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3 years ago

Which points lie on the line y = 3x - 7?

Mathematics

1 answer:

Vikki [24]3 years ago

3 0

The y intercept is (0,-7). some other points would include (1,-5), (2,-2), (3,1), etc

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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

Salvador’s bathroom has a circular window. The radius of the window measures 12 inches. What is the approximate area of the wind

leonid [27]

Answer:

37.68

Step-by-step explanation:

12 times 3.14 = 37.68

6 0

3 years ago

Read 2 more answers

PLEASE HELP ME WITH 11 QUESTIONS BELOW!! THANK YOU

iris [78.8K]

Answer:

The trapezoid has a height of 3 inches so, a shorter base measuring 2.75 inches, and a longer base measuring 4.25 inches is. The total area of the entire figure is 33 square inches.<3

Step-by-step explanation:

7 0

1 year ago

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Jan and Col club together a book of raffle tickets. They agree to share any prize they win in the ratio 2:3. When they win Jan g

nikitadnepr [17]

Answer:

£15

Step-by-step explanation:

For every £2 Jan gets, Cole gets £3.

10 ÷ 2 (Jan) × 3 (Cole) = 15

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2 years ago

Solve for y;-4 -3y>-10

Luden [163]

Answer:

y>2

Step-by-step explanation:

-4-3y>-10

-3y>-10+4

-3y>-6

y>-6/-3

y>2

4 0

3 years ago