Hi



 -3x + 3 = 4x + 10   |Yes!  cross multiplying

  -7x = 7         |subtracting 4x and 3 from both sides 

    x = -1

Hi

Let log indicate a base of ten 

 4^x-2 = 7^3x+1

(x-2)log4 = (3x + 1)log7

  xlog4 - 2log4 = 3xlog7 + log7

    -2log4 -log7 = x(3log7 - log4)

    



  

Hi

A = L*W for a rectangle

A = x^2 + 5x + 6

    factoring

A = (x+3)(x+2)

Either (x+3) or (x+2) would be an expression for the possible length of this rectangle

Hi

Solving for x

x -7/12 = 5/6

   x = 5/6 + 7/12

   x = 10/12 + 7/12

   x = 17/12  or 1 5/12

Hi

11x > 22  |dividing both sides of the inequality by 11

  x > 2

Hi

30 balls in all, 8 of which are green, 10 are red and 12 are yellow

 P(yellow)= 12/30 = 6/15

Hi

solving for x

32x + 43 - 20x = -25 + 30 - 45x

  12x + 43 = 5 - 45x

    57x = -38

      x = -38/57

Hi

Hi

 



One finds the y-intercept by 'reading' it off  the slope intercept form

y-intercept is Pt(0,b)

Hi

 



One finds the x-intercept by exploring when y = 0

  0 = mx + b 

 -b/m = x, the x coordinate of the x-intercept

Hi

equation of an horizontal line can be expressed as y = k where k in constant

Hi

Let s represent the speed of the boat in still water

D = r*t  OR t = D/r

Question states*** (note round trip took 1.75hr)

 12/(s+3) + 12/(s-3) = 1.75hr

Solving for x

 12(s-3) + 12(s+3) = 1.75(s+3)(s-3)

    24s = 7/4(s^2-9)

     7/4s^2 - 24s - 63/4 = 0

       7s^2 - 96s - 63 = 0

  |discarding the negative solution

 s = 14.342 kmph

Hi

Let s represent one of the sides  of the rectangle

Question states*** 

A = L*W = 44m^2

    L*s = 44m^2

     L = 44m^2/s

P = 2W + 2L

P = 2s + 2( 44m^2/s)



  

Hi

difference of two numbers is 9

Let x and (x+9) represent the first and second number respectively

Question states***

 2x + (x+9)  = 24

Solving for x

       3x = 15

        x = 5   Second number is 14  (5+9)

CHECKING our Answer***

  10 + 14 = 24 

Hi

x^2 + 6x +9 = 0

factoring

(x+3)(x+3)=0 Note:SUM of the inner product(3x) and the outer product(3x) = 6x

  One solution x = -3

Hi

f(x) = x^2 + ax + 15 with a minimum value of -12

f(x) = (x+ a/2)^2 - a^2/4 + 15

Using the vertex form of a parabola,  where(h,k) is the vertex

 -a^2/4 + 15 = -12

      27 = a^2/4

      27*4 = a^2

        a = ± sqrt(108)

Hi

Simplifying by combining like terms

(-3x^3-9x^2-5)-(-7x^2-6x-2)

1*(-3x^3-9x^2-5) -1*(-7x^2-6x-2)

  -3x^3 -9x^2 -5 + 7x^2 + 6x + 2

  -3x^3 -2x^2 + 6x - 3

Hi

Simplifying by combining like terms

6x+ (5x-8)

6x+ 1*(5x-8) 

6x+ 5x-8

  11x - 8

Hi

Please repost with complete question so as our Tutors can best

be of an assistance to You.

Hi

 



x+4y=12   |solving for y

  y = (-1/4)x  + 3   y-intercept is Pt(0,3)

Line with same  y-intercept

 y = mx + 3   |using ordered pair Pt(5,4) to solve for m

 4 = m*5 + 3

 1/5 = m  

Hi



 

     9^y = 1/3

       y = -1/2

Hi



 log10,000

  10^y = 10,000

     y = 4

Hi

 1mi = 5280ft 

  80/5280 = 1/66 of a mile

Hi

Using the vertex form of a parabola,  where(h,k) is the vertex

 y = (x - 3)(x + 4)

 y = x^2 + x - 12  |expanding

 y = (x +1/2)^2 - 1/4 - 12  |completing the square

 y = (x + 1/2)^2 - 49/4   Vertex is Pt(-1/2,-49/4), line of symmetry x = -1/2

Hi

Using the vertex form of a parabola,  where(h,k) is the vertex

 y = (x + 3)(x - 4)

 y = x^2 -x - 12  |expanding

 y = (x- 1/2)^2 - 1/4 - 12  |completing the square

 y = (x- 1/2)^2 - 49/4   Vertex is Pt(1/2,-49/4), line of symmetry x = 1/2

Hi

 



x+ 2y = 9  |solving for y

  y = -(1/2)x + 9/2  Slope m = (-1/2)

Parallel lines have identical slopes:

 y = (-1/2)x + b  |using ordered pair Pt( 6,9) to solve for b

 9 = (-1/2)6 + b

 12 = b

 y = (-1/2)x + 12   OR in standard form: x + 2y = 24

Hi

total of 8 vehicles 

Let x and (8-x) represent the number of buses and vans respectively 

Question states***

 51x + 8(8-x) = 150

Solving for x

 43x + 64 = 150

    43x = 86

      x = 2, the number of buses.  6 vans  (8-2)

CHECKING our Answer***

 2*51 + 6*8 = 102 + 48 = 150

Hi

 



4x-5y+3=2x-2y-3  |Solving for y

  2x + 6 = 3y

  y = (2/3)x + 2  Slope m = (2/3) and the y-intercept is Pt(0,2)

Hi, Yes!

2x+4=0 

2x = -4

 x = -2

Hi

 Pt(-8,-1) is the center of the circle, radius of 6

Hi

solving system of linear equations through elimination

2x-y+z=1

x+y-7=2

3x-y+z=0



2x-y+z=1

3x-y+z=0



-2x +y -z=-1  |Mulitplying 1st equation by -1, prior to adding the equations

 3x -y +z=0

  x = -1

x+y-7=2   |Substituting x = -1 into an equation to solve for y

-1 + y = 9

  y = 10

3x-y+z=0  |Substituting x = -1 and y = 10 into an equation to solve for z

 -3 -10 + z = 0

        z = 13

CHECKING our Answer***

2x - y + z =1

 -2 -10 + 13 = 1