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Here is how I would do the second one:

find slope  =  rise/run  = y1-y2 / x1-x2  =  (5- -7)/(2-6) = 12/-4 = -3

Perpindicular slope is    -  1/(-3) = 1/3

Find the midpoint of AB

  x      (2+6)/2 = 4

  y      (5+ -7)/2 = -1      so midpoint is    (4,-1)   and slope is 1/3

            line is     y = 1/3  x  + b     sub in your midpoint to calculate  'b'

                          -1 = 1/3 (4) + b    results in b = -7/3

y = 1/3 x -  7/3

Here is a picture:

1. find gradient 2--6/7-3 = 8/4 = 2

m*m = -1

m= -0.5

sub the information u know into formula

y = mx + c  or   y - y1 = m(x -x1)

y = -0.5x + 0.5

Happy belated birthday, Alan!

Have fun! 

54-10x<20+7x

34<17x

17x>34

x>2

(C).

54 - 10x <  20+7x      add 10x to both sides, subtract 20 from both sides

34 < 17x       divide both sides by 17

2 < x     ⇒    C

Now, if I were to Penelope and Hades or Pandora's box, do you know of any themes of these myths? 

Lol! 

My bank account?    My Bar Tab?   How far my dogs can hike with backpacks on?      

We have 2x+2>10

2x>8

=x>4

So, (A).

12x + 6 > 9x+12         subtract 9x from both sides of the equation

3x + 6 >  12                subtract 6 from both sides

3x > 6                         divide both sides by 3

x >  2

1.  5x - 7x^2 = 3x +4        add 7x^2 to both sides 0f the equation

     5x   =   7x^2 + 3x + 4      subtract 5x from both sides

      0 = 7x^2 -5x +3x+4        simplify

      0 = 7x^2 - 2x + 4          SInce the question states that it is 'radical form'   you will need to use Quadratic Formula (rather than factoring) to find 'roots'

      $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

a = 7    b = -2    c = 4   

    [ 2 +- sqrt((-2)^2 - 4(7)(4) ]   / [ 2(7) ]  = 2 +- sqrt(-108) / 14  =  2+- 6i sqrt(3)  / 14   =  1/7 +- 3/7 i sqrt(3)

Think you can do the second one now?

2.  - x^2 +4x = 13

         x^2 -4x +13 = 0         a = 1   b = -4   c = 13  

No phrases to choose from....!!!!

8y = (x + 1)^2 - 32

8y + 32 = (x + 1)^2

8(y + 4) = (x + 1)^2

The vertex is (-1, -4)

The parabola turns upward

8 = 4p

p = 2

The focus is  (-1, -4 + p)  =  (-1, -4 + 2)   = (-1, -2)

The directrix is  y = -4 - p = -4 - 2  =  -6  ⇒  y = -6

$25 + d = TotalAmount

a)  

y = -(1/4)(x - 2)^2 + 5

y - 5 = (-1/4)(x - 2)^2       multiply through by 4

4(y - 5) = -(x - 2)^2

The vertex  is ( 2, 5)

4p = 4

p = 1

This parabola turns downward

The focus is  (2, 5 - p)  = (2, 5 - 1)   =  (2, 4)

The directrix is  y = 5 + p =  5 + 1  = 6   ⇒   y = 6

Variable  !!!!

Thanks!!!!

CORRECT!!!

.20x + 1.80 < 7.80       subtract  1.80 from both sides

1.20x < 6.00      divide both sides by  1.20

x < 5   ⇒   D

[ The only thing strange here is that if she has   7.80.....she sould be able to buy EXACTLY 5 lbs. of tomatoes !!!]

Ok, so according to what you said, I got choice C (6220 lb/ft^2) for question 1 and for question 2 I got 406.6 which is aprrox 407,000, which is basically choice B for question 2.

Is that correct?

Greek Mythology is my specialty. I know anything and everything. DivideByZero is right though. Do Icarus. Thats the first one that comes to my mind right away.

Thanks, DBZ  !!!!

1   Just put in '3' for 'x' in the equation and do the calculation.....   OK   Need more help than that?

2  Year since 2010  is   2018-2010 = 8     put this value in for 't' and calculate your answer....   Need more help?