Convert the quadratic function from vertex form to standard form: g(x)= 1/2 (x+2)^2-8

Use matrices to solve the system of equations if possible. Use Gaussian elimination with back substitution or gauss Jordan elimi

CaHeK987 [17]

In matrix form, the system is given by

$\begin{bmatrix} -1 & 1 & -1 \\ 2 & -1 & 1 \\ 3 & 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -20 \\ 29 \\ 29 \end{bmatrix}$

I'll use G-J elimination. Consider the augmented matrix

$\left[ \begin{array}{ccc|c} -1 & 1 & -1 & -20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right]$

• Multiply through row 1 by -1.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right]$

• Eliminate the entries in the first column of the second and third rows. Combine -2 (row 1) with row 2, and -3 (row 1) with row 3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 5 & -2 & -31 \end{array} \right]$

• Eliminate the entry in the second column of the third row. Combine -5 (row 2) with row 3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 3 & 24 \end{array} \right]$

• Multiply row 3 by 1/3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right]$

• Eliminate the entry in the third column of the second row. Combine row 2 with row 3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right]$

• Eliminate the entries in the second and third columns of the first row. Combine row 1 with row 2 and -1 (row 3).

$\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 9 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right]$

Then the solution to the system is

$\boxed{x=9, y=-3, z=8}$

If you want to use G elimination and substitution, you'd stop at the step with the augmented matrix

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right]$

The third row tells us that $z=8$ . Then in the second row,

$y-z = -11 \implies y=-11 + 8 = -3$

and in the first row,

$x-y+z=20 \implies x=20 + (-3) - 8 = 9$

5 0

2 years ago

What is thei value of their given digits the 4 in 440

Sedaia [141]

The first 4 on the left has a value of 400. The next 4 has a value of 40. The first 4 is in the hundreds place and the second 4 is in the 10's place.

4 0

3 years ago

The area of a circle is 80.86cm2. Find the length of the radius rounded to 2 DP.

weeeeeb [17]

Answer:

Solution given:

The area of a circle =80.86cm²

we have:

The area of a circle =πr²

substituting value of area of circle we get

80.86cm=3.14*r²

dividing both side by 3.14

80.86/3.14=3.14*r²/3.14

25.75=r²

doing square root on both side

$\sqrt{25.75}=\sqrt{r²}$

r=5.07cm

The length of radius is 5.07cm

5 0

3 years ago

WILL MARK BRAINLIEST!! PLEASE ANSWER AS FAST AS POSSIBLE !!! ANSWER QUESTIONS 1-5! THANKS!!!

Shalnov [3]

Answer: 1. A Please give me a thanks and a brainly

Step-by-step explanation:

7 0

3 years ago

2/3n + 5 greater than 12

Tanzania [10]

2/3n + 5 > 12
2/3n > 12 - 5
2/3n > 7
n > 7 * 3/2
n > 21/2 or 10 1/2

6 0

3 years ago

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