Answer:
![y = 9.1](https://tex.z-dn.net/?f=%20y%20%3D%209.1%20)
Step-by-step explanation:
y can be found using the Law of sines as explained below:
m < Y = 106°
m < X = 58°
WY = x = 8
WX = y = ?
Thus,
![\frac{x}{sin(X)} = \frac{y}{sin(Y)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7Bsin%28X%29%7D%20%3D%20%5Cfrac%7By%7D%7Bsin%28Y%29%7D%20)
![\frac{8}{sin(58)} = \frac{y}{sin(106)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7Bsin%2858%29%7D%20%3D%20%5Cfrac%7By%7D%7Bsin%28106%29%7D%20)
![\frac{8}{0.848} = \frac{y}{0.961}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B0.848%7D%20%3D%20%5Cfrac%7By%7D%7B0.961%7D%20)
Multiply both sides by 0.961 to solve for y
![\frac{8}{0.848}*0.961 = \frac{y}{0.961}*0.961](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B0.848%7D%2A0.961%20%3D%20%5Cfrac%7By%7D%7B0.961%7D%2A0.961%20)
![\frac{8*0.961}{0.848} = y](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%2A0.961%7D%7B0.848%7D%20%3D%20y%20)
![\frac{8*0.961}{0.848}*0.961 = y](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%2A0.961%7D%7B0.848%7D%2A0.961%20%3D%20y%20)
![9.07 = y](https://tex.z-dn.net/?f=%209.07%20%3D%20y%20)
(to the nearest tenth)
<h2><u>Answer :</u></h2>
ㅤㅤㅤㅤㅤ![\bigstar\boxed{\large\bf{\leadsto -\dfrac{28}{9}}}](https://tex.z-dn.net/?f=%5Cbigstar%5Cboxed%7B%5Clarge%5Cbf%7B%5Cleadsto%20-%5Cdfrac%7B28%7D%7B9%7D%7D%7D)
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
<h2><u>Calculation</u><u> </u><u>:</u></h2>
![\bf{⟼ \dfrac{\dfrac{14}{9}}{\dfrac{-1}{3}-\dfrac{1}{6}}}](https://tex.z-dn.net/?f=%5Cbf%7B%E2%9F%BC%20%5Cdfrac%7B%5Cdfrac%7B14%7D%7B9%7D%7D%7B%5Cdfrac%7B-1%7D%7B3%7D-%5Cdfrac%7B1%7D%7B6%7D%7D%7D)
![\bf{⟼ \dfrac{\dfrac{14}{9}}{\dfrac{-2-1}{6}}}](https://tex.z-dn.net/?f=%5Cbf%7B%E2%9F%BC%20%5Cdfrac%7B%5Cdfrac%7B14%7D%7B9%7D%7D%7B%5Cdfrac%7B-2-1%7D%7B6%7D%7D%7D)
![\bf{⟼ \dfrac{\dfrac{14}{9}}{\dfrac{-3}{6}}}](https://tex.z-dn.net/?f=%5Cbf%7B%E2%9F%BC%20%5Cdfrac%7B%5Cdfrac%7B14%7D%7B9%7D%7D%7B%5Cdfrac%7B-3%7D%7B6%7D%7D%7D)
![\bf{⟼\dfrac{14}{9}\times -2}](https://tex.z-dn.net/?f=%5Cbf%7B%E2%9F%BC%5Cdfrac%7B14%7D%7B9%7D%5Ctimes%20-2%7D)
![\bf{⟼\dfrac{-28}{9}}](https://tex.z-dn.net/?f=%5Cbf%7B%E2%9F%BC%5Cdfrac%7B-28%7D%7B9%7D%7D)
⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀
Answer: Three dimensional
Step-by-step explanation:
A rectangular prism is a three-dimensional shape.
[] A one-dimensional shape is a line
[] A two-dimensional shape is a rectangle, circle, etc
[] This means that a rectangular prism is a three-dimensional shape
Answer:
you have a fixed rate of $25, meaning you get a haircut, it's $25
ANY other service is an extra $15
So, let's make the equation...
y=15x+25
Now, to just get a haircut it's $25.
But, let's say you get a haircut+shampoo
It'd be..
y=15(1)+25
y=$40
Another one..
You get a haircut+shampoo+highlight
y=15(3)+25
y=$70
<h2>
Answer:</h2>
The values of x for which the given vectors are basis for R³ is:
![x\neq 1](https://tex.z-dn.net/?f=x%5Cneq%201)
<h2>
Step-by-step explanation:</h2>
We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.
We are given three vectors as:
(-1,0,-1), (2,1,2), (1,1, x)
The matrix formed by these vectors is:
![\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%261%5C%5C0%261%261%5C%5C-1%262%26x%5Cend%7Barray%7D%5Cright%5D)
Now, the determinant of this matrix is:
![\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1](https://tex.z-dn.net/?f=%5Cbegin%7Bvmatrix%7D-1%20%262%20%26%201%5C%5C%200%26%201%20%26%201%5C%5C%20-1%20%26%202%20%26%20x%5Cend%7Bvmatrix%7D%3D-1%28x-2%29-2%281%29%2B1%5C%5C%5C%5C%5C%5C%5Cbegin%7Bvmatrix%7D-1%20%262%20%26%201%5C%5C%200%26%201%20%26%201%5C%5C%20-1%20%26%202%20%26%20x%5Cend%7Bvmatrix%7D%3D-x%2B2-2%2B1%5C%5C%5C%5C%5C%5C%5Cbegin%7Bvmatrix%7D-1%20%262%20%26%201%5C%5C%200%26%201%20%26%201%5C%5C%20-1%20%26%202%20%26%20x%5Cend%7Bvmatrix%7D%3D-x%2B1)
Hence,
![-x+1\neq 0\\\\\\i.e.\\\\\\x\neq 1](https://tex.z-dn.net/?f=-x%2B1%5Cneq%200%5C%5C%5C%5C%5C%5Ci.e.%5C%5C%5C%5C%5C%5Cx%5Cneq%201)