The vertex point would be (1,3)
explanation:
-b/2a:
-(-2)/2(1)
2/2=1
Plug 1 in for all the X’s
y=1^2-2(1)+4
y=3
Answer:
Step-by-step explanation:
To find x₁ and x₂ :
![\left[\begin{array}{ccc}-4&1\\5&4\\\end{array}\right] \times \left[\begin{array}{ccc}x_1\\x_2\\\end{array}\right] + \left[\begin{array}{ccc}11\\-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%261%5C%5C5%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_1%5C%5Cx_2%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11%5C%5C-19%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-11%5C%5C40%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step 1
Multiply first 2 x 2 matrix with 2 x 1 vector, we get
![\left[\begin{array}{ccc}-4x_1&+ x_2\\5x_1&+ 4x_2\\\end{array}\right] + \left[\begin{array}{ccc}11\\-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4x_1%26%2B%20%20x_2%5C%5C5x_1%26%2B%20%204x_2%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11%5C%5C-19%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-11%5C%5C40%5Cend%7Barray%7D%5Cright%5D)
Step 2
Add the 2 x 1 matrices on LHS, we get
![\left[\begin{array}{ccc}-4x_1&+x_2&+11\\5x_1&+4x_2&-19\\\end{array}\right] = \left[\begin{array}{ccc}-11\\40\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4x_1%26%2Bx_2%26%2B11%5C%5C5x_1%26%2B4x_2%26-19%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-11%5C%5C40%5Cend%7Barray%7D%5Cright%5D)
Step 3,
we get
and
Step 4,
Simplify, we get
Step 5,
multiply eqn(1) by 4
we get
Step 6,
eqn (2) - eqn(3)
we get
substituting in eqn (1), we get
so, we get
Therefore
Answer:
X could be 50 and Y could be 2 or vice versa. X and Y can also be 10.
Step-by-step explanation:
Given that Circle O is centered at (3,-2) and the circle passesthroughR(7,1),Thedistance between O and R is the radius (r).r=√(7−3)2(1−(−2))2=√25=5diameter =2⋅r=2⋅5=10.
Answer:
1/12
Step-by-step explanation:
The whole circumference (i.e complete circle) is an arc which measures 360°
in our case, it is given that our arc measures only 30°
the fraction of our arc of 30° to the complete circle of 360° is
30/360
= 3/36
= 1/12
