Hi

Letting y represent constant rate of speed of the second train 

Question states***  Note:  D = r*t and distances the same for both trains

 4.5hr*x = 3.5hr*y

Solving for y

 4.5x/3.5 = y

  (9/7)x  = y

Hi

x    -1, -2, 0, 1, 2, 3

x^2  1,  4, 0, 1, 4, 9

y      2,  8, 0, 2, 8, 18    y = 2x^2   Constant of variation is 2

Hi

Let x represent the number

Question states***

 x + 1/x = 10/3            |good work

Solving for x

 3x^2 + 3 = 10x

3x^2  - 10x + 3 = 0      

factoring

(3x -1)(x - 3) = 0   Note:SUM of the inner product(-x) and the outer product(-3x) = -10x 

(3x -1)=0      x = 1/3

(x - 3) = 0    x = 3

CHECKING our Answer(s)***

  1/3 + 3 = 10/3

  3 + 1/3 = 10/3

Hi

A right triangle has a hypotenuse of 50 feet and a leg of 14 feet:

applying the Pythagorean theorem

length of the other leg = sqrt(50^2 - 14^2)= sqrt(2304) = 48ft

Hi

Let x represent the number

Question states***

 1/x + 2/x^2 = 3

Solving for x

 x + 2 = 3x^2

 3x^2 - x - 2 = 0

factoring

 (3x + 2)(x-1) = 0

  (3x + 2)=0  x = -2/3

  (x-1) = 0   x = 1



CHECKING our Answer(s)***

 1 + 2 = 3

 -3/2 + 2(-3/2)^2 = -3/2 + 18/4 = -6/4 + 18/4 = 12/4 = 3

Hi

Letting n represent the smaller number

 Sum of the two numbers = n + (3n+2)

Hi

Letting w represent credit hours at westside

ALL class fees =  $98*w + $115(15-w)

Hi

two numbers give you a sum of 22

Let x and (22-x) represent the numbers

Question states***

  x(22-x) = -720

  x^2 - 22x-720 = 0

factoring

( x-40)(x+18) = 0

( x-40)= 0 

     x = 40   

 (x+18) = 0

     x = -18   Numbers are -18 and 40

Hi

Hi

(3^3)(3^x)(3^(x-1))=3^12

 3^(3+x+x-1) = 3^12

 3^(2x+2) = 3^12

     2x+ 2 = 12

         x = 5

CHECKING our Answer***

27*243*81 = 531,441

Hi

twelve workers can complete a job in six days or 1/6 of job in 1 day.

  = 1/72 by each worker each day.



After 2 days: 4/6 of job left and 8 workers left to complete:

 8/72 Or 1/9 per day   = 36/6 = 6 days to complete job

Hi

solving the identity 

1-2cos^2 x=2sin^2 x-1

1 = 2cos^2x+2sin^2x-1

1 = 2(cos^2x+sin^2x)-1

1 = 2(1)-1

1 = 1

Hi

Solving 

5x^2=10

 x^2 = 2

  x = ± sqrt(2)

Findng the x-intercepts (when f(x) = 0) 

f(x)=5x^2-10

 0 = 5x^2 - 10

5x^2=10       x = ± sqrt(2)

Hi

Decide whether the pair of lines is parallel, perpendicular or neither.

5x-6y=19    OR  y = (5/6)x - 19/6     | m = 5/6

6x+5y=-30   OR  y = (-6/5)x -6        | m = -6/5

Lines are perpendicular as  5/6*-6/5 = -1

Hi

Decide whether the pair of lines is parallel, perpendicular or neither.

4x+3y=3    OR  y = -4/3x + 1     | m = -4/3

3x+4y=9    OR  y = -3/4x + 9/4   | m = -3/4

Good work on finding the slopes: Neither, it is.

Hi

circle whose diameter has endpoints of (3, 0) and (7, 10)

(3, 0) and 

(7, 10) Midpoint is   (5,5)             |  ( , )

(3, 0) and 

(7, 10  D = sqrt( (-4)^2 + (-10)^2))        |  D =  

  D = sqrt(116) = 2sqrt(29) and r = sqrt(29)

 Standard Form of an Equation of a Circle is 



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

   (x-5)^2 + (y-5)^2 = 29





  

Hi

Find the equation of the circle that has its center at (6,-5) and passes through (1,7).

(6,-5)

(1,7)

 r = sqrt(5^2 + (-12)^2) = 13      |D = 

Standard Form of an Equation of a Circle is 

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



   (x-6)^2 + (y+5)^2 = 169

Hi

Using the point-slope formula, 

line 1 passes through

(-3,-7) and 

(-7,-5)   m = -2/4 = -1/2     | y = (-1/2)x -17/2

line 2 passes through

(-5,-2) and 

(-7,-6)  m =  4/2 = 2         | y = 2x + 8   

 Lines are perpendicular to one another as: -1/2*2 = -1

Hi

Find an equation of the line containing the point (6,9)

 y = -9x + 8         | Yes same as 9x+y=8 

"If" the new line is to be 'perpendicular' to the above..then Yes, its slope = 1/9

New Line:

y-9=1/9(x-6)         | Yes.   

y =1/9(x-6) + 9

y = 1/9(x) - 6/9 + 9

y= (1/9)x + 75/9    OR x-9y = -75

Hi

Find the equation of the perpendicular bisector of the interval joining 

(-5,2) and (3,-4). 

Determining the slope of the line containing this segment: 

(-5,2) and 

(3,-4)  m = 6/-8 = -3/4                   | 

Finding the Midpoint of the segment

(-5,2) and 

(3,-4   Midpoint is Pt(-1,-1)             | (, )

Line perpendicular(slope m = 4/3) passing thru Pt(-1,-1)

  y = (4/3)x + b  |using ordered pair pt(-1,-1) to solve for b

 -1 = -4/3 + b

 1/3 = b

   y = (4/3)x + 1/3  OR 4x - 3y = -1 in standard form.

Hi

Let x represent time to travel 300 miles

Question Sets Up the Proportion

          |Cross multiplying to solve

  200x = 1200

     x = 6 hr

Hi

A 5-pound bag of apples costs $3.50. At the same rate, what would be the cost of 7 pounds of apples

Let x represent the cost of 7 pounds of apples

question Sets up the Proportion

       |Cross multiplying to solve

   5x = 7*3.50

    x = $4.90

Hi

Let x represent Jenny's portion

Jenny: x  

Demi: x/2

Drew: (3/4)x

Question states***

  x + x/2 + 3x/4 = 18in  |Multiplying thru by 4 so as all denominators=1

Solving for x

 4x + 2x + 3x = 72

        9x = 72

         x = 8in

Jenny: 8in  

Demi:  4in

Drew:  6in      |Note: portions total 18in  

Hi

Let x represent the number of cups of the 18$ solution

Question states*** "Mixing"

 .18x + .25*16 = .20(16+x)

Solving for x

  18x + 25*16 = 20(16+x)   |multiplying thru by 100

        5*16 =  2x

        40 = x            

CHECKING our Answer***

 .18*40 + .25*16 = 7.2 + 4 = 11.2 = .20*56

Hi

How do you graph the following inequality:  

 y ≤ x?

  I. Graph the line y = x  Pt(0,0), Pt(1,1) etc on the line (plot Pts and connect with line)

  II. Shade area 'below'/including the line



 
Solved by pluggable solver: Plot Any Inequality
Graphing function : 

  

  


 

 

Hi

if the length of a side of a cube is 17cm,what is its volume?

   17^3 = 4913 cm^3          V(cube) = s*s*s

Hi

Note: in a 30-60-90 Rt triangle, ratio of its sides is 1:sqrt(3):2 

one side it's 7 radical 3

 the other side would be: 7

 the hypotenuse would be:14     |giving a ratio of 7:7sqrt(3):14

CHECKING our Answer***

using the Pythagorean Theorem

  49 + 49*3 = 14^2 = 196  

Hi

1) Explain how you might go about constructing a quadratic equation whose solutions are -5 and 7.

  The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0. 

 f(x) = (x+5)(x-7) = 0

 f(x) = x^2 -2x -35



2) Effects of coeficient a on graph of y = a^2 + bx + c

  a > 0  Parabola opens upward (blue)

For example: x^2 + 2x + 1

   a < 0  Parabola opens downward (green)

For example: - x^2 + 2x + 1 

Hi

1. x+y = 5   OR   y = -x + 5   |x 0,1,2,-1,-2

  x    -x + 5

 0	5

 1	4

 2          3

-1	6

-2	7

Plotting points and connecting with a line to graph

Hi

"If" the last term in the numberator is 20x^2

Hi

three more than five times a number is the same as thirty more than twice the number.

Let x represent the number

Question states***

 5x + 3 = 2x + 30

Solving for x

    3c = 27

     c = 9

CHECKING our Answer***

 45+3 = 18+30 = 48