer:

x = 52

Step-by-step explanation:

128 + x = 180

180 - 128 = x

x = 52

Have a nice day!

Answer:

y= 12

Step-by-step explanation:

3(-12)-24

-36-24

-12

The longest side of a triangle is opposite the largest interior angle, and the shortest side is opposite the smallest angle.

Triangle

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Angle

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

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Answer:

17-5

Step-by-step explanation:

lol XD I spent alot of time trying to answer this you better say thanks

Answer: m= 0 ; b= 16

(5,16) (-10,16)

Step-by-step explanation:

y=16 so dont need to find y cause it already there so (5,16) (-10,16)

m=y^2- y^1 / x^2-x^1

16-16 / -10-5 = 0/-15 = 0. So m= 0

b is y-intercept and we have y=16 so b=16

Answer:

y = [tex]\frac{1}{3}[/tex] x - 6

Step-by-step explanation:

9y - 3x = -54

We want in the form

y = mx + b

9y - 3x = -54  Add 3x to both sides

9y - 3x + 3x =  3x - 54

9y = 3x - 54   Divide all the way through by 9

[tex]\frac{9y}{9}[/tex] = [tex]\frac{3x}{9}[/tex] - [tex]\frac{54}{9}[/tex]

y = [tex]\frac{3}{9}[/tex] x - 6

We can simplify [tex]\frac{3}{9}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{1}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x - 6

On solving the provided question, we can say that - the function value will be [tex]g(x) = -3 + 12x + 15[/tex] and

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

Here,

[tex]y =a(x-x1)(x-x2),[/tex] y equals a(x-5)(x+1)

g(x) = -3(x-5)(x+1)

[tex]g(x) = -3(x-5)(x+1)[/tex]

g(x) = -3 + 12x + 15

y-intercept of g(x) is (0,15)

Therefore , the solution to the given problem of the equation comes out be  y-intercept of g(x) is (0,15).

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Answer:

Step-by-step explanation:

cos theta = (adjacent side) / (hypotenuse) = 1/6.  The adjacent side has length 1 and the hypotenuse length 6.  The opposite side has length

√(6^2 - 1^2) = ÷√35

and so sin theta = (opp side) / (hypotenuse) = (√35) / 6

and tan theta = [(√35) / 6] / (1/6), or √35

Answer:

I have a screenshot so here you go

Step-by-step explanation:

Answer:

7.7 x x/100 = 16

x100             x100

7.7x = 1,600

Divide by 7.7 on both sides:

X = 207.79 around 208

Answer:48.13%

Step-by-step explanation:

7.7÷16×100=48.125%

Rounded to nearest hundredth=48.13%

Answer:

वि स्कुल माध्यामिक विद्यालय निम्न माध्यामिक विद्यालय व्यवस्थापन समिति सम्पादन र प्रकाशनमा बुटवलबाट निस्कने एक्सरे साप्ताहिकमा एक पटक साप्ताहिकमा छापिएको थियो। प्रकाशित

Answer:

Activity 1

1. a.8, b.4, c.8, d.12

2. a.10, b.8, c.20, d.40

3. a.16, b.9, c.40, d.27

Activity 2

1. a.10, b.40, c.15

2. a.4, b.35, c.14

3. a.80, b.20, c.2.5

Answer:

x = 5√2

Step-by-step explanation:

The triangle on the right is a special right triangle, so we know that the adjacent side to 60° is 5. Since the left triangle is a 45-45-90, the hypotenuse is the leg times √2, so the value of x is 5√2

If the coach buys the packs of Gummi Bears at $0.60 and resales them at $1 , then the percent markup for the candy is (d) 67% .

The price for which the Coach buys Gummi Bears is = $0.60 ;

the price at which the Coach resales them is = $1 ;

So , the Markup is the difference in the price of purchase and price of resale of the candy ,

that means ; the [tex]Markup = \$1 - \$0.60[/tex] ;

= $0.4

So , the Percent Markup is = [tex]\frac{0.4}{0.6} \times 100[/tex]

= 66.66666...

≈ 67% .

Therefore , the percent Markup for the Candy is 67% .

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As a result, using the values provided, we can turn these data into a bar graph.

A graph is a type of non-linear data structure that consists of nodes, also called vertices, and edges. Any two edges can connect the nodes, which are also known as vertices in a graph. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 5, and 4, 50.

Here,

The gene contributes to the development of pigment.

Yes, factors such as temperature, light cycle, and the presence of mutagens can affect the color of the fur.

In the evolution chart, Mcl provided has ullets that it runs. In mature solutions, the dominating truit moderate is thus always present.

Therefore, using the supplied numbers, we may convert these data into a bar graph.

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Answer: The answer is C

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

A right cone is a cone whose apex is located along its center axis and whose axis is perpendicular to its base.

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Answer:

y- intercept = 0

Step-by-step explanation:

the linear function can be expressed in slope- intercept form, that is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁ , y₁ ) = (4, - 4) and (x₂, y₂ ) = (- 2, 2) ← 2 ordered pairs from the table

m = [tex]\frac{2-(-4)}{-2-4}[/tex] = [tex]\frac{2+4}{-6}[/tex] = [tex]\frac{6}{-6}[/tex] = - 1

the line crosses the y- axis at (0, 0 ) ⇒ c = 0

y = - x + 0, that is

y = - x ←  is the linear function defining the ordered pairs in the table

9514 1404 393

Answer:

  95

Step-by-step explanation:

The sequence of first differences is ...

  32 -25 = 7

  37 -32 = 5

  47 -37 = 10

  58 -47 = 11

  71 -58 = 13

  79 -71 = 8

These seem to have no pattern, so the sequence is not arithmetic, geometric, quadratic, or any other common type.

If we look at the digits of the numbers in the series, we see they have sums of ...

  2 +5 = 7

  3 +2 = 5

  3 +7 = 10

  4 +7 = 11

  5 +8 = 13

  7 +1 = 8

  7 +9 = 16

That is, the difference between a number and the next in sequence appears to be the sum of the digits of the number. This rule tells us the next number is ...

   79 +(7+9) = 95 . . . next number in sequence

_____

Additional comment

Sometimes, finding the rule is as much a right-brain activity as it is one of logic or deduction. Often, it is not obvious or easy. Questions like this one are intended to help you learn to think "out of the box."

the measure of the missing leg is 5.38

or 5.4

Step-by-step explanation:

s is for Squared

Cs= As+Bs

let's say 14cm was side a

Bs=Cs-As

Bs= 15s-14s

Bs=225-196

Bs=29

B= square root of Bs

B=5.38

Answer:

5.4

Step-by-step explanation:

c² = a² + b²

15² = 14² + b

225 = 196 + b

b = 225 - 196

= 29

= 5.4

The required slope of the linear equation is -3 which values shown in the table.

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The table is given in the question as follows:

x          y

-4       -15

-2        9

0         3

2        -3

4         -9

As per the question, we take the given points are (0, 3) and (4, -9).

So we can substitute these values into the formula:

m = (-9 - 3) / (4 - 0)

m = -12 / 4

Apply the division operation, and we get

m = -3

Therefore, the required slope of the linear equation is -3.

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Answer:

207.24 in.

(This is not a rounded answer)

Step-by-step explanation:

So, this will be very fun, simple, and easy!

First thing we do is use this formula, A(s) = 2πrh + 2πr²

We don't know the surface area yet, and that's what we are looking for, so first off we go ahead and plug in the radius, which is 6 divided by 2, and that's 3! The height is 8 inches!

Let's plug in 3.14 for pie too.

A(s) = 2(3.14)3(8) + 2(3.14)3²

Let's start solving.

A(s) = 150.72 + 2(3.14)3²

3 squared is 9!

A(s) = 150.72 + 56.52

A(s) = 207.24 inches

So, the answer is...207.24 in.! THat is the correct answer, but if I'm wrong, please comment so I can change my answer! Thanks for the points, have a great day or else!

The polygon presented will have nine sides. This suggests that a nonagon is the necessary polygon.

Divide the number of triangles in the polygon by 180° to determine the sum of its inner angles. Where is the number of sides, the formula for computing the sum of internal angles is (n 2) 180. In a regular polygon, all internal angles are equal.

The following are crucial polygon formulas: A polygon with "n" sides has a total interior angle sum of 180 degrees (n-2) A "n-sided" polygon has [n(n-3)]/2 diagonals. A regular n-sided polygon's internal angles are measured as [(n-2)180°]/n.

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The equation 0⁵ + (-1)⁴ involving exponents is solved to get

1

The way of representing huge numbers in terms of powers is known as an exponent.

Exponent, then, is the number of times a number has been multiplied by itself. exponents are also referred to as raise to power

When a zero is raised to the power of any number will yield zero zero, this is because when zero keep multiplying itself zeo will be the resulat repeated times

hence for the equation  0⁵ + (-1)⁴ the part that has zero will give zero remaking the part with a negative number

= 0⁵ + (-1)⁴

= (-1)⁴

= -1 * -1 * -1 * -1

= 1 * 1

= 1

hence the answer is 1

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The graph from the function is a linear graph

From the question, we have the following parameters that can be used in our computation:

g(x)=(x+2)(x−1)−x 2

Express properly

So, we have the following representation

g(x) = (x + 2)(x − 1) − x²

Next, we set x = 0, 1, 2 and 3 to determine the table of values

g(0) = (0 + 2)(0 − 1) − (0)² = -2

g(1) = (1 + 2)(1 − 1) − (1)² = -1

g(2) = (2 + 2)(2 − 1) − (2)² = 0

g(3) = (3 + 2)(3 − 1) − (3)² = 1

So, the table is

x        0         1        2        3

g(x)     -2      -1        0        1

From the table above, we can see that as x increases by 1, y constantly increase by 1

This means that the function is a linear function

See attachment for the graph

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On solving the provided question, we can say that the sequence what we tell on day 3 = he sold 5; on day 4 = he sold 7; on day 5 = he sold 9

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.

here,

on day 1 = he sold 1

on day 2 = he sold 3

on day 3 = he sold 5

on day 4 = he sold 7

on day 5 = he sold 9

.

.

.

.

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Answer:

x=7

Step-by-step explanation:

97 = 10x + 27

97 - 27 = 10x

70 = 10x

70/10 = x

7=x

Answer:

X=7

HOPE THIS HELPS

-Todo ❤️

Step-by-step explanation:

97=10x+27

-27. -27

70=10x

/10. /10

X=7