CPhill

OK....using my method we have

y = slope ( x -   x coordinate ) + y coordinate

y = (1/3) ( x -  - 3 )    + 7

y = (1/3)( x + 3) + 7

y = (1/3)x + (1/3)(3) + 7

y = (1/3)x + 1 + 7

y = (1/3)x + 8

Is that easy, RP ???

First one

Cost   = Sq Ft   x Price per Sq Ft  =

440.25 * .89  =

$391. 82

Second one

Friend #1 can paint 75% of his house in 3.25 hours.

Friend #2 can paint 60% of his house in 2.96 hours.

Friend #3 can paint 56% of his house in 2.89 hours. 

To see which can paint the fastest....take the given time and divide by the percent expressed as a decimal...the "least" answer is the fastest

So...we have

3.25 /.75

2.96 / .60

2.89 / .60

Can you finish it, DP????

Thanks, DP   !!!

And welcome.....!!!

Yep....the slope of your line =   - ( 1/ -3) = 1/3

And the point is ( -3, 7)

Do you want to  try it, RP???

I'll check it

Let x be the number of feet of fence on each side of the area  perpendicular to the barn

So......the side parallel to the barn is (100 - 2x)

So....the area, A  =   x(100 - 2x)  

A = -2x^2 + 100x

This will be a parabola turning downward

The x coordinate that maximizes the area is given by the x coordinate of the vertex =

-100 / [ 2 * -2] =   -100 / -4   =   25 ft  = x

So....the dimensions are     (25) (100 - 25) = 25 ft x  75 ft

And the max area is    25 * 75   =  1875 ft^2

OK....we have

y = slope   ( x - x coordinate ) + y coordinate

y = 2 ( x -  - 5 ) - 8

y = 2 ( x + 5) - 8

y = 2x + 10 - 8

y = 2x + 2

8 + pi       [ 2i + 1 ]              16i + 2pi^2 + 8 + pi

_____     ________ =        ________________ =

2i - 1        [2i  + 1 ]                 4i^2 - 1

8  + (16 + p - 2p) i               8    + ( 16 - p) i 

_______________    =      ______________

        -5                                    -5

Note  YEEEEEET.....that this will only be a real number when  16 - p = 0

So....16 - p = 0...so p = 16

So we will have

8 + 0i                   8

____ =          -    ___

 -5                       5

CORRECTED ANSWER.....thanks YEEEEEET for spotting my earlier error !!

In the form   Ax + By = C      [this is known as standard form ]

The slope is given by -A/B

So......A = 6    and B = -3

So....slope =   -6/ - 3  = 2

So.....since parallel lines  have equal slopes

We want to write a line with a slope of 2 passing through  (-5, -8)

Can you do it now, RP ???

For the second one we have

96 = (1/3) (base area) (height)

96 = (1/3)  [ x (3x + 1) ] (12)

96 = 4 [x (3x + 1) ]   divide both sides by 4

24 = x (3x + 1)  

24 = 3x^2 + x      rearrange as

3x^2 + x - 24  = 0      factor

(3x - 8) ( x + 3) = 0

Setting each factor to 0 and solve for x and we have that

x = 8/3 cm    or  x = - 3cm

Reject the second answer

So...the base area is (x) (3x + 1) = (8/3) (3(8/3) + 1 ) = (8/3)(8 + 1) = (8/3)(9) =

24 cm^2

Rom  made  a slight typo

√[ 11/36] = √11/√36 = √11 / 6

No biggie...!!!