Factor
3x ^2 +20x+12

Answer:

Step-by-step explanation:

Left

When a square = a linear, always expand the squared expression.

x^2 - 2x + 1 = 3x - 5                Subtract 3x from both sides

x^2 - 2x - 3x + 1 = -5

x^2 - 5x +1 = - 5                      Add 5 to both sides

x^2 - 5x + 1 + 5 = -5 + 5

x^2 - 5x + 6 = 0

This factors

(x - 2)(x - 3)

So one solution is x = 2 and the other is x = 3

Second from the Left

i = sqrt(-1)

i^2 = - 1

i^4 = (i^2)(i^2)

i^4 = - 1 * -1

i^4 = 1

16(i^4) - 8(i^2) + 4

16(1) - 8(-1) + 4

16 + 8 + 4

28

Second from the Right

This one is rather long. I'll get you the equations, you can solve for a and b. Maybe not as long as I think.

12 = 8a + b

17 = 12a + b         Subtract

-5 = - 4a

a = - 5/-4 = 1.25

12 = 8*1.25 + b

12 = 10 + b

b = 12 - 10

b = 2

Now they want a + b

a + b = 1.25 + 2 = 3.25

Right

One of the ways to do this is to take out the common factor. You could also expand the square and remove the brackets of (2x - 2). Both will give you the same answer. I think expansion might be easier for you to understand, but the common factor method is shorter.

(2x - 2)^2 = 4x^2 - 8x + 4

4x^2 - 8x + 4 - 2x + 2

4x^2 - 10x + 6    The problem is factoring since neither of the first two equations work.

(2x - 2)(2x - 3)     This is correct.

So the answer is D

Answer:

Step-by-step explanation:

The question required a tree diagram (see attachment)

Required

Determine P(Red)

To do this, we simply each path that leads to red on the attached tree.

So, we have:

P(Red) is then calculated as:

Hence, the probability of selecting Red is 0.44

Answer:

Step-by-step explanation:

Using logarithmic rule:

Given the equation:

Taking log with base 5 both sides we have;

Apply the logarithmic rule:

or

Therefore, as a logarithmic equation is,