Answer:
$23.6
Step-by-step explanation:
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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2/3 = 0.666
7/6 = 1.166
1/8 = 0.125
9/10 = 0.9
from least to greatest : 1/8 , 2/3 , 9/10, 7/6
This equation is separable, but 
doesn't have an elementary antiderivative. However, we can use the fundamental theorem of calculus to find a solution in terms of an integral:
Answer:
Step-by-step explanation:
124 degree angle and "3a - 2b" angle are supplementary (in a straight line -- add upto 180 degrees). So we can say and write:
124 + "3a - 2b" = 180
3a - 2b = 180 - 124
<u>3a - 2b = 56</u>
<u></u>
Now,
"2a + 3b" and "3a - 2b" are also supplementary. So we can write:
2a + 3b + 3a - 2b = 180
<u>5a + b = 180</u>
<u></u>
Lets solve this 2nd equation for b:
5a + b = 180
b = 180 - 5a
We put this into 1st equation and solve for a:
3a - 2b = 56
3a - 2(180 - 5a) = 56
3a - 360 +10a = 56
13a = 56 + 360
13a = 416
a = 416/13
a = 32
Now, finding b:
b = 180 - 5a
b = 180 - 5(32)
b = 20
So,
a = 32, b = 20
