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o-na [289]
3 years ago
13

2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

+ 6x4 +6x3 = 28 3x, + 7x2 + 4xz +10x4 +lxs = 41 4x, + 6x2 + 2x3 +7x4 + 4x3 = 29
Mathematics
1 answer:
ratelena [41]3 years ago
4 0

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29

The associated matrix to the system is

\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]

3.

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]

Using backward substitution we have that

0x_5=-140, then 0=-140 and this is absurd. Then The system is inconsistent.

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The volumes of two cubes are 32ft^3 and 1372ft^3
ser-zykov [4K]

Answer:

1) 8 : 343

2) 42.875 or 42 ⅞

3) 4 : 49

4) 16ft²

Step-by-step explanation:

Volume of cube: s³

Surface area of cube: 6s²

_____________________

32ft^3 and 1372ft^3 →

32 : 1372 = 8 : 343

343 / 8 = 42 ⅞ = 42.875

s³ → 6s²

s³ = 8, s = 2, s² = 4.

s³ = 343, s = 7, s² = 49.

These are proportional so it is already in the simplest ratio so it is not necessary to multiply by 6.

s³ → 8 : 343

6s² → 4 : 49

(4 / 49) × 196ft² = 16ft²

4 0
3 years ago
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SOVA2 [1]

Answer:

8+2\sqrt{20\\}\\

Step-by-step explanation:

2+2+2+2+\sqrt{20\\}\\+\sqrt{20\\}\\=8+2\sqrt{20\\}\\

4^2+2^2=h^2

20=h^2

h=\sqrt{20\\}\\

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3 years ago
What is the length of side DG?<br><br><br> 12 in.<br><br> 32 in. <br><br> 36 in. <br><br> 30 in.
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Answer:

36 in

Step-by-step explanation:

The ratio of proportionality between the two similar triangles is 1:6, which you can find by dividing the corresponding side length measures from each triangle (3/18 = 4/24). Then you can set up a proportion:

1/6 = 6/x, which you can solve to get x = 36

8 0
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A book sold 31,700 copies in its first month of release. Suppose this represents 8.8% of the number of copies sold to date. How
elena-14-01-66 [18.8K]

For this case we propose a rule of three:

31700 ------------> 8.8%

x ----------------------> 100%

Where "x" represents the number of copies sold to date.

x = \frac {100 * 31700} {8.8}\\x = \frac {3170000} {8.8}\\x = 360,227.273

Thus, to date 360,227 copies of the book have been sold.

ANswer:

To date, 360,227 copies of the book have been sold.

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ArbitrLikvidat [17]
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