solving equation by using FOIL method

The FOIL Method is a process used in algebra to multiply two binomials. The lesson on the Distributive Property, explained how to multiply a monomial or a single term such as 7 by a binomial such as (4 + 9x).

But, what if there was a binomial instead of a single term outside of the parentheses? That is, what if a binomial was being multiplied by another binomial? An example of this is given in the problem.
Let's see an algebra question on this .

Question:-
Solve the equations by using foil method.

(y+1)(2y-3) = 25

Answer:-

Let's see how to solve equations using FOIL method.



(y+1)(2y-3) =25

2y²-3y+2y-3=25

2y²-y-3 = 25

2y²-y-3-25=0

2y²-y-28=0

2y²-8y+7y-28=0

2y(y-4)+7(y-4)=0

(y-4)(2y+7)=0

y-4=0 or 2y+7=0

y=4 or y= -7/2

y = 4 or -7/2 is the Answer

Completing the Square Method

Sometimes the roots of a quadratic equation cannot be obtained by simple factorization. So, a more general method is used. This method, which is based on the fact that any quadratic equation may be written in the form of (x+p)² = q, where p and q are real numbers, is known as completing the square method.

Question:-

Solve the equation by completing the square method.

2x²-7x+9=(x-3)(x+1)+3x

Answer:-

2x²-7x+9 = x²+x-3x-3+3x
-x²-x+3 -x²-x+3
---------------------------
x²-8x+12 = 0

now we solve this quadratic equation by completing the square method

x²-8x=-12

x²-8x+(8/2)²=(8/2)²-12

x²-8x+16 = 16-12

(x-4)² = 4

taking the square root on both sides, square root symbol looks like √ .

√(x-4)²= √4

x-4 = ±2

We also can use square root calculator to get these values.

x-4 = +2 or x-4 = -2

x=6 or x=2 is the answer

This equation have just one variable.similarly we can also work on linear equations in two variables

Problem on Finding Area of Rectangle

Topic : Area of rectangle
The area of a square is denoted by the formula Area = width * height
To calculate the area of a plane figure we use formulas such as area of triangle, square ,rectangles , or circles.

Here is a simple example for you
Question:
The cost of enclosing a rectangle garden with fence all round at rate 75 paisa / meter is Rs 300. If the length of the garden is 120 meters. Find the area of the garden in square meters.

Answer:









We know that,

Cost = Rate x Perimerter (as fencing is done at perimeter)
Let the width of garden be "w"
300 = 0.75 * 2(w + 120)
300 = 1.50 (w + 120)
divide both sides by 1.5
300/1.5 = 1.5/1.5(w+120)
200 = (w+120)
w+120 =200
subtract 120 from both sides
w = 80,

so width = 80 meters

Area of the feild = length *width
= 80 *120
= 9600 m²

Problem on factorization

factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained. However, factors are not needed to divide evenly because they are still divisible by any number. For example, technically 3 and 8/3 are factors of 8. But, when factoring for tests teachers are looking for the even divisibility of the numbers.

Question:-

factorise m⁸-n⁸

Answer:-

(m⁸-n⁸)

=(m⁴²)-(n⁴²)

=[m⁴+n⁴][m⁴-n⁴]

=[m⁴+n⁴][(m²)²-(n²)²]

=[m⁴+n⁴][m²+n²][m²-n²]

=[m⁴+n⁴][m²+n²][m+n][m-n]


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problem on slope-intercept form

Topic:- slope-intercept form

The slope intercept form is probably the most frequently used way to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line.

This math help gives you an example problem .

Question:-

Write the equation of a line perpendicular to y = 2/3 x-5 passing through(7,4)

Answer:-

   y = 2/3 x - 5 is of the form y = m x + c ,Which is slope-intercept form comaparing equation 1 and 2


we have slope m = 2/3

Two lines which are perpendicularto each other will satisfy the condition

 m1 * m2 = -1


slope of the line perpendicular to

y = 2/3 x - 5 is

   m2 = -3/2

equation of any line passing through (7,4) and having slope -3/2 is

  y-4 = -3/2 (x-7)

   2y+3x-29=0

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a word problem on equations

Topic:-Equations

solving equations is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in

The equations above are examples of an equality: a proposition which states that two constants are equal. Equalities may be true or false.
Equations are often used to state the equality of two expressions containing one or more variables. In the reals we can say, for example, that for any given value .Here is a word problem on equations

Question:-

Solve

"Five times the difference of x
and 8 is lees than or equal to 20"

Answer:-

Let's bring it to a equation form.


Difference of x and 8 = x-8


Five times the difference of x  and 8 = 5(x-8)

less than or equal to 20 means  <=20             

Let's put together

5(x-8)<=20

Now let's go ahead and solve this


5(x-8)<=20

     5x - 40 < =20   Adding 40 on
        +40    +40   Both sides
  --------------------
         5x <= 60


Divde with 5 on both sides

         5x      60
        ---- <= ------
          5        5

          x< = 12

12 is the Answer.





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Question on Limits and Convergence of Number Sequence

In Number theory tutorialoffered by TutorVista will help you to solve problem related to number sequences, calculating limits and continuity of the sequence.

Topic : Limits and convergence of given number sequence.

Decrease in the value of the numbers in the sequence is said to be sequence convergence.

Question : Write the first five terms of the sequence, determine whether the sequence converges, and if so find its limit.





Solution :

General term will be given as ,



















So 0.5, 0.167, 0.083, 0.05, 0.03 Thus we can observe that the values goes on decreasing.
Hence the number sequence converges.

Nows lets find it's limit by ratio test



















For more help contact math help or calculus help.