Answer:
a = 0, b = -15
Step-by-step explanation:
Given two complex number Z1=3cispi and z2=5cis(pi/2)
In polar form;
z1 = 3(cospi + isinpi)
z1 = 3(-1+i0)
z1 = -3+0i
Z2 = 5(cospi/2 + isinpi/2)
Z2 = 5(0+i)
Z2 = 0+5i
Z1*Z2 = (-3+0i)(0+5i)
Z1*Z2 = 0 - 15i +0i + 0i²
Z1*Z2 = 0-15i
comparing 0-15i with a + bi;
a = 0 and b = -15
Answer:
The first, second, and fifth statements are correct.
Step-by-step explanation:
We are given a circle with the equation:

And we want to select the statements that are true.
First, we can convert the equation into standard form. We can group each variable:

And complete the square for the first term:

Factor and simplify:

We can rewrite our equation as:

So, this tells us that we have a circle centered on (1, 0) with a radius of 3 units.
In this case, the first statement, second statement (the point (1,0) is on the x-axis), and fifth statements are correct (the square root of 9 is also 3).
Answer: 
Step-by-step explanation:
The area of a rectangle can be calculated with the formula:

l: the length of the rectangle.
w: the width of the rectangle.
The area of the remaning wall after the mural has been painted, will be the difference of the area of the wall and the area of the mural.
Knowing that the dimensions of the wall are
by
, its area is:

As they are planning that the dimensions of the mural be
by
, its area is:

Then the area of the remaining wall after the mural has been painted is:

Answer:
f(-3) = 16
Step-by-step explanation:
You substitute -3 to x.
f(-3) = 2(-3)² - 5(-3) - 17
f(-3) = 16.
As for the coordinates, the coordinates plotted in the graph above are (1,-1) and (2,-2).