Grape jam costs $7.20 for a case of 12 and sells for $0.89 per jar. What is the markup per jar to the nearest cent?

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

In a bag there are 40 pieces of candy: 7

Slav-nsk [51]

Answer:

37.5

Step-by-step explanation:

because if you calculte percent = to 37.5 that is why it sis the correct answer

3 0

3 years ago

Read 2 more answers

How do I solve it and find the coordinates

qwelly [4]

Check picture for working out

8 0

3 years ago

Read 2 more answers

7: In the rhombus, m∠1=10x, m∠2=x + y, and m∠3= 5z. Find the values of x, y, and z.

malfutka [58]

Angles 1, 2, and 3 are all 90°.

10x = 90
.. x = 9

x +y = 90
.. y = 81

5z = 90
.. z = 18

The values of (x, y, z) are (9, 81, 18).

7 0

3 years ago

17) List the ways five dogs a Beagle, a Collie, a Greyhound, a Poodle and a

Gnoma [55]

Answer:

10 pairs

It is a combination

Explanation:

This is a combination because the order does not matter: the Beagle - Collie couple is the same as the Collie - Beagle couple, so it is only counted once.

The formula for combinations is:

$C(m,n)=\dfrac{m!}{n!\cdot (m-n)!}$

For five diffferent dogs to be put in pairs, the number of different pairs is:

$C(5,2)=\dfrac{5!}{2!\cdot (5-2)!}=\dfrac{5\times 4}{2}=10$

4 0

3 years ago