The numeric value of the composite function at x = 2 is given as follows:
(f ∘ g)(2) = 33.
<h3>Composite function</h3>
The composite function of f(x) and g(x) is given by the rule presented as follows:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
In the context of this problem, the functions are given as follows:
The composite function is:
(f ∘ g)(x) = f(-2x) = (-2x)² - 3(-2x) + 5 = 4x² + 6x + 5.
At x = 2, the numeric value is given as follows:
(f ∘ g)(2) = 4(2)² + 6(2) + 5 = 33.
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Answer:
Step-by-step explanation:
Answer:
6x - 18
Step-by-step explanation:
5x + 3y + x- 3y +(-3) + (-15)
The correct answer is A. 3:4 = 9:12
Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
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b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
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c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
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d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
