Answer:
d) 

Step-by-step explanation:
i¹= i
i²= -1
i³= -i
i⁴= 1
i¹²⁴= i^(124 +0)
i^124 . i^0
i^(4×31) . i^0 = 1³¹. i^0
1.i^0= i^0
= 1
a) i^179= i^(176+3)
i^176 . i³ = i^(4×44) . i³
1⁴⁴. i³ = 1. i³
= -i
b) i^582 = i^(580 + 2)
i^580 . i²= i^(4×145) . i²
1^145 . i²= 1.i²
= -1
c) i^165= i^(164+1)
i^164 . i¹ = i^(4×41) . i¹
1⁴¹ . i¹ = 1.i
= i
d) i^740= i^(740+0)
i^740 . i^0 = i^(4×185) . i^0
1^185 . i^0 = 1. i^0
= 1
i¹²⁴= i^740 = 1
 
        
             
        
        
        
All these equations are in the form of ax^2 + bx + c = 0, where a, b, and c are some numbers. the discriminants of equations like this are equal to b^2 - 4ac. if the discriminant is negative, there are two imaginary solutions. if the discriminant is positive, there are two real solutions. if the discriminant is 0, there is one real solution.
<span>x^2 + 4x + 5 = 0
</span>b^2 - 4ac
4^2 - 4(1)(5)
16-20
-4, two imaginary solutions.
<span>x^2 - 4x - 5 = 0
</span>b^2 - 4ac
(-4)^2 - 4(1)(-5)
16 + 20
36, two real solutions.
<span>4x^2 + 20x + 25 = 0
</span>b^2 - 4ac
20^2 - 4(4)(25)
400 - 400
0, one real solution.
        
             
        
        
        
Answer:

Step-by-step explanation:
<u>Right Triangles
</u>
They have a right angle (90°) and a longer side called the hypotenuse opposite to the right angle. The legs and the hyponetuse form two angles that must sum 90°, and they comply:

Where opp-leg is the opposite leg to  
The rope from the top of a tree house is 85-foot long. It's the hypotenuse (L) of the triangle it forms with the ground and the tree. The angle of 45° is opposite to the height of the tree (h).

We can solve for h


 
        
             
        
        
        
The answer is h= 2.9
steps:
-1.8 = h-4.7
+4.7 +4.7
2.9 = h
        
                    
             
        
        
        
The pints of ice cream for the students is an illustration of metric units
Nadia needs 12 pints of ice cream for the 24 students
<h3>How to determine the pints of ice cream?</h3>
The given parameter is:
Students = 24
She needs one cup for each student in the class.
So, the number of cups needed is:
Cups = 24
1 cup makes 1/2 pint.
So, we have:
Pint = 1/2 * 24
Pint = 12
Hence, Nadia needs 12 pints of ice cream for the 24 students
Read more about metric units at:
brainly.com/question/2004114