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Degger [83]
3 years ago
11

[10] In the following given system, determine a matrix A and vector b so that the system can be represented as a matrix equation

in the form AX = b. In the given linear system, solve for y without solving for X, Z and w by using Cramer's rule, x + y + 2 + 2w = 3. -7x – 3y + 5z - 8w = -3 4x + y + z + w = 6 3x + 7y - Z + w = 1
Mathematics
1 answer:
irina1246 [14]3 years ago
7 0

Answer:

y=-\frac{158}{579}

Step-by-step explanation:

To find the matrix A, took all the numeric coefficient of the variables, the first column is for x, the second column for y, the third column for z and the last column for w:

A=\left[\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right]

And the vector B is formed with the solution of each equation of the system:b=\left[\begin{array}{c}3\\-3\\6\\1\end{array}\right]

To apply the Cramer's rule, take the matrix A and replace the column assigned to the variable that you need to solve with the vector b, in this case, that would be the second column. This new matrix is going to be called A_{2}.

A_{2}=\left[\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right]

The value of y using Cramer's rule is:

y=\frac{det(A_{2}) }{det(A)}

Find the value of the determinant of each matrix, and divide:

y==\frac{\left|\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right|}{\left|\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right|} =\frac{158}{-579}

y=-\frac{158}{579}

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natta225 [31]
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so,
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So,
27 is <em>45%</em> of 60.
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3 years ago
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elixir [45]

Answer:

A

Step-by-step explanation:

so basically batting average is hits with no strikeouts or catches. add all the hits 50+10+5+11 which is 76. take 76/260 (76 hits out of 260 tries) to get .29

5 0
3 years ago
What 5 consecutive odd numbers equal 200
dimulka [17.4K]

Answer:

{36, 38, 40, 42, 44}

Step-by-step explanation:

You are implying that you are adding up 5 consecutive numbers, and should use the word "add" or the word "sum."

"The sum of 5 consecutive odd numbers is 200" leads to:

x + (x+2) + (x+4) + (x+6) + (x+8) = 200.  Note how each number is 2 more than the number preceding it.  In this way you can guarantee that all of the 5 numbers are odd.

Summing up, we get 5x + 20 = 200, or 5x = 180.

Dividing both sides by 5, we get x = 36.

Then the 5 consecutive integers are

{36, 38, 40, 42, 44}.  These add up to 200.

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Please ensure that you have copied down this problem correctly.

5 0
3 years ago
HELP 40 POINTS
Tom [10]
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0
3 years ago
1. if the bearing of p from y is 048° what is the bearing of y from p .
Helen [10]

Answer:

See below and image

Step-by-step explanation:

180 + 48 = 228

180 + 55 = 235

5 0
1 year ago
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