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3 years ago

What is the missing term to make these ratios equal 21 : 3 = :9

Mathematics

2 answers:

Morgarella [4.7K]3 years ago

7 0

Answer:

63:9 is equal to 21:3

Step-by-step explanation:

Zielflug [23.3K]3 years ago

4 0

63. The ratio 63:9 is equal to 21:3 because 3x3 is 9 and 21x3 is 63

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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

A class of 118 students went on a field trip. They took 10 vehicles, some vans (x) and some buses (y). Find the number of vans a

I am Lyosha [343]

Answer:

Solve for x+y=10

6x+35y=118

Step-by-step explanation:

I would solve it for you but my calculator isn't working rn. You could also use a picture calculator and it will give you a more in depth explanation. Hope this helps!

7 0

3 years ago

The point G(6,4) is rotated 180° clockwise around the origin. What

siniylev [52]

Answer:

Step-by-step explanation:

when (x,y) is rotated through 180 then new coordinates are (-x',-y')

G(6,4)→G'(-6,-4)

5 0

3 years ago

The diagram below show the dimensions of a container of sand that is shaped like a rectangular prism . The container is filled u

monitta

Answer:

Its B

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Find the slope of each line 2-3. please help thank you.

atroni [7]

2)
(-3, 3) (2,0)
slope = (3-0)/(-3-2) = -3/5

3)
y = 3
so slope = 0

7 0

3 years ago