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Is there a mistake in your question? Because I can't find any number up to 10,000 of having a GCD  > 1 ??

thank u

This was posted here as well: https://web2.0calc.com/questions/find-a-b-c-if-the-graph-of-the-equation-y-ax-2-bx-c-is-a-parabola-with-vertex-5-3-vertical-axis-of-symmetry-and-contains-the

Hope this helped!

x^2  + 3x - 28  =    ( x  + (-4) )  (  x - ( - 7 ) )             a   = -4     b  = -7

x^2 - 10x - 56  =   (x - 14 ) ( x + 4)  =  ( x + 2(-7) )  ( x + 4)       c  = 4

So

2c - a   =

2(4) - (-4)  =

8  + 4   =

12

3/4     the numerator is perimeter and is measured in feet    to convert to inches , multiply by 12       3 x 12 = 36 in

          the denominator is area and is expressed in feet².... to convert to inches² , multiply by 12 x 12 = 144   4 x144 = 576 in²

36/576 = 1/16   

y = -16t^2 +80 t         describes the height.....soooooo

height = 36 ft

36 = -16 t^2 +80t    

-16t^2+80t -36 =0       Now use the Quadratic Formula to determine the values of t.....there will be TWO....one (the smaller) will be on the way up and the other will be t for the way down.....obviously you want the smaller one....

  \(t = {-b \pm \sqrt{b^2-4ac} \over 2a}\)    a = -16    b = 80    c = -36         You should be able to do this now....or you are in the wrong class for your abilities so far

\( \frac{x-3}{x^2-10x+16} \)

Factor  the  denominator  as   ( x - 8) ( x - 2)

Note that  if  x  =  8   or  x  = 2   then the denominator  will be  =  0

So......these  are the two values  where the rational function is  undefined

And the sum of these  =   10

Multiply 1.75 ft and 1.25 ft then covert the sum to inches by multiplying it by 12.

.... you'll need to multiply by 12 x 12 = 144 sq in  / sq foot       not just multiply by 12 alone....      just a heads up FYI

If   6 walls can be painted in 54 min.....then 1 wall can be painted in 9 min

Which  means that  each person can paint    1 /( 9 * 4)  =  1/36  of the wall in one minute

So  6 people can paint  6 (1/36)  = 1/6 of a wall in 1 minute

So....the number of  minutes that it would take them to paint  7 walls =  

7  / (1/6)    =   7 * 6    = 42  min

54 min * 4 people / 6 walls =   36  min-people/ wall

36 min-people/wall   x   7 wall/6 people = 42 min

arcsin (-2/3)= -41.81 degrees   (this is the same as 318.19 degrees)

            also       = 221.81 degrees

via calculator.

1) All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

I solve this with linear programming  (and a little Agebra)

Let x  = weight of sack of sugar

Let y = weight of a sck of flour

We  have these inequalities

2x + 3y  ≤ 40

y - 2x ≤  5

Set  these up as  equalities

2x + 3y  = 40      (1) 

y  -2x   =  5       ⇒   y = 5 + 2x     (2)

Sub (2) into (1)   and we have that

2x +3( 5 + 2x) =  40

8x + 15  = 40

8x = 25

x = 25/8   =   3.125 lbs  

So...max weight for a sack of flour  = 5 + 2(3.125)  =  11.25 lbs  

See the graph here : https://www.desmos.com/calculator/pjcr7qcxiz

The max for the weight of a sack of flour occurs at (3.125, 11.25)

OK....let the tower height  = H

And we have that

sin 32°  =   H  /  45      rearrange as  H  =  45 * sin (32°)

And  when the new cable is attached we have that

sin (angle we are loooking for)   = H  / 100

sin (angle we are looking for)  =   [ 45 * sin (32°) ] / 100

Take  the arcsin

arcsin  (   [ 45 * sin (32°) ] / 100 )  =  angle we are looking for    ≈  13.8°

Oh wow I forgot the basics...LOL!

 weight of a sack of sugar  =  x

weight of a sack of flour  = y

wait- what do the variables represent?

stop cheating on your aops homework bruh

Here's a hint for #1.

We can create inequalities like this:

3x+4y ≤ 40

2y-3x ≤5

To solve this problem, try to get y to the biggest possible value. Hope this helped!!!

              C

                        7

D            15                 E  =  38°

We can find CD  with the Law of Cosines

CD  =  sqrt [  15^2  + 7^2  - 2(15)(7)cos (38°) ]    ≈   10.42 

Woops! Sorry. I will post the answer to number 1 soon.

If you can help please on the other question plz

thanks for #2! that cleared things up. for #1.. it's a similar problem but the numbers are different.