The original can be rewritten as

. Because i^2 is equal to -1, we can replace the -1 in each radicand with i^2, like this:

. Now, i-squared is a perfect square that can be pulled out of each radicand as a single i.

. 24 has a perfect square hidden in it. 4 * 6 = 24 and 4 is a perfect square. So let's break this up, step by step.

and then

. We will now multiply the i and the 2i, and multiply the square root of 6 times the square root of 6:

. 36 itself is a perfect square because 6 * 6 = 36. So we will do that simplification now.

. Multiplying the 2 and the 6 gives us

. But here we are back to the fact that i-squared is equal to -1, so 2(-1)(6) = -12. See how that works?
When the dilation is around the origin, we just have to multiply each coordinate by the scale factor.
We're starting from A(2,2), B(2,5), C(6,5) and D(6,2) and scaling by 3 so the image A'B'C'D' is
Answer: A'(6,6), B'(6,15), C'(18,15), D'(18,6)
The answer is B because when yku combine like terms (x) 2/5 + 1/5 you get 3/6. Then when you simplify the equations, you turn -1/4 into -2/8 to match the 5/8. From there you just subtract 2/8 from 5/8 getting 3/8.
Answer:
Option b. 
Step-by-step explanation:
step 1
In the right triangle ABC
<em>Find the sine of angle CAB</em>
---> the sine of angle CAB is equal to divide the opposite side angle CAB (BC) by the hypotenuse (AC)
substitute
simplify
---->equation A
step 2
In the right triangle BDC
<em>Find the sine of angle CBD</em>
---> the sine of angle CBD is equal to divide the opposite side angle CBD (DC) by the hypotenuse (BC)
substitute
----> equation B
step 3
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and BDC are similar by AA Similarity Theorem
therefore
m∠CBD≅m∠CAB
equate equation A and equation B
solve for DC
step 4
Find the value of AD

substitute the values
