With qudratic equations and complex numbers

19. 7, 14 and 24

20. 2 seconds

Step-by-step explanation:

Question 19:

We have a triangle with perimeter 45cm.

Assuming its shortest side to be x, we can write expressions for each of its sides and form an equation.

shortest side ---> x

one side is twice as long as the shortest side ---> 2x

remaining side is 25cm less than the square of the shortest side ---> x^2-25

Combing these to get:

Now factorizing this quadratic equation to get:

Therefore, the lengths of three sides of this triangle are:

x ---> 7

2x ---> 2*7 ---> 14

---> (7*7)-25 ---> 24

Question 20:

The height h (in feet) of the rock after t seconds is given by the equation:

a) initial height of the rock = 144 feet

b) Putting h = 80 to find the the seconds after the rock is dropped will it be 80 feet above the water.

The time will be 2 seconds.

step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.