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2 years ago

What is (3²-2³)⁶⁶ total

Mathematics

1 answer:

horrorfan [7]2 years ago

6 0

Answer:

Step-by-step explanation:

(3²-2³)⁶⁶ = (9 - 8)⁶⁶ = (1)⁶⁶ = 1

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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

1 year ago

Hearts win. In a new card game, you start with a well-shuffled full deck and draw 3 cards without replacement. If you draw 3 hea

Afina-wow [57]

Answer: −1.409

Step-by-step explanation:

Probability of drawing 3 hearts: 13/52 * 12/51 * 11/50 = 0.013

Probability of drawing 3 black cards: 26/52 * 25/51 * 24/50 = 0.118

Probability of other draw: 1 - 0.013 - 0.118 = 0.869

0.013 * (50 - 5) = 0.585

0.118 * (25 - 5) = 2.353

0.869 * (0 - 5) = -4.347

Expected value: 0.585+ 2.353 - 4.347 = -1.409

7 0

3 years ago

What is four hundred eight thousand,seventeen in standard form and expanded form?

mestny [16]

408,017 is in standard form and
400,000+8,000+10+7=408,017 is expanded form
sixty five thousand and fifty eight is word form
60,000+5,000+50+8=65͵058 is expanded form

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3 years ago

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In 2012, the population of a City was 6.89 million. The exponential growth rate was 3.13% per year

MrRa [10]

Answer:

in 2018 it will be 8.09 million

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3 years ago

Quadrilateral WXYZ has the vertices W(-5, 2), X(-4, -2), Y(3, 1), and Z(2, -5). The quadrilateral is dilated by a scale factor o

vladimir2022 [97]

I’m not sure but is maybe c

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3 years ago

What is (3²-2³)⁶⁶ total​

What is (3²-2³)⁶⁶ total