Look at picture
y=_

the height of the baseball after 5 seconds is feet

Step-by-step explanation:

We expect the equation for y to be quadratic. Since the table is obviously symmetrical about x=3, we can start with the vertex form ...

  y = a(x -3)² +b

Filling in the values from the first two table points, we get

  For (x, y) = (0, 6):

     6 = a(0 -3)² + b       ⇒   9a +b = 6

  For (x, y) = (2, 22):

     22 = a(2-3)² +b       ⇒   a +b = 22

Subtracting the second equation from the first gives ...

  (9a +b) -(a +b) = (6) -(22)

  8a = -16 . . . . . . collect terms

  a = -2 . . . . . . . . divide by 8

The second equation above tells us ...

  b = 22 -a = 22 -(-2) = 24

So, our equation for y is ...

  y = -2(x -3)² +24

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The value of y for x=5 is ...

  y = -2(5 -3)² +24 = 16

The height of the ball after 5 seconds is 16 feet.

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116