Answer:
1.
2. undefined
3. .
4. .
5. .
6.
Step-by-step explanation:
1. The required line passes through . The slope of the line joining the points is given by the formula,
or
Either of them yields the same result.
Substitute into the first formula to get,
You can write this as a mixed number to obtain:
2. The given line passes through .
Observe that the first coordinates are the same for both points. This implies that, the line is vertical.
The slope of all vertical lines are undefined.
3. The average rate of change of the function on the interval is given by:
.
The given function is
.
.
4. The given function is
.
.
5. From the graph
.
.
.
6. The given equation is :
Add to both sides.
Divide through by 2.
Compare this function to
The slope is
Answer:
Automation means something that does not require human input, automatic.
The correct answer is: [C]: " f(x) ≤ x² − x − 1 " .<span>
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Explanation:
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Note that the graph has a solid line. This means that the correct equation for the graph contain either: 1) </span>≤ or: 2) ≥ .
We note that all of the answer choices provided have either: ≤ or: <span>≥ .
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Let us start with a point on the graph that is "not shaded" (i.e. that is NOT a solution: " (0, 2) " ; that is: when "x = 0" , y = 2" .
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Try this for all the answer choices:
Choice: [A]: " y ≥ x² − x − 1 " ;
→ " 2 ≥ 0² − 0 − 1 " ? ;
→ " 2 ≥ 0 − 1 " ? ;
→ "2 ≥ -1 " ? Yes!
So we can rule out "Choice: [A]" .
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Try Choice: [B]:
→ " y ≤ −x² − x −1 " ;
→ " 2 ≤ −(0²) − 0 − 1 " ?
→ " 2 ≤ 0 − 0 − 1 " ?
→ " 2 ≤ -1 " ? No! So this is a possible solution.
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Now, let's try Choice: [C]"
→ " y ≤ x² − x − 1 " ;
→ " 2 ≤ 0² − 0 − 1 " ? ;
→ " 2 ≤ 0 − 1 " ? ;
→ " 2 ≤ -1 " ? ; No! So this is possible answer.
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Now, let's try the last answer choice: [D]:
→ " y ≥ −x² − x − 1 " ;
→ " 2 ≥ −0² − 0 − 1 " ? ;
→ " 2 ≥ 0 − 0 − 1 " ? ;
→ " 2 ≥ - 1 " ? ; No! So this is a possible answer!
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Now, we have narrow our choices to B, C, and D.
Now , among these choices, which of these fits a point with the shaded region?
Let us pick a point: "(2, 0) " that, is, when "x = 2, y = 0 " .
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Let us start with: "Choice: [B] " :
→ " y ≤ −x² − x −1 " ;
→ " 0 ≤ −(2²) − 2 − 1 " ?
→ " 0 ≤ -4 − 2 − 1 " ?
→ " 0 ≤ -7 " ? No! So we can rule out "Choice B" .
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Now, let us try "Choice: [C]" :
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→ " y ≤ x² − x − 1 " ;
→ " 0 ≤ 2² − 2 − 1 " ? ;
→ " 0 ≤ 4 − 2 − 1 " ? ;
→ " 0 ≤ 1 " ? ; Yes! So; this should be the correct answer:
Answer choice: [C]: " f(x) ≤ x² − x − 1 " ;
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Let us try " Choice: [D]"— to confirm that "Choice: [D]" is incorrect:
→ " 0 ≥ −(2²) − 2 − 1 " ;
→ " 0 ≥ −(2²) − 2 − 1 " ? ;
→ " 0 ≥ − 4 − 2 − 1 " ? ;
→ " 0 ≥ − 7 " ? ; No! So we can rule out: "Choice: D<span>" .
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The correct answer is: [C]: " f(x) ≤ x² − x − 1 " .
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Answer:
14- 25/p
There should be no equal sign since it is an expression
Step-by-step explanation: