What is 339.12 rounded to the nearest tenth

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

find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through

Nat2105 [25]

Easy peasy
slope=(change in rise)/(change in run)
aka
slope between points (x1,y1) and (x2,y2) is
slope=(y2-y1)/(x2-x1) since y is rise/up and x is run/leftright

points

(-7,-9) and (-5,-8)
x1=-7
y1=-9
x2=-5
y2=-8
remember minusing a negative means addin a positive
slope=(-8-(-9))/(-5-(-7))=
(-8+9)/(-5+7)=1/2

slope=1/2

positive slopes go from bottom left to top right

since it is less than 1
it is more horizonal than vertical

4 0

3 years ago

Which expression can be used to find the radius of a circle with a diameter of 90 inches?

rjkz [21]

The answer to this is C, 90/2

6 0

2 years ago

Read 2 more answers

Jennie makes quilts. She can make 7 quilts with 21 yards of material. How many yards of material would be required to make 12 qu

nlexa [21]

$\frac{7}{21} = \frac{12}{yards} \\ \\ 7*yards=21*12 \\ \\ 7yards=252 \\ \\ yards=36$