Answer: 3 + 7i
Step-by-step explanation:
Equation expanded: 12 + 5i - 9 + 2i // now simplfy
12 - 9 = 3
5i + 2i = 7i
// together, we get
3 + 7i
The diagrams showing pairs of adjacent angles and the given description is shown in the attachments below.
<h3>What are Adjacent Angles?</h3>
Adjacent angles are angle that share the same vertex and also has a side in common.
a. An obtuse angle is greater than 90°.
Figure 1 shows a pair of adjacent angles that are obtuse which are ∠ABD and ∠CBD
b. Figure 2 shows two adjacent angles, ∠ABD and ∠CBD whose sum equals 180 degrees.
c. Figure 3 shows two adjacent angles, ∠ABD and ∠CBD whose sum equals 60 degrees.
Learn more about adjacent angles on:
brainly.com/question/25713164
Answer:
d = 13.8 feet
Step-by-step explanation:
Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder. That formula is

We will use 3.141592654 for pi; if the tank HALF filled with water is at 20 feet, then the height of the tank is 40 feet, so h = 40; and the volume it can hold in total is 6000 cubic feet. Filling in then gives us:

Simplify on the right to get

Divide both sides by 125.6637061 to get that

Taking the square root of both sides gives you
r = 6.90988299
But the diameter is twice the radius, so multiply that r value by 2 to get that the diameter to the nearest tenth of a foot is 13.8
₇P₅ is a permutation. you can find this setting in the statistics menu of your scientific calculator (i think).
If you don't have a scientific calculator, you can use the following formula:
nPr = 
₇P₅ = 
= 
= 
= 7 * 6 * 5 * 4 * 3
= 2520
Answer: C
Answer:
x = 6
y = 4
Step-by-step explanation:
Apply the angle bisector theorem to solve for x and y respectively.
✔️4/(9 - x) = 8/x
Cross multiply
4*x = 8(9 - x)
4x = 72 - 8x
Add 8x to both sides
4x + 8x = 72
12x = 72
12x/12 = 72/12
x = 6
✔️y/2 = 6/3
Cross multiply
3*y = 6*2
3y = 12
3y/3 = 12/3
y = 4