Hi,

 

Hi,

How do you solve for the x-intercept in the equation 

x+2y=6   ||when y  = 0

x = 6

 Pt(6,0) is where the line cross the x-axis

 

Hi,



factoring

(2x + 9y)(2x - 9y)

Checking with FOIL

F	First terms  4x^2

O	Outside terms -18xy

I	Inside terms  +18xy

L	Last terms    -81y^2

 

 

Hi,

the circumradius of triangle whose sides are 3,4 and 5? P = 12, s = 6

r =  

 

Hi,

What is the sum of the solutions of |x -1| -4 = -2

|x -1| -4 = -2

|x -1| = 2

(x-1) = 2,  x = 3

(x-1) = -2,  x = -1

 3 + -1 = 2

 

Hi,

did You mean  or 



  ||Solve the equation for

 

Hi,

What is the square feet inside a circumference of 438 feet?

      

Similarily:

      

 

Hi,

How far  can the members of a bicycling club ride out into the country at a speed of 12 mph 

and return over the same road at 8 mph if they travel a total of 10 hours? 

 D = rt   or D/r = t

  x/12mph + x/8mph = 10hrs   |Multiplying thru by 24 so as all denominators = 1

   2x + 3x = 240

    5x = 240

     x = 48mi

CHECKING our Answer***

    48mi/12mph + 48mi/8mph = 4hr + 6hr = 10hr

 

Hi,

d^2 - 10d + 25 

(d-5)(d-5) = 

Check factoring Using FOIL

F	First terms  d^2

O	Outside terms -5d

I	Inside terms  -5d

L	Last terms    25

 

Hi,

What is the radical form of:

 m^2.5

 m^(5/2)

 

 

Hi,

 

Hi, Previously Posted



 
Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables


  

  

  

  

  

  

  First let . This is the matrix formed by the coefficients of the given system of equations.

  

  

  Take note that the right hand values of the system are , , and  and they are highlighted here: 

  

  

  

  

  These values are important as they will be used to replace the columns of the matrix A.

  

  

  

  

  Now let's calculate the the determinant of the matrix A to get . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver.

  

  

  

  Notation note:  denotes the determinant of the matrix A.

  

  

  

  ---------------------------------------------------------

  

  

  

  Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix  (since we're replacing the 'x' column so to speak).

  

  

  

  

  

  

  Now compute the determinant of  to get . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant.

  

  

  

  To find the first solution, simply divide the determinant of  by the determinant of  to get: 

  

  

  

  So the first solution is 

  

  

  

  

  ---------------------------------------------------------

  

  

  We'll follow the same basic idea to find the other two solutions. Let's reset by letting  again (this is the coefficient matrix).

  

  

  

  

  Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix  (since we're replacing the 'y' column in a way).

  

  

  

  

  

  

  Now compute the determinant of  to get .

  

  

  

  To find the second solution, divide the determinant of  by the determinant of  to get: 

  

  

  

  So the second solution is 

  

  

  

  

  ---------------------------------------------------------

  

  

  

  

  

  Let's reset again by letting  which is the coefficient matrix.

  

  

  

  Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix  

  

  

  

  

  

  

  Now compute the determinant of  to get .

  

  

  

  To find the third solution, divide the determinant of  by the determinant of  to get: 

  

  

  

  So the third solution is 

  

  

  

  

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

  

  Final Answer:

  

  

  

  

  So the three solutions are , , and  giving the ordered triple (6, 4, 2)

  

  

  

  

  Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant.

  

  

  

 

Hi,



 
Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables


  

  

  

  

  

  

  First let . This is the matrix formed by the coefficients of the given system of equations.

  

  

  Take note that the right hand values of the system are , , and  and they are highlighted here: 

  

  

  

  

  These values are important as they will be used to replace the columns of the matrix A.

  

  

  

  

  Now let's calculate the the determinant of the matrix A to get . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver.

  

  

  

  Notation note:  denotes the determinant of the matrix A.

  

  

  

  ---------------------------------------------------------

  

  

  

  Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix  (since we're replacing the 'x' column so to speak).

  

  

  

  

  

  

  Now compute the determinant of  to get . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant.

  

  

  

  To find the first solution, simply divide the determinant of  by the determinant of  to get: 

  

  

  

  So the first solution is 

  

  

  

  

  ---------------------------------------------------------

  

  

  We'll follow the same basic idea to find the other two solutions. Let's reset by letting  again (this is the coefficient matrix).

  

  

  

  

  Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix  (since we're replacing the 'y' column in a way).

  

  

  

  

  

  

  Now compute the determinant of  to get .

  

  

  

  To find the second solution, divide the determinant of  by the determinant of  to get: 

  

  

  

  So the second solution is 

  

  

  

  

  ---------------------------------------------------------

  

  

  

  

  

  Let's reset again by letting  which is the coefficient matrix.

  

  

  

  Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix  

  

  

  

  

  

  

  Now compute the determinant of  to get .

  

  

  

  To find the third solution, divide the determinant of  by the determinant of  to get: 

  

  

  

  So the third solution is 

  

  

  

  

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

  

  Final Answer:

  

  

  

  

  So the three solutions are , , and  giving the ordered triple (6, 4, 2)

  

  

  

  

  Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant.

  

  

  

 

Hi,

E=120

 I=3.5 = 7/2

 R=E*I

 R=  =  = 420

 

Hi,

I=240

 w=I/3

 A=I*W

 A=  = 80

 

Hi,

(125^2/3)1/2





   5^1 = 5

 

Hi

   

 

Hi,previously Posted

Use the equation 2x+y=12 

what is the missing numbers in the ordered pairs ?

Do not understand exactly Your Inquiry:

a couple of ordered pairs would be the intercepts: (0,12) and ( 6,0)

 

Hi,

Use the equation 2x+y=12 

what is the missing numbers in the ordered pairs ?

Do not understand exactly Your Inquiry:

a couple of ordered pairs would be the intercepts: (0,12) and ( 6,0)

 

Hi,

solve the equation

   |Multiplying thru by 15 so as all denominators = 1

     6x - 5x = 75

        x = 75

CHECKING our Answer***

30-25=5

 

Hi,

If you multiply a number by 5 and then add 8, the result is 68.

Write as we Read:

 5x + 8 = 68

   5x = 60

    x = 12

 

Hi,

find the length of the sides of tiangle whose vertices are 

(1,4),

(-4,0)  D = sqrt(4^2 + 5^2) = sqrt(41)

(3,-3   D = sqrt(3^2 + -7^2) = sqrt(58)  longest side C

(1,4),  D = sqrt(-7^2 + 2^2) = sqrt(53)

 41 + 53 = 94 > 58

 If A, B and C are the sides of a triangle where C is the longest side, then we can say the following

i) If A^2+B^2 = C^2 is true, then we have a right triangle

ii) If A^2+B^2 > C^2 is the case, then we have an acute triangle.***** 

iii) If A^2+B^2 < C^2, then we have an obtuse triangle.

 

Hi,

Percy is 47 years old and his son Zachary is 16 years old. 

In how many years' time will Percy be twice Zachary's age?

  47 + x = 2(16+x)

  47 + x = 32 +  2x

      15yrs = x

 

Hi,

if width of a reactangular field is 44 ft and height of a rectangular field is 39 ft,

then area of a reactangular field is ?  A = 44ft· 39ft = 1716 ft^2

 

Hi,re TY..Yes! typo on the extra zero. Note highlighted: amount + 60% increase = 37000. 

Sales at a local ice cream shop went up 60% in 5 years.

37,000 ice cream cones  sold in the current year...

  

  x(1.60) = 37000

       x  = 37000/(1.60)

       x = 23,125, the number of ice cream cones sold 5 years ago.

 

Hi,Re TY..sry misunderstood Your inquiry... Good work!

 

             x^0 =  

 

  

     5 = x+5

      0 = x

 

Hi,

There are 10 more sophmores than the number of juniorsin an algebra class.

 80 students in this class

   (x+10)+ x = 80

     2x + 10 = 80

       2x = 70

        x = 35, juniors and 45 sophmores

CHECKING our Answer***

    35 + 45 = 80

 

Hi,

Note:Standard Form of an Equation of an Hyperbola opening up and down is:

   where Pt(h,k) is a center  with vertices 'b' units up and down from center and foci  from center along x = h

(y+5)^2/36 - (x+2)^2/25 =1  C(-5,-2) V(,-5,-8) & V(-5,4), F(-5, -2±)

See below descriptions of various conics                         

Standard Form of an Equation of a Circle is  

where Pt(h,k) is the center and r is the radius





 Standard Form of an Equation of an Ellipse is  where Pt(h,k) is the center. (a positioned to correspond with major axis)

 a and b  are the respective vertices distances from center and ±are the foci distances from center: a > b



Standard Form of an Equation of an Hyperbola opening right and  left is:

   where Pt(h,k) is a center  with vertices 'a' units right and left of center and foci {{sqrt(a^2+b^2) from center along y = k.



Standard Form of an Equation of an Hyperbola opening up and down is:

   where Pt(h,k) is a center  with vertices 'b' units up and down from center along x = h.



the vertex form of a parabola opening up or down,  where(h,k) is the vertex.

The standard form is , where  the focus is (h,k + p)



the vertex form of a parabola opening right or left,  where(h,k) is the vertex.

The standard form is , where  the focus is (h +p,k )

 

Hi,

If x1 = - 2; x2 = 5; y1 = 3; y2 = - 7, 

 (5,-7) and 

 (-2,3)   = -10/7 

 

Hi,

x=7y+24

 x=(7/4)y 

My work:

 (7/4)y = 7y+24

 multiply each side by 4 

7y=28y+96

 divide by 7 

y= 4y+(96/7)

 move the Y and 96/7 to the other side

Yes!  -(96/7) = 3y   and y = -32/7  and x = (7/4)(-32/7) = -8

(-8, -32/7) Independent system, one solution

CHECKING our Answer***

 -8 = 7(-32/7) + 24 = -8

A consistent system has at least one solution.

An inconsistent system has no solutions.

An independent system has exactly one solution. ****

Andependent system has infinitely many solutions.



 

 

Hi, Re: TY, this is a trinomial (3 different type of terms) 

424 = x^2 + 36x 

 x^2 + 36x- 424 = 0





x is -45.35, 9.35  (rounded to 2 decimal points)