Answer:
angle m1 = 14 degrees
Step-by-step explanation:
angle ABD = 70 deg
angle m1 + angle m2 = 70 deg
angle m2 = 4 * angle m1
angle m1 + (4 * angle m1) = 70 deg
5 * angle m1 = 70 deg
angle m1 = 14 deg
Answer:
B:
Step-by-step explanation:
brainliest pls
Here’s one way: 128 / 7 = 18.28 weeks || 7 x 18 = 126 || 128 - 126 = 2 (remainder).
Answer: About 18 weeks and 2 days.
Hope this helps!
Answer:
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Solution of the given system of equations
x = 3 and y= 2
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given system of equations are
4x - y = 10 ...(i)
8x +5y = 34...(ii)
The matrix form
A X = B
![\left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}10\\34\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-1%5C%5C8%265%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%5C%5C34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Step(ii):-</em></u>
<u><em>By using matrix inversion method</em></u>
<u><em></em></u>
<u><em></em></u>
<u><em></em></u>
|A| = ad-b c = 4(5) - 8(-1) = 20+8 = 28
Given matrix
![A = \left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-1%5C%5C8%265%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![AdjA = \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=AdjA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![A djA = \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]](https://tex.z-dn.net/?f=A%20djA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Inverse of the matrix
<u><em></em></u>
![A^{-1} = \frac{1}{|A|} A djA =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B%7CA%7C%7D%20A%20djA%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Step(iii)</em></u>:-
The solution of the given system of equations by using matrix inversion method
X = A⁻¹ B
![X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]\left[\begin{array}{ccc}10\\34\\\end{array}\right]](https://tex.z-dn.net/?f=X%20%3D%20A%5E%7B-1%7DB%20%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%5C%5C34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5X10+1X34\\-8X10+4X34\\\end{array}\right]](https://tex.z-dn.net/?f=X%20%3D%20A%5E%7B-1%7DB%20%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5X10%2B1X34%5C%5C-8X10%2B4X34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\frac{1}{28} \left[\begin{array}{ccc}84\\56\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D84%5C%5C56%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Final answer</em></u>:-
Solution of the given system x = 3 and y= 2
Answer:
![Hypotenuse=10](https://tex.z-dn.net/?f=Hypotenuse%3D10)
Step-by-step explanation:
<h3>
The missing figure is attached.</h3>
For this exercise you can use the following Trigonometric Identity:
![sin\alpha=\frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=sin%5Calpha%3D%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
Let be "x" the hypotenuse of this right triangle.
You can identify from the figure that, in this case:
![\alpha=60\°\\\\opposite=5\sqrt{3}](https://tex.z-dn.net/?f=%5Calpha%3D60%5C%C2%B0%5C%5C%5C%5Copposite%3D5%5Csqrt%7B3%7D)
Then, knowing these values you can substitute them into
:
![sin(60\°)=\frac{5\sqrt{3}}{x}](https://tex.z-dn.net/?f=sin%2860%5C%C2%B0%29%3D%5Cfrac%7B5%5Csqrt%7B3%7D%7D%7Bx%7D)
Finally, you need to solve for "x" in order to find the lenght of the hypotenuse.
This is:
![x*sin(60\°)=5\sqrt{3}\\\\x=\frac{5\sqrt{3}}{sin(60\°)}\\\\x=10](https://tex.z-dn.net/?f=x%2Asin%2860%5C%C2%B0%29%3D5%5Csqrt%7B3%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B5%5Csqrt%7B3%7D%7D%7Bsin%2860%5C%C2%B0%29%7D%5C%5C%5C%5Cx%3D10)