Algebra Third Grade

College grade algebra:

Example 1 :
What is the sum of 7 and 8? Express this statement by using place holder.
Solution :

We can write this statement, in short, as
7 + 8 = ?.

The answer for this problem would be 7 + 8 = 15.

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Trinomials

We have to follow the following steps for factoring type of trinomials:(Trinomial factor calculator)

We must follow the following steps for factoring type of trinomials
1. Look for the sign of third term.
2. if the sign of third term is positive then they must divide the coefficient of middle term in one parts in such a way that sum of these one part is equal to the middle terms and product of these one parts is equal to the coefficient of third term.
3. Take the common parts out and solve.
Ex : factorize x2 + 14x + 24
Sol :
Step1. Sign of third term is positive
Step 2. Coefficient of middle term is 14. So they will divide in one parts such that the sum of these one parts is 14 and product of these one parts is 24. Clearly these one parts will be 12 and 2.
Step3.
x2 + 14x + 24
= x2 + (12 + 2 )x + 24
= x2 + 12x + 2x + 24
= x ( x + 12 ) + 2 ( x +12 )
= (x + 12 ) (x + 2 )
So x2 + 14x + 24 = (x +12 ) (x +2)
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Introduction to indices
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Online Fraction Simplifier

Fraction Simplifier:

• Adding fractions:

This involves the following methods:

• Like Denominator method:

fraction with the equal denominator can be added directly add the numerators. And then we can simplify the fractions.

Online fraction simplifier- Example 1: +

Here the denominators are same so the sum of the numerators be 2

The fraction is .

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sine cos and Tan rules

Sine cos and tan rules

Sine RULE : when it comes to investigating the properties of a triangle the Sine Rule is exceptionally helpful. ,the Sine Rule will even work for scalene triangles. It finds use in pure mathematics as well as mechanics where triangles formed by vectors often need to be investigated.

COS RULE : In rule in trigonometry cosine rule can be used. It can be used to find out features of non right triangles.

TANGENT RULE : law of tangents for the same purpose that you use the law of sines and the law of cosines: To solve a triangle (that is, find the lengths of all of its sides and the measure of all of its angles).

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Algebraic fraction

Coefficient Variation formula

Arithmetic Question

What are are the arithmetic means between 24 and 72 .

A ) - 36, 48, - 60
B ) 37, 50, 63
C ) 36, 48, 60
D ) 36, - 48, - 60

Steps to derive

1 Given data: a₁= 24, a₅ = 72

2 The arithmetic sequence is 24, a₂, a₃, a₄ , 72

3 a_n = a₁ + (n - 1)d
[Use the formula for the n^th term.]

4 a₅ = a₁ + (5 - 1) d
[Substitute the values.]

5 72 = 24 + 4d
[Substitute the values.]

6 d = 12

7 a₂ = a₁ + d = 24 + 12
[a_{n + 1} = a_n + d.]

8 a₂ = 36.

9 a₃ = a₂ + d = 36 + 12 = 48

10 a₄ = a₃ + d = 48 + 12 = 60

11 So, the three arithmetic means are 36, 48, and 60.

Hence the right answer is Option C