Answer:
6
Step-by-step explanation:
since;
1/3 of 12 = 4
so,
(2/3) of x = 4
x=4(3/2)= 6
So focusing on x^4 + 5x^2 - 36, we will be completing the square. Firstly, what two terms have a product of -36x^4 and a sum of 5x^2? That would be 9x^2 and -4x^2. Replace 5x^2 with 9x^2 - 4x^2: 
Next, factor x^4 + 9x^2 and -4x^2 - 36 separately. Make sure that they have the same quantity inside of the parentheses: 
Now you can rewrite this as
, however this is not completely factored. With (x^2 - 4), we are using the difference of squares, which is
. Applying that here, we have
. x^4 + 5x^2 - 36 is completely factored.
Next, focusing now on 2x^2 + 9x - 5, we will also be completing the square. What two terms have a product of -10x^2 and a sum of 9x? That would be 10x and -x. Replace 9x with 10x - x: 
Next, factor 2x^2 + 10x and -x - 5 separately. Make sure that they have the same quantity on the inside: 
Now you can rewrite the equation as
. 2x^2 + 9x - 5 is completely factored.
<h3><u>Putting it all together, your factored expression is

</u></h3>
Answer: 6 cm
Step-by-step explanation:
6 cm is the radius because half the diameter is the radius
Answer:
10) - 45 degrees
12) 0 degrees
Step-by-step explanation:
10)
Find the x and y components that define the vector that joins C with D:
x-component: -4 - (-8) = - 4 + 8 = 4
y-component: 4 - 8 = -4
use the tangent function to find the angle
:

12)
Find the x and y components that define the vector that joins A with B:
x-component: 7 - 4 = 3
y-component: - 1 - (-1) = -1 + 1 = 0
use the tangent function to find the angle
:

Answer:
16 1/12
Step-by-step explanation:
The LCD of 6 1/3 + 5 1/2 + 4 1/4 is 12; 12 is evenly divisible by 3, 2 and 4.
We can rewrite this expression as:
6 + 5 + 4 + 1/3 + 1/2 + 1/4, or
15 +4/12 + 6/12 + 3/12, or
15 + 13/12, or
16 1/12