Can someone pls. help me with these math questions..?

Question

1solve equation by using the quadratic formula.

x^2-14+40=2x^2-16x+32

#2find the midpoint of the line segments withthe given endpoints.

(5,9)&(9,0)

#3

solve the equation grapically by finding x-intercepts.

x^2-x-4=0

#4

assume that the sales of a certain appliance dealer are approx. by a linear function. suppose that sales were $5000 in 1982 and $73,500 in 1987. let x =0 represent 1982. find the equation giving yearly sales S(x).

#5

solve the inequality

-6<4q-1<0

Thank you for helping!

Answer 1

1. I think you are missing an x for 14. So I will solve the:

   x^2 - 14x + 40 = 2x^2 - 16x + 32

   Move everything to one side and simplify to get:

   x^2 - 2x - 8 = 0

   The quadratic equation is x = (-b (+ or -) root(b^2 - 4ac))/2a

    So we plug in x = (2 (+ or  -) root(x^2 - 4*1*(-8)))/2

                        x = (2 (+ or  -) 6)/2

                         x = 4 or -2

2. The midpoint given two points (x1, y1) &amp; (x2, y2) is just

  ( (x1 + x2)/2, (y1 + y2)/2)

   So given (5,9) and (9,0)

   The midpoint is ((5+9)/2 , (9+0)/2) = (7, 4.5)

3. x^2 - x - 4 = 0

   Solve graphically? I guess you should draw it out, but i&#039;ll solve it for you analytically since I can&#039;t draw here.

   x^2 - x - 4 = 0

   where a = 1, b = -1, c = -4.

   Use the quadratic equation to get x = (1 (+ or -) root (17)) / 2

   Its a disgusting number so I don&#039;t know why you are being asked to solve graphically. The best you can do is give an estimate, or you typed the equation wrong.

4. So, let the x-axis be the year where 0 is 1982 and the y-axis be the sales. You are given two points:

   (0, 5000) although i think it should be 50 000

   (5, 73500)

slope is 13700 (get it by (y1 - y2)/(x1 - x2))

The equation of the line right now is:

y = 13700x + b

We use one of the given points to find b

5000 = 13700(0) + b which implies b = 5000

so the equation of the line is y = 13700x + 5000

or S(x) = 13700x + 5000

If in 1982, sales were actually $50 000, then do the same steps.

5. -6 &lt; 4q - 1 &lt; 0

    -5 &lt; 4q &lt; 1           Add 1 throughout

  -5/4 &lt; q &lt; 1/4         Divide by 4 throughout

And there is your answer, if you want it in decimal format, then

  -1.25 &lt; q &lt; 0.25

Hope that helps.