How to find the factors for an equation

Topic:-Factors of an equation

what is factorization : the decomposition of an object a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into prime factors 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.
Let's look an example on it.

Question:-

Solve x²+16x+69=6

Answer:-
x²+16x+69=6

x²+16x+69-6=0

x²+16x+63=0

For factoring it ,we find two factors of 63
which add up to 16,they are 9 and 7

x²+9x+7x+69=6

Pair these terms

x(x+9)+7(x+9)=0

(x+9)(x+7)=0

x+9=0 0r x+7=0

x= -9 or x= -7

So x= -9 or -7 is the answer.

For more help on this ,you can reply me.

A word problem on Distance

Distance is a numerical description of how far apart objects are. In everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over").

If we have a map which shows the distance between two cities and they have given distance as well.

Let's see how to find the actual distance ...

Question:-

On a road map ,if 10 miles is equal to 1 cm.Them find the value for 40 miles and find the actual distance as well.



Answer:-

10 miles=1 cm

40 miles=?

Let's take it as 'x'

We take the ratio and equate them.

10       40
----- = -------
 1        x

      40
 x = ------
      10


 x =4
So
40 miles = 4 cm on map

Now,using the same ratio


Distance on map = 45 cm

  we know 1 cm = 10 miles

Actual Distance = 45*10

               = 450 miles

For more help on this ,you can reply me.

Probability problems

Topic:Probability

Probability, is a way of expressing knowledge or belief that an event will occur or has occurred.

Here is some probability problems ,which help you to understand the concept much better.

Questions & Answers

1- Julie was given two bags full of goodies. There were 10 chocolate bars and 5 mint
candies in bag A. There were 7 chocolate bars and 2 strawberry mini-pies in bag B.
She wanted to eat a chocolate bar. From which bag should she take the candy (so that
the probability of taking a chocolate bar was greater)?

Ans:-

She should take a candy from bag B, because P (A) = 0.67 < P (B) = 0.78.

2- Mike’s class made a project about pets. There were 21 students in his class. Nine had
dogs, five had only cats, three had cats and hamsters and the rest had no pets at all.
They randomly picked out a name.
a) What was the probability that that student had a dog?
b) It turned out the student didn’t have any pets. They randomly picked out a
second name (excluding the first chosen). What is the probability that that
student had at least a cat?

Ans:

a) The probability that the student had a dog is 9/21, so P = 0.43.

b) The probability that the student had at least a cat is 8/20, so P = 0.4.

I hope it helped you ,for more math help ,you can reply me.

Question to Find the Slope of given Straight line Equation

Here is a Linear Programming problem on Slope and y intercept of a Straight line, Straight line equation is a linear equation in two variables.
Slope is a the ratio of the altitude change to the horizontal distance between any two points on the line.
y-intercept is the y-value of the point where the graph of the function or a relation intercepts the y-axis of the rectangular coordinate system (x = 0)

Topic : Slope and y-intercept of a Straight Line

This the simple and direct question to find slope and y intercept.

Problem : Given straight line is 4x -8y - 32 = 0, find the slope and y-intercept of the straight line.
Solution :
Slope is always denoted by 'm'
and Slope = - Co-efficient of x / Co-efficient of y
So from the given straight line 4x - 8y - 32 = 0
=> - 4/- 8 = 1/2
Slope = 1/2

Now to find y-intercept
put x = 0 in the given straight line linear equation,
So 4x - 8y - 32 = 0
-8y - 32 = 0
=> - y = 32/8
=> y = - 4
=> y-intercept is (0,-4)

You can find lot more problems related to the linear programming problems in geometry help and algebra help.

Word Problem on Equation of Circular Orbit of a Satellite

Satellites revolving around the earth forms a circular orbit, hence below word problem describes how to derive equation of that circular orbit which is same as finding equation of circle.

Topic : Circular Orbit of a Satellite

Circular Orbit is considered from the center of the earth.

Question : Weather Satellites. Earth is represented on a map of a portion of the solar system so that its surface is the circle with equation. A weather satellite circle 0.6unit above earth with the center of its circular orbit at the center of earth. Find the equation of the orbit of the satellite on this map.

Solution :

Equation is x² + y² + 2x + 4y - 4091 = 0

adding and subtracting 1 and 4 ;

x² + 2x + 1 + y² + 4y + 4 = 4091 + 1 + 4

(x+1)² + (y+2)² = 4096

(x+1)² + (y+2)² = 64²

So the earth is represented by (x+1)² + (y+2)² = 64²

given a weather satellite circle 0.6unit above earth with the center of its circular orbit at the center of earth.

So radius of this orbit would be 64.6

Thus the equation of orbit is

(x + 1)² + (y + 2)² = (64.6)² = 4173.16

x² + 2x + 1 + y² + 4y + 4 = 4173.16

x² + y² + 2x + 4y + 4 = 4173.16

x² + y² + 2x + 4y = 4173.16

x² + y² + 2x + 4y = 4168.6

So orbit is represented by the equation x² + y² + 2x + 4y -4168.6 = 0


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Question to List Formulas for Volume of Geometrical Figures

Topic : Volume Formulas

Question : List the Formula for all kind of Geometrical figures.

Solution :

Problem to Find Unknown Values of Angles of Triangles

Topic : Angles of Triangle