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2 years ago

5

listed in the table is the percentage of students who choose each type of milk at lunchtime. use the table to determine the meas

ure of the central angle you would draw to represent banana milk in a circle graph.

1 answer:

sladkih [1.3K]2 years ago

5 0

Answer:

i cant see the picture its blocked

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

The geometric mean of 8 and 2 is<br><br> 5<br> 3<br> 4<br> 16

igomit [66]

Answer:5

Step-by-step explanation:

<h3><u>(8 + 2)</u> <u>sum of values </u> = <u>10</u> = 5</h3><h3> 2 number of values 2</h3><h3 />

There is equal spacing between the mean and the extremes

8 - 5 = 3

5 - 2 = 3

5 0

2 years ago

Solve, using linear combination. <br> 3x + y = 4<br> 2x + y = 4

nataly862011 [7]

X would be 0 while Y would be 4

3x+y=4
-(2x+y=4)
----------------
x=0

Plug in x to any of those two equations in their original form

3(0)+y=4

0 + y = 4

y = 4

8 0

2 years ago

Write a subtraction problem involving regrouping that has ted reading 304 pages. Answer your question

kari74 [83]

How about this:

The book has 712 pages. Ted has already read 408 pages, so he has 304 left to read.
712 - 408 = 304

4 0

2 years ago

Kyle has 64 baseball cards and must give away 1/4 of his figures away. How many cards will Kyle give away? What fractions of his

Dafna11 [192]

kyle regalara 16 figuras y le quedara 3/4 de ellas

4 0

2 years ago