Answer:

Step-by-step explanation:
Given
z = 1 + √3 i
Let 
Squaring both sides

Comparing real and imaginary part
Re(LHS)=Re(RHS)
...........................(1)
comparing Im(LHS)=Im(RHS)
√3=2pq

Substitute q in equation (1)


Let 



we take only Positive value because 
x=2.5

thus 

thus,

No, as if you reduce 4/16 it is 1/4, not 3/5, therefore they are not equivalent.
Answer:
$2500 at 8%.
$2900 st 5%.
Step-by-step explanation:
Let x be the amount invested at rate of 8% and y be the amount invested at the rate of 5%.
We have been given that Heather has divided $5400 between two investments. We can represent this information as:
The return on her investment is $345.
Earnings from the investment at 8% will be 8% of x.
Earnings from the investment at 5% will be 5% of y.


We will use substitution method to solve our system of equations. From equation (1) we will get,
Substituting this value in equation (2) we will get,




Therefore, Heather has invested an amount of $2900 at 5%.
Let us substitute y=2900 in equation (1) to solve for x.



Therefore, Heather has invested an amount of $2500 at 8%.
Answer:
Area of shaded region = 351.68 cm²
Step-by-step explanation:
Area of a circle = πr²
where r = radius = 3.14
Area of bigger circle = 3.14 × 11²
= 3.14 × 11 × 11
= 379.94cm²
Area of smaller circle = 3.14 * 3²
= 3.14 × 3 × 3
= 28.26cm²
Area of shaded region = Area of bigger circle - Area of smaller circle
= (379.94 - 28.26) cm²
= 351.68 cm²
Hi there !
The answer is B. angle 4.
An alternate interior angle is diagonally across one angle on the inside of the transversal. Opposite of 5 on the inside is angle 4.
Hope this helps !