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OK.....

The function is positive where it is above the x-axis. Looking at the graph, we can see it is above from (-infinity,-2) and (0,4).

Thank you so much CPhill !

I think you might have

y = -4x^2 + 22x + 12

In the form     Ax^2 + Bx + C.....the x coordinate of vertex is given by  -B / [2A]

So...here the x coordinate of the vertex is  -22/ {2 * - 4)  =  -22/-8  =  11/4  = 2.75

And to find the y coordinate we have   -4(11/4)^2 + 22(11/4) + 12   = 42.25

So....the vertex is (2.75, 42.25 )

y intercept.....let x = 0   and we have   -4(0)^2 + 22(0) + 12  =    12

x  intercept ......let y = 0  and solve for x

0 = - 4x^2 + 22x + 12      divide through by - 2

0 = 2x^2 - 11x - 6       factor

(2x + 1 ) ( x -6)  = 0      set  each factor to 0 and solve for x  and we have  x = -1/2  and x = 6

And those are the x intercepts

The axis of symmetry  is just    x =  the x cooordinate of the vertex =  2.75

Here are your limitations (what you need to do):

• Use all three numbers
• Use the + and divide only once in the expression and you have to use both of them in an expression

You can use as many parentheses as you want, and you can vary the order of the numbers.

The answer actually was 8/15. Do you know how?

\(c = \lambda \nu\\ c = 3\times 10^8 m/s\\ \nu = 530 \times 10^3 ~s^{-1}\\ \text{I trust you can multiply}\)

Thanks for the help!!!

Actually, the answer was 3/16. Do you know why?

I don't know what unit you are in, so this may differ than other answers. Dilation preserves angles, but not side lengths. However, all side lengths are reduced or extended by the same ratio, so the ratio of sides will remain the same. So no matter the scale factor, sin α′ will remain the same.

Hope this helps!

If I'm reading this right, then there are 6 squares of cardboard, all of equal area. They have side length of 8, so 8 * 8 * 6 = 384. I might have gotten this wrong, for it's hard to do without a picture.

Hope this helps!

Each square is 8 x 8 so then mutltiply that by the number of squares 8x8 = 64 then multiply it by 6

Oh, I get it now. I see. Thanks a lot for your help (and time)!!!

Parallel lines mean equal angles, which means similar triangles. We can set up a ratio y like this. \(\frac {12}{5} = \frac {y}{3}\) using ratio of sides. Cross multiply, and you get 5y = 36. So y = 36/5.

Do the same for x. \(\frac {17}{x} = \frac {36/5 + 3}{6}\) . I don't like fractions over fractions, so imma make it a decimal to make it easier. \(\frac {17}{x} = \frac {10.2}{6}\) . Cross multiply and you get 10.2x = 102. Solving for x gets us x = 10

We have the angle bisector theorem .......we have that

45 /50  = z / 20

9/10 = z / 20       multiply both sides by 20

20 * (9/10) = z

(20/10) * 9  = z

2 * 9 = z

18 = z