another one 2 more after this

We find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

What is the tangent of the angle?

The ratio of the right-angle triangle's base or perpendicular is known as the tangent of the angle.

The ratio of two of the right-angled triangle's three sides is used to define the sine, cosine, and tangent of an acute angle.

Here,

We have to find out how is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used.

We concluded that a right triangle can be used to determine the tangent of any acute angle, by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

Hence, we find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

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On solving the provided question, we can say that by mean score the population will be 20192

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:Divide by how many digits there are after adding up all the digits. the total divided by the count.

A sample of 12th grade students who took the National Assessment of Education Progress year 2000 mathematics test had a mean score of 250

200/4

= 50

50*e^{-2}

the population will be 20192

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You will always get one triangle. This is because of the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle is always 180°.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon.

The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

The inner angles of every triangle sum up to 180°, 180°, 180°, 180°. Angles in a triangle are the total (sum) of the angles at each of its three vertices.

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Answer:

Statement 1) Corresponding angles

Statement 2) Congruent

Statement 3) 150 degrees

Statement 4) Vertical Angles

Statement 5) Congruent

Statement 6) 150 degrees

Statement 7) Alternate exterior angles

Statement 8) Congruent

Statement 9) Alternate Interior angles are congruent

Step-by-step explanation:

Explanation:

1) I've learned this before

2) Not all Corresponding angles are obtuse

3) Corresponding angles have the same measure

4) I've learned this before

5) Vertical Angles are congruent

6) Same reason as before

7) I've learned this before

8) Alternate Interior angles are congruent

9) I've learned this before

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The linear function y = 25x - 79 is plotted on a graph with x - intercept at 3.16

A graph of a linear function is a line that goes through the origin (0, 0). The line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line can be positive, negative, zero, or undefined.

In this problem, the linear function given y + 4 = 25(x - 3) can be written in slope - intercept form and then plotted in a graph using a graphical calculator.

y + 4 = 25(x - 3), the linear function can written;

y + 4 = 25(x - 3) = y + 4 = 25x - 75 ;

This becomes y = 25x - 75 - 4;

Collecting like terms

y = 25x - 79

Plotting this on a graph;

The line passes through the x - axis at 3.16 which is the x - intercept

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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.

What is a complex fraction?

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)

Step 1 - 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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This is a function that takes in a geometry object as an input and calculates its area. It then returns the calculated area as an output.

1. Create a function with the desired name and parameters. In this case, the function is called “getArea” and takes in a geometry object as a parameter:

function getArea(geometry)

2. Calculate the area of the geometry using the “area” function in GEE:

var area = geometry.area();

3. Return the calculated area:

return area;

4. End the function:

This function will take in a geometry object and return its area. This can be used to calculate the area of any geometry, such as a polygon or a line. This is a useful function for GEE applications, as it can be used to quickly calculate the area of any given geometry.

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When adding multi-digit numbers, it's a good idea to employ the commutative property. However, counting up becomes simpler if pupils are aware that they can change the order of the addends and begin adding with the larger number FIRST.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Here, a and b may be fractions, decimals, whole numbers, or even integers.

For instance, 1+2=2+1 and 2x3=3x2.

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Answer:

5.6

Step-by-step explanation:

56% = 0.56

5.6 > 56%

the smallest angle will yield the shortest opposite side, likewise the largest angle will yield the largest side, Check the picture below.

The sample space of the experiment is 52.

The possibility that an event will occur among all potential events is known as probability. It ranges from 0 to 1. The probability is calculated by dividing the number of things by all of the items. Population includes the sample. When studying the entire population is challenging, it is studied.

52 cards in a deck

There are 12 face cards.

The experiment needs a sample space of 52 to find the face cards.

Given that a regular deck of cards is available.

The sample space required for the experiment to determine the probability of face cards must be found.

A face card may or may not be revealed when we pull a card from the deck. So, in order to rule out the possibility that a face card is present at the end of the deck, we must draw every card from a regular deck.

52 samples are therefore required for the experiment.

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Answer:

[tex]h = -42[/tex]

Step-by-step explanation:

First, subtract 54 from both sides.

[tex]h = 4^2 - 16 \div 4 - 54[/tex]

Then, evaluate the right-hand expression using the order of operations:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

We'll first evaluate the exponent in 4²:

[tex]4^2 = 4 \times 4 = 16[/tex]

[tex]h = 16 - 16 \div 4 - 54[/tex]

Next, we can evaluate the division:

[tex]16 \div 4 = 4[/tex]

[tex]h = 16 - 4 - 54[/tex]

Finally, perform the subtraction.

[tex]16 - 4 - 54 = -42[/tex]

[tex]h = -42[/tex]

Answer:

[tex] \sf \: h = - 42[/tex]

Step-by-step explanation:

Given equation,

→ h + 54 = 4² - 16 ÷ 4

Now the value of h will be,

→ h + 54 = 4² - 16 ÷ 4

→ h + 54 = 16 - 4

→ h + 54 = 12

→ h = 12 - 54

→ [ h = -42 ]

Hence, value of h is -42.

A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol.

A few more constant examples are :

The number of days in a week represents a constant.

Substitute:

m*o+b=18

m+b=20

Apply Zero Property of Multiplication:

b=18

m+b=20

Substitute into one of the equations:m+18=20

Rearrange unknown terms to the left side of the equation:m=20-18

Calculate the sum or difference:m=2

The solution of the system is:

b=18

m=2

The answer is b=18 m=2

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Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

For each secant, the sum of the lengths from R to the circle's intersection points is the same:

=>RS*RT = RQ*RP

=>40(40 +31) = (44)(PQ +44)

=>40(71)/44 = PQ +44

=>PQ = 2840/44 -44 = 64 6/11 -44 = 20 6/11

=>PQ ≈ 20.5

Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

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Using the unit conversion and converting all the distance units to inches, The final answer is 7575 inches.

Divide the smaller unit's value by the quantity of smaller units required to create the larger unit. Multiply to change from a larger to a smaller unit. Divide to change from a smaller unit to a larger one. We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometers. In this situation, one must convert from kilometers (km) to centimeters (cm).

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics.

13 yard = 468inches

2ft = 24 inches

total 268+24+13 = 505inches

505*15 = 7575 inches

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The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.

The equivalent is the expression that is in different forms but is equal to the same value.

Simplify all the equations, then we have

A. 2 + x = 5, to simplify the equation, then we have

2 + x = 5

x = 3

B. x + 1 = 4, to simplify the equation, then we have

x + 1 = 4

x = 3

C. 9 + x = 6, to simplify the equation, then we have

9 + x = 6

x = - 3

D. x + (- 4) = 7, to simplify the equation, then we have

x - 4 = 7

x = 11

E. - 5 + x = - 2, to simplify the equation, then we have

- 5 + x = - 2

x = 3

The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.

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Thus, It is possible to visually assess whether a limit exists as x approaches a by looking at the function f (x) and g (x) graphs, which are 1 and 5 when x is very close to x=a.

In mathematics, a limit is the value that a function, a sequence, or an index approaches as an input or an index gets closer to a particular value. Limits are essential to the study of calculus and mathematical analysis since they are used to define continuity, derivatives, and integrals.

Here,

From the function f (x) and g graphs shown here ( x)

1) lim f (x) plus lim g ( x )

= -1 + 2 = 1

2) f (-1) + lim g ( x)

= 3 + 2

= 5

Therefore , the solution of the given problem of limit comes out be 5.

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Answer:

The most likely suspect for the hard drive being very active even though the computer is not being used and is not connected to the Internet is malware. Malware is a type of software that is designed to cause harm to a computer system, and it can often run in the background without the user's knowledge.

To write an expression in factored form, its products needs to be deduced.

What is an expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Factoring is the process of representing a given number or algebraic statement as the product of its components.

For example - Consider the binomial 3x^2-9x.

On simplifying it -

3x^2-9x = 3x(x-3)

So, here 3x^2-9x is the expanded form and 3·x·(x-3) is the factored form.

Another example is - Consider y^2-100.

The terms used here can all be expressed as squares.

y^2 − 100 = y^2 − 10^2

(y + 10)(y − 10)

The factors in this case are (y + 10) and (y - 10).

Therefore, the products are the factors of an expression.

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log with base 10 is mainly used to simplify manual computation and it is also related to the decimal system. if we calculate the log of any variable with base 10, then an integer just greater than that calculated value gives the number of digits in that number.

likewise, log with base 2 is used in digital and computer applications where binary system prevails.

The worth of log e is around equal to 0.4342944819 where log e has a base value equal to 10.

1. The value of log e base 10 is around equal to 0.4342944819.

2. The value of log e with base e, that is, ln the e value is equal to 1.

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The length of the sides RS, ST and TR are √72, √41 and √37 in the scalene triangle RST.

The distance between any two points A(a,b) and B(c,d) in the plane is given by,

AB = √((c-a)²+(d-b)²)

Here, it is given that the points of the triangle are R(-4,4) S(-2,-2) T(2, 3).

The triangle is scalene so length of every side is different.

Now, Using the above formula,

RS = √((2+4)²+(-2-4)²)

RS = √(36+36)

RS = √72

ST = √((2+2)²+(3+2)²)

ST = √(16+25)

ST = √41

TR = √((2+4)²+(3-4)²)

TR = √(36+1)

TR = √37

So, Brian is correct, the triangle is a scalene triangle.

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The maximum possible total amount of money would be  = 13.23  £

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one.

Given,

To the nearest pound, tim has £8

To the nearest 50p, sue has £4.50

so, to the nearest pound, tim has £8

=>  7.5   ≤  Tim  has   <  8.5

sue has £4.50

to the nearest 50 p

=>  4.25  ≤   Sue   <  4.75

=> possible total amount of money

= 7. 5 +  4.25 ≤    Amount <  8.5 + 4.75

=>   11.75   ≤    Amount <  13.25

maximum possible total amount of money would be less than 13.25

and in term of paisa   maximum <  4.75   = 4.74

and maximum less than   <  8.5  = 8.49

Hence maximum possible total amount of money would be  = 13.23  £

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The correct option is option A , the sample points of a sample space are equally likely events.

In probability when two the occurrence of two events are having a 50 - 50 possibility then those two events are said to be equally likely events. Example , on tossing a coin the probability of getting a H or a tail is 1/2 . Therefore, these events are said to be equally likely events.

Probability is a field of mathematics which tells us about the possibility of occurrence of an event. P = number of favorable outcomes / total number of outcomes , is the formula to calculate probability.

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On solving the provided question, we can say that - 11g +4= 3r-6 the value of this equation is -10/3

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

11g +4= 3r-6

g = 0

3r = -10

r = -10/3

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The solution to the exponential equation 8^(x/2)/4^(x/3) = 2^(-5/2) is given as follows:

x = -6/5.

The exponential equation for this problem is defined as follows:

[tex]\frac{8^{\frac{x}{2}}}{4^{\frac{x}{3}}} = 2^{-\frac{5}{2}}[/tex]

Both 8 and 4 are powers of 2, as follows:

Applying the power of power rule (multiplying the exponents), the expression on the left side can be rewritten as follows:

[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{-\frac{5}{2}}[/tex]

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence:

[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{\frac{3x}{2} - \frac{2x}{3}}[/tex]

The subtraction is obtained as follows:

3x/2 - 2x/3 = 9x/6 - 4x/6 = 5x/6.

(as the least common factor of 2 and 3 is of 6).

Then the simplified expression is of:

[tex]2^{\frac{5x}{6}} = 2^{-\frac{5}{2}}[/tex]

As the exponential function y = 2^x is injective, the solution is obtained as follows:

5x/6 = -5/2.

10x = -12

x = -6/5.

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Answer:

y = -1/5x - 3.6

Step-by-step explanation:

(2, -4) and (-3, -3)

m = -3+4/ -3-2

m = 1/-5

m = -1/5

y = -1/5x + b

-4 = -1/5(2) + b

-4 = -0.4 + b

b = -3.6

y = -1/5x - 3.6

The simplified value of the given expression ⇒ [(-1 / 5 j) + (3 / 4) - 5 / 2j - (7 / 8)] is computed at ⇒ [(-27 / 10 j) - (1/ 5)]

An algebraic expression is one that was created in mathematics by using integer variables, constants, and algebraic operations.

However, since they are not produced by using integer constants and algebraic operations, transcendental numbers like such and e are not algebraic. The production of is commonly stated as a geometric expression, although the definition of e requires an infinite number of algebraic operations. An expression can be reduced to a rational fraction by using the properties of arithmetic operations.

You can write the given expression as:

⇒ (-1 / 5 j) + 3 / 4 - 5 / 2j - 7 / 8

When we simplify the formula and apply the fractional operations to the result, we get:

⇒ (-27 / 10 j) - (1/ 5)

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Answer:

Estimation: 300 Billion times bigger

Actual: 290 Billion times bigger

Step-by-step explanation:

Lets group the coefficients together and the exponents together.

[tex](\frac{6.1}{2.1})(\frac{10^7}{10^{-4} })[/tex]

We can round 6.1 to 6.

We can round 2.1 to 2.

[tex](\frac{6}{2})(\frac{10^7}{10^{-4} })[/tex]

[tex](3)(\frac{10^7}{10^{-4} })[/tex]

Subtract the exponent from the denominator from the exponent of the numerator.

[tex](3)(10^{7-4*1} )[/tex]

[tex](3)(10^{7+4} )[/tex]

[tex](3)(10^{11} )[/tex]

[tex]3*10^{11}[/tex]

[tex]10^{11}[/tex] is 100 billion.

3 times 100 billion is 300 billion.

a=12,d=17-12=5

nth term =a+(n-1)d

36th term=12+(36-1)5

=12+(35×5)

12+175

36th term=187

Answer: 187

Step-by-step explanation: 17 - 12 = 5 and 22 - 17 = 5

aₙ = a₁ + (n - 1) d

where a₁ = 12, n = 36, d = 5

a₃₆ = 12 + (36 - 1) 5

a₃₆ = 12 + 35 × 5

a₃₆ = 12 + 175

a₃₆ = 187

187 is the 36th term

Answer:

slope = (3/2)

Step-by-step explanation:

point 1: (-1, 1); Point 2: (1, 4)

            (x₁, y₁)              (x₂, y₂)

y₂ - y₁         4 - 1            3            3

----------- = ------------ = --------- = -------

x₂ - x₁          1 - (-1)       1 + 1          2

I hope this helps!