Answer:
C.
Step-by-step explanation:
The GCF of 28 and 12 is 4
Soo... Distribute it to find the factors. 28/4=7 and 12/4 is 3.
4(7+3)
![\bf \begin{array}{clclll} -6&+&6\sqrt{3}\ i\\ \uparrow &&\uparrow \\ a&&b \end{array}\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bclclll%7D%0A-6%26%2B%266%5Csqrt%7B3%7D%5C%20i%5C%5C%0A%5Cuparrow%20%26%26%5Cuparrow%20%5C%5C%0Aa%26%26b%0A%5Cend%7Barray%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ar%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%0A%5Ctheta%20%3Dtan%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7Bb%7D%7Ba%7D%20%5Cright%29%0A%5Cend%7Bcases%7D%5Cqquad%20r%5Bcos%28%5Ctheta%20%29%2Bi%5C%20sin%28%5Ctheta%20%29%5D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.
thus
Answer:
A.

B. Yes, Pablo can buy 2 pair of pants and 4 shirts.
Step-by-step explanation:
A. Let x be the number of pairs of pants and y be the number of shirts.
We have been given that Pablo wants to purchase 6 additional clothing pieces for his wardrobe. We can represent this information as:

We are also told that each pair of pants costs $20 and each shirt costs $15. So the cost of x pairs of pants will be 20x and cost of y shirts will be 15y.
As Pablo wants to spend $100 on clothing, so we can represent this information as:

Therefore, the system of equation representing the given situation will be:


B. To find if Pablo can buy 2 pair of pants and 4 shirts we will substitute x=2 and y=4 in our both equations.





We can see that x=2 and y=4 satisfies our both equation, therefore, Pablo can buy 2 pair of pants and 4 shirts.
Let's solve this problem step-by-step.
STEP-BY-STEP EXPLANATION:
First, we will establish that the shape of the window is a semi-circle. This means we must use the formula for the perimeter of a semi-circle to obtain the perimeter of the window.
The formula for the perimeter of a semi-circle is as follows:
Let perimeter of window or semi-circle = P
P = [ 2( Pi )r / 2 ] + 2r
Where r = radius of circle or semi-circle
From this, we will simply use the value of the radius given from the diagram in the problem and substitute it into the formula to obtain the perimeter of the window.
P = [ 2( Pi )r / 2 ] + 2r
r = 20
THEREFORE:
P = [ 2( Pi )( 20 ) / 2 ] + 2( 20 )
P = 20( Pi ) + 40
P = 102.83...cm^2
P = 102.8cm^2 ( to the nearest tenth )
FINAL ANSWER:
Therefore, the perimeter of the window is 102.8cm^2 ( to the nearest tenth ).
Hope this helps! :)
Have a lovely day! <3
We can use inverse sin to calculate the angle, and we get around 56 degrees (but for the answer I'll give the most accurate one). For cos we get around 55, and for tan we get .25.
I might have done tan wrong but I hope you get the point.