Hi,

5 - digit numbers using the 4 digits: 5, 4 , 0, 8

(first digit cannot be zero) There are  = 768 of them

 

Hi,

y= x-3    line:  slope m = 1

 x-intercepts ( 3,0)           ||  when y = 0

y-intercepts  (0,-3)

 

Hi,

y=x^2-9    parabola: V(0,-9),  line of symmetry x = 0(y-axis)

 x-intercepts (± 3,0)           ||  when y = 0

y-intercepts  (0,-9)

 

Hi,

x^2+y^2=4   Circle: C(0,0),  r = 2

 x-intercepts (± 2,0)

y-intercepts  (0,± 2)

 

Hi,

 2 and 7 placed on the line

2(-1) = -2   and 7(-1)=  -7  also placed on the line

Original numbers are on the opposite side of 0, but the same distance from 0

 

Hi,

A TV originally priced at $2,400 is on sale for 20% off. (paying 80%)

What is the sale price

  = $1920

 

Hi,

                       Three sides of a triangle are are 2, 4, and 5

 the two smallest size of a similar triangle are 6 and 12

  and ,   

 

Hi,

Note: Important to read entire question before planning a way of solving.

alisha brother is 10 years old

alisha brother is 6 years younger than alisha: alisha is 16

alisha is 5 years younger than her sister:  sister is 21

 

Hi,

3x+3y+6z=27

x-y+5z=-1

5x+y+z=-2

using Crame'sr rule is one way of solving



 
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 (-23/10, 77/10, 9/5)

  

  

  

  

  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,

x+y+z=-9

x-y+5z=-19

5x+y+z=-29

 x = -5,   y = -1,    z = -3



 
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 (-5, -1, -3)

  

  

  

  

  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,

x +y = 8

x +3.25y = 17   | Subtracting the 2nd EQ from 1st EQ to eliminate x

   -2.25y = - 9

        y =  4   and x = 4      

 

Hi,

3(x+5)-2(y-1)=6

x+4(y+3)=13



3x+15-2y+2=6

x+4y+ 12=13



3x-2y = -11    |multiplying 1st EQ by 2 and adding to the second

 x+4y = 1

 7x = -21

  x = -3   and y = 1      

 

Hi,

 h=  -16t^ + 112t    Note: 

 h =  -16(t-7/2)^2 + 16*49/4

  h =  -16(t-7/2)^2 + 196  



Note: vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  



Parabola opening Downward  V(3.5,196)

how long will it take for the object to reach it's maximum height?  

 will take 3.5 sec to reach max height of 196 ft

 

Hi,

A pizza place offers 3 different cheeses and 8 different toppings. 

In how many ways can a pizza be made with 1 cheese and 3 toppings?

  WAYS

 

Hi,

A delicatessen offers 4 different breads, 4 cheeses, and 6 different meats. 

In how many ways can a sandwich be made with 1 bread,1 cheese and 2 meats?  

   

 

Hi,

Write the equation of a circle that has the center on the x-axis, 

a radius of 1, and passes through the point 

(,)

  (x,0)

 D =  = 1  ,  -x  =±  , x = 

  

 

Hi,

Write the equation of a circle in which the endpoints of the diameter are at 

(-2,-3) and at 

(4,5)  D =   r = 5

       M = (2/2, 2/2) = (1,1) the center

 

Hi,

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

Line thatpasses through the points 

(-4, -1) and 

 (2, -4)  m = 3/-6 = -1/2     

 y = (-1/2)x + b

  |Using ordered pair (x,y): (2,-4)  to solve for b 

   -2 = b

 y = (-1/2)x - 2

 

Hi,

The admission fee at a county fair is $1.50 for children and $4.00 for adults.

 On a particular day, 2200 people enter the fair and $5050 is collected. 

How many children and how many adults attended? 

Question states***

 y + x = 2200  0r  

4.00y + 1.50x = $5050

 4y + 1.5(2200-y) = 5050

         2.5y = 1750  

            y = 700 , the number of adult tickets, children 1500

and...

 

Hi,



log[27](6)+log[27](18)-log[27](4) = 

 

Hi,



let x^2 = p



(x-4)(x+2) = 0

  x = 4  ⇒   p =  x^2 = 16   and...

Note: x = -2( p = 4) is an extraneous solution  as  4 -4 - 8 ≠ 0  

 

Hi,

Note: 

 

Hi,

 

Hi,

Note: the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex  



Assume you meant: 

  

parabola opening Upward a = 3 > 0,    Vmin(4,-51)

a. Is f(4) a minimum or maximun

 b. What is the value?  -51

 c. The domain of f is?  x is any real number

 d. The range of f is?   f(x) > -51

 

Hi,

ax^2 +bx + c = 0

x^2-2x+10=0       

discriminant







     ||   i^2 = -1

 = ± 6i ,  NO real solutions, Note: parabola will NOT cross x-axis





Simplify: 

   || multiplying both numerator and denominator by conjugate (4-i).  Note:  i^2 = -1 







   

 

Hi,

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.

line through (4,-4) with a slope m =  -9/4



  |Using ordered pair (x,y): (4,-4)  to solve for b

5 = b

 y = (-9/4)x + 5   (Note: line slants to the left (back 4 Up 9) from point(4,-4)

using point-slope form as the directions state





      || which also says:  y = (-9/4)x + 5)

 

Hi,

If the following can be factored...



What 2 numbers have a product of 144 and sum of 24???

F	First terms

O	Outside terms   

I	Inside terms  + x   = 24x

L	Last terms    



another:



What 2 numbers have a product of 9 and sum of 6???

F	First terms

O	Outside terms   

I	Inside terms  +   = 6x

L	Last terms    

 

Hi, Previously Posted

The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side 

If the third side is 16 cm long, find the length of the hypotenuse.

Applying the Pythagorean Theorem

 16^2 + x^2 = y^2      | y = (2x-4)

 256 + x^2 = 4x^2 - 16x + 16 

  3x^2 -16x - 240 = 0

 

 

        x = 12cm, the other leg    (throwing out negative solution for unit measure)

 Hypotenuse is 20cm

and...

 

 

Hi,

The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side 

If the third side is 16 cm long, find the length of the hypotenuse.

Applying the Pythagorean Theorem

 16^2 + x^2 = y^2      | 

 256 + x^2 = 4x^2 - 16x + 16 

  3x^2 -16x - 240 = 0

 

 

        x = 12cm, the other leg    (throwing out negative solution for unit measure)

 Hypotenuse is 20cm        

and...

 

 

Hi,

A test consists of multiple choice questions worth 3 points and essay questions worth 5 points.

The test has 17 questions that are worth a total of 65 points.

  3x + 5y = 65       | x+y = 17  0r   y = 17-x

 3x + 5(17-x) = 65

   -2x = -20

     x = 10, number of multiple choice questons,  7 essay questions

and...

 

 

Hi,

A circle with the equation (x + 4)2 + (y - 3)2 = 9 is reflected over the line y = -1.