Help! I'm a little stumped when it comes to variables in matrices. An explanation would be super rad! What is the determinant of A = [ -2 2 b 0 3 a 0 0 -5 ]

30

Step-by-step explanation:

To find the determinant of a 3x3 matrix, you can use this method. (See picture.)

Start with the first number in the top row, and block off the row and column.  A 2x2 matrix will be left.  Find the determinant of this 2x2 matrix, and multiply it by the number in the top row.

Repeat for the other two numbers in the top row.  Add the first result, subtract the second, and add the third.

det A = -2 [(3)(-5) − (a)(0)] − 2 [(0)(-5) − (a)(0)] + b [(0)(0) − (3)(0)]

det A = -2 (3)(-5) − 0 + 0

det A = 30

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.