Oofrence

Oh i didn't think about the discriminant, thanks!

We are looking for all complex numbers that are equidistant from  3, -i and 3i. Since these three points are not collinear, we know there is a unique such point (the circumcenter of the triangle formed by the three numbers in the complex plane).

The numbers equidistant from  and  are on the perpendicular bisector of the segment connecting -i and 3i in the plane. This perpendicular bisector is Im(z)=1, so the imaginary part of  is 1.

The numbers equidistant from 3 and 3i are on the perpendicular bisector of the segment connecting 3 and 3i in the plane. This perpendicular bisector is simply Re(z)=Im(z). Combining this with Im(z)=1 tells us that z=1+i.

Let g(x) = ax + b. Then g(f(x)) would be a(2x-3) + b

a(2x-3) + b = 2ax -3a + b = 5-4x

The x coefficients must match up, and the constants must match up as well, so 

2ax = -4x

a = -2

We can then plug it into 2ax - 3a + b

-4x +6 + b = 5-4x

6 + b = 5

b = -1

so g(x) = -2x-1

x=4

g(x)= -2(4) - 1 = -8 - 1 = -9

How long will the annuity last for?

What is the question?

For

1) the reason is given, as shown above

2) the reason is the additive property of equality. You are adding 11 to both equations

3) the reason is the distributive property. You are expanding the parentheses and multiplying both values by 5

4) the reason is the subtraction property of equality. Similar to the additive property, but instead of adding, you are subtracting by 15

5) the reason is the additive property of equality, you are adding both sides of the equation by y

6) and the final reason is the division property of equality, as shown above

it would really help people understand your equation if you look at the Sticky Topics section, and click on the How to display latex properly

So using what you said in the problem, d = rt ( distance = rate x time), we can apply things from the problem into it. The distance is 32.12m and the rate is 8.8m/min.

So d = 32.12 and r = 8.8

32.12 = 8.8t

Then you can divide both sides by 8.8 to get \(t = 3.65\) \(minutes\)

Okay.

For number 1, you aren't modifying the shape at all, and only shifting it to the left, so the area is still \(10\)

For number 2, you are enlarging the shape by 6 times, so the area is 6 x 10 = \(60\). You don't need to worry about the x-6 because that is only shifting the shape to the right by 6 units, and not modifying the shape itself

For number 3, you are decreasing the shape 2 times, so the area is 10 / 2 = \(5\). Just like the question before, you don't need to worry about the -x because it is simply creating the reflection of the shape, preserving the area of the shape itself.

never mind, i found out how ridiculously easy this was. Sorry