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In mathematics algebra 2 is one of the main part . It explains the quantity, letters and other symbols. It indicates variables, equations, objects, polynomials, and expressions etc. Algebra II homework solves Pre-algebra 2, Algebra I, Algebra 2, Geometry. Generally, also you can get help with solved algebra 2 answers Algebra 2 evolved from the rules and operations of arithmetic which begins with the four operations: addition, subtraction, multiplication and division of numbers.

Algebraic expression Algebraic expression denotes one number or one quantity. That is, just like the sum of 5 and 2 is one quantity, which result is 7, The sum of X and Y is one quantity, that is, X + Y. help with algebra 2 problems solved
Linear equation: The combination of the variables is known as linear equations, constant and operators, which makes a straight line when we graphed that linear equation.

Learning linear algebra

Linear algebra is a division of math concerned with learns of vectors, with families of vectors recognized vector spaces and by purpose to input one vector also output another, according to definite rules. These functions are identified linear chart and are frequently signify by matrices. Linear algebra is essential to made easy for modern math and its applications.

An elementary function of linear algebra is to the resolution of systems of linear equations in some indefinite. Also get more help with parts of a circle More difficult applications are everywhere, in areas as different as abstract algebra and efficient analysis. Linear algebra has an existing representation in systematic geometry and made easy for common in operator theory. It has wide applications in the usual math. Nonlinear arithmetical form can frequently be approximated through linear ones.

Let us understand how sin2x works

The trigonometric identity is the identity of angles. The trigonometric identity is also called as circular identity. They are used for relating the angles of a triangle to the lengths of the sides of a triangle. The trigonometric identity is essential for the basic study of triangles and representation of periodic phenomena, surrounded by many other applications. One of the trigonometric identity is the sine identity.Question: Solve, sin2x × sin x = 0, to get the angle value of x from the double angle.

Solution: Given that, sin2x × sin x = 0.
We know that, sin2θ = 2sinθ cosθ,
=> sin2θ = 2sinθ cosθ,
Now plug the value of sin2x in the equation sin2x + sin x = 0, we get,
=> (2sin x cos x) × sin x = 0,
=> 2sin x cos x × sin x = 0,
=> 2sin²x × cos x= 0,
Split the given expression into two terms, we get,
=> 2sin²x = 0, and sin x = 0,
=> sin²x = 0, and sin x = 0,
=> sin x = 0, and sin x = 0,
=> x = sin⁻¹(0), and x = cos⁻¹(0),

=> x = 0° (or) 360°, and x = 90°,

General Knowledge Questions

Get help on easy GK Questions

General knowledge questions are meant for improving IQ.
It helps growing children in widening their knowledge base which in turn enables them to understand various concepts and theories in a comparatively easier and better manner you can also get help on good general knowledge questions and answers. Students with better general knowledge sense are most likely excel in their educational carrier.

Simultaneous Equations

Definition of Simultaneous Equations

 A pair of "Simultaneous equations" is two equations which are both true at the same time. You have two equations which have two unknowns to be found.

Example

 A man buys 3 fish and 2 chips for £2.80

A woman buys 1 fish and 4 chips for £2.60

How much are the fish and how much are the chips?

 First we form the equations. Let fish be f and chips be c.

We know that:

3f + 2c = 280    (1)

f + 4c = 260      (2)

 There are two methods of solving simultaneous equations. Use the method which you prefer:

Elimination

 This involves changing the two equations so that one can be added/ subtracted from the other to leave us with an equation with only one unknown (which we can solve). We can 'change' the equations by multiplying them through by a constant- as long as we multiply both sides of the equation by the same number it will remain true.

 In our above example:

 Doubling (1) gives:

6f + 4c = 560 (3)

 Since equation (2) has a 4c in it, we can subtract this from the new equation (3) and the c's will all have disappeared:

(3)-(2) gives 5f = 300  ∴ f = 60

Therefore the price of fish is 60p

 So we can put f=60 in either of our original equations. Substitute this value into (1): 3(60) + 2c = 280 ∴ 2c = 100

c = 50

Therefore the price of chips is 50p

Substitution

 The method of substitution involves transforming one equation into x = (something) or y = (something) and then substituting this something into the other equation.

 So,Rearrange one of the original equations to isolate a variable.

Rearranging (2): f = 260 - 4c

Substitute this into the other equation:3(260 - 4c) + 2c = 280∴ 780 - 12c + 2c = 280 ∴ 10c = 500

∴ c = 50

Substitute this into one of the original equations to get f = 60 .

 Harder simultaneous equations

 To solve a pair of equations, one of which contains x2, y2 or xy, we need to use the method of substitution.

Example

 2xy + y = 10  (1)

x + y = 4        (2)

Take the simpler equation and get y = .... or x = ....

from (2), y = 4 - x    (3)

this can be substituted in the first equation. Since y = 4 - x, where there is a y in the first equation, it can be replaced by 4 - x .

sub (3) in (1), 2x(4 - x) + (4 - x) = 10

∴ 8x - 2x2 + 4 - x - 10 = 0

∴ 7x - 2x2 - 6 = 0

∴ 2x2 - 7x + 6 = 0  (taking everything to the other side of the equals sign)

∴ (2x - 3)(x - 2) = 0

∴ either 2x - 3 = 0 or x - 2 = 0

therefore x = 1.5 or 2 .

 Substitute these x values into one of the original equations.

When x = 1.5,  y = 2.5

when x = 2, y = 2

Using Graphs

 You can solve simultaneous equations by drawing graphs of the two equations you wish to solve. The x and y values of where the graphs intersect are the solutions to the equations.

Example

 Solve the simultaneous equations 3y = -2x + 6 and y = 2x -2 by graphical methods.

  

  From the graph, y = 1 and x = 1.5 (approx.). These are the answers to the simultaneous equations.

Mean, Median, Mode, and Range

Mean, Median, Mode, and Range

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.
The "range" is just the difference between the largest and smallest values.

• Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.
The median is the middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved
The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

mean: 15
median: 14
mode: 13range: 8

Note: The formula for the place to find the median is "( [the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer. Either way will work.

• Find the mean, median, mode, and range for the following list of values:
1, 2, 4, 7

The mean is the usual average: (1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5
The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are an even number of numbers. In this case, the median is the mean (the usual average) of the middle two values: (2 + 4) ÷ 2 = 6 ÷ 2 = 3
The mode is the number that is repeated most often, but all the numbers appear only once. Then there is no mode.
The largest value is 7, the smallest is 1, and their difference is 6, so the range is 6.

mean: 3.5
median: 3
mode: none
range: 6

The list values were whole numbers, but the mean was a decimal value. Getting a decimal value for the mean (or for the median, if you have an even number of data points) is perfectly okay; don't round your answers to try to match the format of the other numbers.

• Find the mean, median, mode, and range for the following list of values:
 8, 9, 10, 10, 10, 11, 11, 11, 12, 13

The mean is the usual average:

(8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13) ÷ 10 = 105 ÷ 10 = 10.5

The median is the middle value. In a list of ten values, that will be the (10 + 1) ÷ 2 = 5.5th value; that is, I'll need to average the fifth and sixth numbers to find the median:

(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5

The mode is the number repeated most often. This list has two values that are repeated three times.
The largest value is 13 and the smallest is 8, so the range is 13 – 8 = 5.

mean: 10.5
median: 10.5
modes: 10 and 11range: 5

While unusual, it can happen that two of the averages (the mean and the median, in this case) will have the same value.
Note: Depending on your text or your instructor, the above data set may be viewed as having no mode (rather than two modes), since no single solitary number was repeated more often than any other. I've seen books that go either way; there doesn't seem to be a consensus on the "right" definition of "mode" in the above case. So if you're not certain how you should answer the "mode" part of the above example, ask your instructor before the next test.
About the only hard part of finding the mean, median, and mode is keeping straight which "average" is which. Just remember the following:

mean: regular meaning of "average"
median: middle value
mode: most often

(In the above, I've used the term "average" rather casually. The technical definition of "average" is the arithmetic mean: adding up the values and then dividing by the number of values. Since you're probably more familiar with the concept of "average" than with "measure of central tendency", I used the more comfortable term.)

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• A student has gotten the following grades on his tests: 87, 95, 76, and 88. He wants an 85 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?
The unknown score is "x". Then the desired average is:

(87 + 95 + 76 + 88 + x) ÷ 5 = 85

Multiplying through by 5 and simplifying, I get:

87 + 95 + 76 + 88 + x = 425
                      346 + x = 425
                                x = 79
He needs to get at least a 79 on the last test.