You can put this solution on YOUR website!
The given expression is:



cross multiply now we get :

4 * x = 8 * 3

==> 4x = 24

divide by 4 on both sides

==>

==> x = 6

thus the solution

You can put this solution on YOUR website!
1) By data it is given that price is related to diameter by a quadratic equation.

A general quadratic equation is given by f(x) =

We shall write it as y = f(x) =

==> y =

So now lets plug in all the given set of values, in the form of co-ordinates. This implies that it forms 3 equations.

3.39 = 64a + 8b + c ------------(1)

5.12 = 144a + 12b + c -----------(2)

7.29 = 256a + 16b + c -----------(3)

Let solve them simlutaneously.

Subtracting (1) & (2), we get:

1.73 = 80a + 4b --------------(4)


subtracting (2) & (3), we get:

2.17 = 112a + 4b ------------(5)

subtracting (4) & (5)

0.44 = 32a

==> a = 0.01375

Now by back substituion we find b

1.73 - 1.1 = 4b

0.63 = 4b

==> b = 0.1575

substitute the a and b value in one of the equations. So we get:

3.39 = 0.88 + 1.26 + c

3.39 - 2.14 = c

c = 1.25

Thus the quadratic equation would be

y =


Price of a 14 inch pizza would be just plug in x = 14 in the above equation we get:





y = $6.15

==============================================================================

2) Solve for x. = 0

The given equation can be written as:

= 0


= 0

Using the quadratic formula we find the roots.



Substituting for the values we get:












Taking 2 as a common factor we get:

So the roots are: 5 + 7i/2 and 5 - 7i/2

The solutions are 5 + 7 i /2, 5-7 i/2

=============================================================================

3) What is the maximum product of two numbers whose sum is -6? What numbers yield this product? The max product is?

Let x and y be the two numbers.

It is given that the product is maximum and the sum is negative six.

so lets find the multiples of 6. They are + -1, +- 2, +-3, +-6

Taking them 2 at a time we find that -3 and -3 when added gives us -6

And their product gives us 9 which is the maximum number.

Hence the solution.

===========================================================================
4) solve for "n"
N = /6

This can be written as:

6N =



Using the quadratic formula we get:



Substituing for the values, we get:









Thus the solution.

Regards

If you stil have any doubts you can get back to me.. I'm a online teacher.. I'll help you..

You can put this solution on YOUR website!
Here goes the examples.

Let P(x) be a third degree polynomial as per the data given by you.

So P(x) =

and Q(x) be a fourth degree polynomial.


Q(x) =


So the addition of these would result in the following


Adding like terms we get:

P(x) + Q(x) =


thus the degree of the resulting polynomial would be equal to 4

Thus the solution


Regards

You can put this solution on YOUR website!
The given equation represents a parabola since the term x is in terms of a quadratic and it is a parabola facing above(opening upwards) .
So on a graphing Calculator, just go and plug in the equation and say plot(graph)

The graph of the given curve looks as shown below.




Regards

You can put this solution on YOUR website!


by observing the graph we cn find that -1 and +1 are the first twoo roots.
The other 3 roots are repeated roots and it would be 2.

This can be factorised by the method of trail and error method and then by synthetic division method.

by the trail and error method we find that 1 is the first factor



Then the second equation is agin siplified

here we find that x + 1 is a factor.

So will be the next eqn.


So the last eqn will be can be factored and thus we get repeated roots

hence, the roots are x = 1, -1, 2, 2, 2

(x - 1)(x + 1)(x- 2)(x - 2)(x - 2)

Are the roots of the eqn

Thus the solution

Regards
Chitra

You can put this solution on YOUR website!
Let "x" ft be the width of the rectangle

So lenght will be "3 + x" ft

Given area = 40 ft^2


We know that the area of the rectangle is given by lenght times breadth


40 = x * (x + 3)


40 = x^2 + 3x


==> x^2 + 3x - 40 = 0

==> by the method of factoring we find


==> x^2 + 8x - 5x - 40 = 0


==> x(x + 8) - 5(x + 8) = 0

==> x = 5 Or x = -8

We dont consider the negative values of x.

Therfore x = 5 ft will be the width

and x + 3 = 5 + 3 = 8ft will be the lenght of the rectangle


thus the solution

You can put this solution on YOUR website!
The given conic is:



To find the x-intercept put y = 0











(x + 1)(x - 7) = 0


==> x = -1 or x = 7

these are 2 x - intercepts


To find the y- intercept put x = 0


==> y = 0 - 6(0) - 7


==> y = -7


This is the one y intercept.


Graph looks this way:

You can put this solution on YOUR website!
Here by the data that is given -

Distance = 28 miles

time taken is 30 mins

Let us convert the time in minutes to hours
1 hr = 60 mins
x hr = 30 mins

==> x = 1/2 hr

==> x = 0.5 hr

We have to calculate the speed.

Speed = Distance traveled / time taken


Speed = 28/0.5

Speed = 56 miles/hour

You can put this solution on YOUR website!
I assume that you have to solve for the given question. If that is not the instruction given in your question then revert .. I'll help you

The given equation is:

-15 + 8x = -31

==> 8x = -31 + 15

==> 8x = -16

==> x = - 2

You can put this solution on YOUR website!
The given expression is:



==> 2a + 10 = 20

==> 2a = 20 - 10

==> 2a = 10

==>

==> a = 5

thus the solution.

You can put this solution on YOUR website!
Given that 5 gallons of gas runs for 100 miles
So therfore 12 gallons runs for -- miles

5 -----> 100
12 -------> x ?

x = (12 * 100)/5

x = 12 * 20

x = 240

thus the solution.

You can put this solution on YOUR website!
Hey hello..
Get back to me with the sums.. I'll surely help you with the solutions.. You can avail a free demo too on this Chapter..

Regs
Math Tutor

You can put this solution on YOUR website!
The given expression is:




When x = 3, just plugin the above equation.











==>


Thus the solution.

You can put this solution on YOUR website!
The given expresion is:

(2a)(5a)(6a)

==> (2 * 5 * 6) * (a * a * a)

==> (60) *

==>

Thus the solution

You can put this solution on YOUR website!
The given equations are:

2y = x + 6 ---------------(1)

-3x + 2y = -2 --------------(2)


Substituting (1) in (2) we get:

-3x + x + 6 = - 2

-2x = -2 - 6

-2x = -8

x = 4

By back substitution we get the "y" value:

2y = 10

==> y = 5

So we observe that the line intersects at (4,5) for both the graphs.



Hence the given system of equations are Consistent & Dependent

Thus the solution.


Here are the notes that will help you determine the category under which they fall.

If the two equations describe the same line, and thus lines that intersect an infinite number of times, the system is dependent and consistent.
If the two equations describe lines that intersect once, the system is independent and consistent.
If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent.

You can put this solution on YOUR website!
The graph is as follows:

You can put this solution on YOUR website!
Let "x" represent the autograph of the movie stars and "y" represent the autograph of the tv celebrities.
So according to the given data, she has 9 more autographs of the tv celebs than the movie stars.
So y = x + 9

Now let us wirte the equation

250x + 75y = 2300

Substitute for "y" we get:

250x + 75(x + 9) = 2300

250x + 75x + 675 = 2300

325x = 1625

x = 5

Pluggin back we get the value of y.

y = x + 9

y = 5 + 9

y = 14

Thus, the solution.

You can put this solution on YOUR website!
The given expression is:



Here we observe that b^2 is the highest factor among the variables.

Then among the numbers both are multiples of 7. so take out 7 as a common factor.




Thus the solution.

You can put this solution on YOUR website!
Let the numbers be x & y.

According to the data given we write "x" in terms of "y".

x = 3y + 7

Given that:
2(3y + 7) + 4y = 44

6y + 14 + 4y = 44

10y = 44 - 14

10y = 30

y =

y = 3

By back substitution, we get:

x = 3(y) + 7

x = 3(3) + 7

x = 9 + 7

x = 16

Thus the values are x = 16 & y = 3

Hence, the solution.

You can put this solution on YOUR website!
The given data is:
Distance traveled = 750 miles and

Time taken = 7.5 hours

Here lets find the speed of the plane.

Speed = distance traveled/ time taken
S = 750/7.5
S = 100 miles per hour


Now we shall calculate for the rest of the data.

Distance remains the same 750 miles

but time taken = 3 hours

Therfore Speed = dist/time

Speed = 750/3

Speed = 250 miles


Thus the solution.

You can put this solution on YOUR website!
The given equations can be written as:
y = 1 - x
y = 4 - 2x
They can be graphed as:

You can put this solution on YOUR website!
The given expression is:



This can be written as:




Taking LCM, we get:











Thus, the solution.

You can put this solution on YOUR website!
The given expression is:

=


By cross multiplying we get:

(2x + 5)(x - 1) = (x + 3)(2x + 3)

Simplifying the above equation using the distributive property, we get:


=


Grouping all the terms we get:


3x - 5 - 9x - 9 = 0


-6x - 14 = 0

6x + 14 = 0

6x = -14

x = -14/6

x = -7/3

Thus, the solution.


regs

You can put this solution on YOUR website!
Let the total number of apples that the basket contains = "x"

Lets write the data as given in the problem.

+ 10 + 1 = x

Adding all the like terms we get:

+ 11 = x

==> + 11 = x

==> 11 = x -

==> 11 =


==> 11 =

==> x = 120

Hence there are 120 apples in the basket.

Thus the solution


Regards

You can put this solution on YOUR website!
A number (n > 1) which is divisible by 1 and itself is called a prime number

These are the list of prime numbers between 1 and 100

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
53 59 61 67 71 73 79 83 89 97


regs

You can put this solution on YOUR website!
Let the age of Tom be "x" yrs.

Therefore, the age of Tom's father is 3x yrs.

Given that 4 yrs ago, he was 4 times as old as tom. Therfore the equations are:

3x - 4 = 4(x - 4)

3x - 4 = 4x - 16

16 - 4 = 4x - 3x

12 = x

Therfore, Tom is 12 yrs old

Hence his father would be 3 times as tom. that is equal to 3(12) = 36 yrs

Hence the solution

regs

You can put this solution on YOUR website!
Let x and y be 2 numbers.

Givent hat their sum is equal to 40.

x + y = 40

Also given that one number(x) is 8 more than the other (y)

Therfore x = 8 + y

Now by back substituion we get:

(8 + y) + y = 40

2y = 40 - 8

2y = 32

y = 16

Now by back substituion we get:

x = 8 + y

x = 8 + 16

x = 24

Thus the solution.

You can put this solution on YOUR website!
The given equation is:

y = -2x + 4 and

y = 1x + 2

Subtracting both the equations we get:

-3x + 2 = 0

-3x = - 2

3x = 2

x =

Now by back substitution in one of the equations we get:

y = 1(2/3) + 2

y = 2/3 + 2

Taking LCM, we get:

y = 8/3

==> y = 8/3

Thus, the solution.

regs

You can put this solution on YOUR website!
The given problem can be stated like this:

The base of the triangle is 11 ft and the altitude is 11 ft.

So we are supposed to measure the height of the ladder which forms the hypotenuse of the ladder.

We therefore use the pythagoras theorem to find the height of the ladder.
let the height be "x" feet









x = 15.5563

So to the nearest thousandth is 15.6000 ft

You can put this solution on YOUR website!
The equation for y can be written as:

15x + 10y = 400

==> 10y = 400 + 15x

==> y = (400/10) + (15/10)x

==> y = 40 + 1.5x

The graph of the above equation is:

You can put this solution on YOUR website!
THE TRUTH TABLE FOR THE GIVEN COMPUND PROPOSITION IS AS FOLLOWS:

p Q ~Q (~Q ^ P) (~Q ^ P) --> ~Q
T T F F T
T F T T T
F T F F T
F F T F T

OR THIS CAN ALSO BE WRITEN IN THE FORM OF 0'S ADN 1'S
THAT IS REPLACE T BY 1 AND F BY 0

THUS WE FIND THAT THE GIVEN PROPOSITION IS A TAUTOLOGY

REVERT TO ME IF YOU STIL HAVE MANY DOUBTS ABOUT THE DISCRETE MATH

REGS