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Juli2301 [7.4K]
2 years ago
14

Given the following absolute value function find the range. ƒ(x) = |x + 5| - 8

Mathematics
1 answer:
balandron [24]2 years ago
7 0
The result of an absolute value operation is never negative. So the smallest that the expression |x+5| can be is 0. 

Tacking on "-8" to |x+5| leads to |x+5|-8

The range of this is [-8, infinity) since the smallest |x+5|-8 can be is -8. All I did was subtract 8 from the smallest value of |x+5|

Final Answer: choice C)
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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
1,000 more than 37,542
Hitman42 [59]

the answer is 1,000 + 37,542 so it is 38,542

7 0
3 years ago
The global surface water area is 361, 132,000 square metres. Calculate the volume of water needed to cause a 3mm in sea level.
vovangra [49]

Answer:

The volume of water is 396 cubic meter.

Step-by-step explanation:

Area of water, A = 132000 square meter

Height, h = 3 mm = 0.003 m

The volume of water is given by

V = Area x height

V = 132000 x 0.003

V = 396 cubic meter.

3 0
3 years ago
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Gre4nikov [31]

Step-by-step explanation:

V = 4/3 × 22/7 × 3³

= 4/3 × 22/7 × 27

= 113.14

3 0
3 years ago
Read 2 more answers
Which set dose - 4/9 belong A integers B whole numbers C natural numbers D rational numbers​
Mrac [35]

Answer:

-4/9 is a rational number

Step-by-step explanation:

Rational numbers are the numbers you can make by dividing one integer by another, so in other words a fraction.

4 0
2 years ago
Read 2 more answers
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