There are 85 seats in each section. 2125 divided by 25 is 85.
Answer:
19
Step-by-step explanation:
5 people in total, divide equally from 95
Answer:
y = -
x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 2) ← 2 points on the line
m =
=
= - 
The line crosses the y- axis at (0, 6) ⇒ c = 6
y = -
x + 6 ← equation of line
The diagonals of a rectangle are congruent
meaning AC and BD are congruent
c/3 = 4-c
multiply both sides by 3
c = 12 -3c
add 3c to both sides
4c = 12
divide both sides by 4
c = 3
So the diagonals are
AB = c/3 = (3)/3 = 1
BD = 4-c = 4- (3) = 1
Hope this helps
Answer:
For h= 25, b in the plane spanned by a1 and a2
Step-by-step explanation:
![a1= \left[\begin{array}{c}1\\2\\-1\end{array}\right] \\a2 = \left[\begin{array}{c}-7\\-7\\2\end{array}\right] \\\\b = \left[\begin{array}{c}3\\-22\\h\end{array}\right]](https://tex.z-dn.net/?f=a1%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5C%5C-1%5Cend%7Barray%7D%5Cright%5D%20%5C%5Ca2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-7%5C%5C-7%5C%5C2%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5Cb%20%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C-22%5C%5Ch%5Cend%7Barray%7D%5Cright%5D)
we have to find value of h for which b in the plane spanned by a1 and a2.
For this the linear systems given by the following augmented matrix must be consistent.
![\left[\begin{array}{cc|c}1&-7&3\\2&-7&-22\\-1&2&h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C2%26-7%26-22%5C%5C-1%262%26h%5Cend%7Barray%7D%5Cright%5D)
Reduce the augmented matrix into row echelon form:
![R_{2} - 2R_{1} , R_{3} + R_{1}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&-5&h+3\end{array}\right]\\\\7R_{3}+5R_{2}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&0&7h-175\end{array}\right]](https://tex.z-dn.net/?f=R_%7B2%7D%20-%202R_%7B1%7D%20%2C%20R_%7B3%7D%20%2B%20R_%7B1%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C0%267%26-28%5C%5C-0%26-5%26h%2B3%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C7R_%7B3%7D%2B5R_%7B2%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C0%267%26-28%5C%5C-0%260%267h-175%5Cend%7Barray%7D%5Cright%5D)
For system to be consistent:
