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jolli1 [7]
3 years ago
6

I don't understand can someone help

Mathematics
1 answer:
Aliun [14]3 years ago
6 0

Answer:

C

Step-by-step explanation:

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In Exercises 40-43, for what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infini
svet-max [94.6K]

Answer:

If k = −1 then the system has no solutions.

If k = 2 then the system has infinitely many solutions.

The system cannot have unique solution.

Step-by-step explanation:

We have the following system of equations

x - 2y +3z = 2\\x + y + z = k\\2x - y + 4z = k^2

The augmented matrix is

\left[\begin{array}{cccc}1&-2&3&2\\1&1&1&k\\2&-1&4&k^2\end{array}\right]

The reduction of this matrix to row-echelon form is outlined below.

R_2\rightarrow R_2-R_1

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\2&-1&4&k^2\end{array}\right]

R_3\rightarrow R_3-2R_1

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&3&-2&k^2-4\end{array}\right]

R_3\rightarrow R_3-R_2

\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&0&0&k^2-k-2\end{array}\right]

The last row determines, if there are solutions or not. To be consistent, we must have k such that

k^2-k-2=0

\left(k+1\right)\left(k-2\right)=0\\k=-1,\:k=2

Case k = −1:

\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-1-2\\0&0&0&(-1)^2-(-1)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-3\\0&0&0&-2\end{array}\right]

If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.

Case k = 2:

\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&2-2\\0&0&0&(2)^2-(2)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&0\\0&0&0&0\end{array}\right]

This gives the infinite many solution.

5 0
3 years ago
14=3/8 find the quotient
ANTONII [103]

Answer:

The equation is always false

Step-by-step explanation:

5 0
3 years ago
Which of the following graphs represents a function?
kirza4 [7]

The third graph represents a function.

In a function, every input (x value) has <em>exactly</em> one output (y value). If even a single input has zero or two outputs, the graph does not represent a function.

A good way of testing this is using a vertical line. As you move a vertical line from left to right across a graph, it should always be touching exactly one point on the graphed line.

In this case, every graph fails this vertical line test except for the third graph, so the third graph represents a function.

8 0
2 years ago
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There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun
Brrunno [24]

Answer:

1/3 and 1.5

Step-by-step explanation:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

There are 5 Multiples of 3 on the Spinner and 3 multiples of four.

5/15 is the probability for a multiple of 3 which can be simplified to 1/3

3/15 is the probability for a multiple of 4 which can be simplified to 1/5

Hope this Helps!

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3 years ago
THIS IS DUE IN 5 MINUTES
PilotLPTM [1.2K]

Answer:

The answer is 6!!!

Step-by-step explanation:

7 0
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