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Novosadov [1.4K]
3 years ago
10

Really need help on this asap!!!!!

Mathematics
1 answer:
marusya05 [52]3 years ago
6 0

Answer:

srry

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
It costs $109 per night to rent a motel room in Georgia. There is a one-time $30 non-refundable deposit required. How much will
Ne4ueva [31]

Answer:

$793.00

Step-by-step explanation:

109x7=763

763+30=793

8 0
3 years ago
Read 2 more answers
So this should be one of the last few ones
sergeinik [125]

Answer:

A

Step-by-step explanation:

Because you have to use the Pythagorean theorem to solve for this.

8 0
3 years ago
Find the measure of the indicated angle to the nearest degree.
Yuliya22 [10]

Answer:

37

Step-by-step explanation:

tan(theta)=perpendicular/base

tan(theta)=3/4

theta=arctan(3/4)=37

8 0
3 years ago
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In basketball, Katrina makes 6 out of every 9 free throws. Her coach claims that if she tries 15 free throws she should make 10
zloy xaker [14]
Yes, Thats 2/3 rds of the equation
5 0
3 years ago
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