Answer:
Step-by-step explanation:
given is a system of linear equations in 3 variables as
This can be represented in matrix form as
AX=B Or
![\left[\begin{array}{ccc}-1&-4&2\\1&2&-1\\1&1&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-10\\11\\14\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-4%262%5C%5C1%262%26-1%5C%5C1%261%26-1%5Cend%7Barray%7D%5Cright%5D%20%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-10%5C%5C11%5C%5C14%5Cend%7Barray%7D%5Cright%5D)
So solution set
X would be 
|A|=-1(-1)+4(0)+2(-1)=--1
Cofactors of A are
-1 0 -1
-2 -1 -3
0 1 2
So inverse of A is
1 2 0
0 1 -1
1 3 -2
Solution set would be
x=12
y=-3
z=-5
Because the vertex of the parabola is at (16,0), its equation is of the formy = a(x-10)² + 15
The graph goes through (0,0), thereforea(0 - 10)² + 15 = 0100a = -15a = -0.15
The equation is y = f(x) = -0.15(x - 10)² + 15
The graph is shown below.
Part A
Note that y = f(x).
The x-intercepts identify values where the function or y=0. The x-intercepts occur at x=0 and x=20, or at (0,0) and (20,0).
The maximum value of y occurs at the vertex (10, 15) because the curve is down due to the negative leading coefficient of -0.15.
The curve increases in the interval x = (-∞, 10) and it decreases in the interval x = (10, ∞).
Part B
When x=12, y = -0.15(12 - 10)² + 15 = 14.4When x=15, y = -0.15(15 - 10)² + 15 = 11.25
The average rate of change between x =12 to x = 15 is(11.25 - 14.4)/(15 - 12) = -1.05
This rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases in the interval x =[12, 15].
Answer:
Measure of central tendency is a value that represents a typical, or central, entry of a data set. The most common measures of central tendency are: • Mean (Average): The sum of all the data entries divided by the number of entries. ... The standard deviation measure variability and consistency of the sample or population.
Step-by-step explanation:
The volume formula is V= l x L x H, l=width, L=Length, H= Depth, so
2x3 _ 9x2 + 7x + 6 = l x L x (2x + 1), because H=(2x + 1), so
l x L= (2x3 _ 9x2 + 7x + 6 )/ (2x + 1) = (2x3 _ 9x2 + 7x + 6 ) X [1/(2x + 1)]
case1: l= (2x3 _ 9x2 + 7x + 6 ) or L= 1/(2x + 1), case2: L= (2x3 _ 9x2 + 7x + 6 ) or l= 1/(2x + 1)
the why question:
perhaps there is similarity of value between volume and l, or volume and L
That would be :
4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substitute for y)
PROOF: y + 5x = x²<span> + 10
</span> (4x - 10) + 5x = x² + 10
4x - 10 = x² -5x + 10
<span>
</span>0 = x2 – 9x + 20<span> (liked terms are grouped and simplified)
PROOF: </span> 4x - 10 = x² -5x + 10
4x = x² -5x + 10 + 10
0 = x² -5x -4x + 20
0 = x² - 9x + 20
Solving:
x² - 9x + 20 = 0
x² - 5x - 4x + 20 = 0
(x - 5) (x - 4) = 0
⇒ x = 4 (as question says) OR x = 5
