Answer:
All of them are correct except for number 15
Step-by-step explanation:
Number 15 is D.
Answer:
Option A.) 43°
Step-by-step explanation:
Part 10)
step 1
Find the length of side EG
see the attached figure to better understand the problem
we know that
In the right triangle EGF
----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
![cos(65^o)=\frac{EG}{11}](https://tex.z-dn.net/?f=cos%2865%5Eo%29%3D%5Cfrac%7BEG%7D%7B11%7D)
solve for EG
![EG=(11)cos(65^o)\\EG=4.65\ cm](https://tex.z-dn.net/?f=EG%3D%2811%29cos%2865%5Eo%29%5C%5CEG%3D4.65%5C%20cm)
step 2
Find the measure of angle D
In the right triangle DEG
----> by TOA (opposite side divided by adjacent side)
substitute the given values
![tan(D)=\frac{4.65}{5}\\\\D=tan^{-1}(\frac{4.65}{5})=43^o](https://tex.z-dn.net/?f=tan%28D%29%3D%5Cfrac%7B4.65%7D%7B5%7D%5C%5C%5C%5CD%3Dtan%5E%7B-1%7D%28%5Cfrac%7B4.65%7D%7B5%7D%29%3D43%5Eo)
Answer:
- D = -87
- Dx = 174
- Dy = -435
- Dz = 0
- (x, y, z) = (-2, 5, 0)
Step-by-step explanation:
The determinant of the coefficient matrix is ...
![D=\left|\begin{array}{ccc}2&5&3\\4&-1&-4\\-5&-2&6\end{array}\right|\\\\=2(-1)(6)+5(-4)(-5)+3(4)(-2)-2(-4)(-2)-5(4)(6)-3(-1)(-5)\\\\=-12+100-24-16-120-15=\boxed{-87}](https://tex.z-dn.net/?f=D%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%265%263%5C%5C4%26-1%26-4%5C%5C-5%26-2%266%5Cend%7Barray%7D%5Cright%7C%5C%5C%5C%5C%3D2%28-1%29%286%29%2B5%28-4%29%28-5%29%2B3%284%29%28-2%29-2%28-4%29%28-2%29-5%284%29%286%29-3%28-1%29%28-5%29%5C%5C%5C%5C%3D-12%2B100-24-16-120-15%3D%5Cboxed%7B-87%7D)
The other determinants are found in similar fashion after substituting the constants on the right for each of the above matrix columns, in turn.
Those determinants are ...
![D_x=\left|\begin{array}{ccc}21&5&3\\-13&-1&-4\\0&-2&6\end{array}\right|=174](https://tex.z-dn.net/?f=D_x%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D21%265%263%5C%5C-13%26-1%26-4%5C%5C0%26-2%266%5Cend%7Barray%7D%5Cright%7C%3D174)
![D_y=\left|\begin{array}{ccc}2&21&3\\4&-13&-4\\-5&0&6\end{array}\right|=-435](https://tex.z-dn.net/?f=D_y%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%2621%263%5C%5C4%26-13%26-4%5C%5C-5%260%266%5Cend%7Barray%7D%5Cright%7C%3D-435)
![D_z=\left|\begin{array}{ccc}2&5&21\\4&-1&-13\\-5&-2&0\end{array}\right|=0](https://tex.z-dn.net/?f=D_z%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%265%2621%5C%5C4%26-1%26-13%5C%5C-5%26-2%260%5Cend%7Barray%7D%5Cright%7C%3D0)
The solutions are ...
x = 174/-87 = -2
y = -435/-87 = 5
z = 0
That is, (x, y, z) = (-2, 5, 0).
Any ratio simply takes the form (A/B)
Let throws = T , games = G
T = 36
G = 16
ratio of free throw to game = T/G
T/G = 36/16 = 9/4