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Brums [2.3K]
3 years ago
6

Mathematics puzzle from my calculus text book.

Mathematics
1 answer:
xenn [34]3 years ago
4 0

Answer:

{ \tt{g(x) = a {x}^{2} + bx + c = 0 }} \\ { \tt{f(x) =  {a'x}^{2} + b 'x + c' = 0}} \\ { \boxed{ \bf{f(g(x)) = g(f(x))}}} : \\ { \tt{ =(  \frac{a}{a'})x {}^{2}   + ( \frac{b}{b'}) x} +  \frac{c}{c'} } = 0

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Find the difference.
Vsevolod [243]

5.\\12\dfrac{3}{10}-7\dfrac{7}{10}=11\dfrac{10+3}{10}-7\dfrac{7}{10}=11\dfrac{13}{10}-7\dfrac{7}{10}=4\dfrac{6}{10}=4\dfrac{6:2}{10:2}=\boxed{5\dfrac{3}{5}}\\\\11-7=4\\\\\dfrac{13}{10}-\dfrac{7}{10}=\dfrac{13-7}{10}=\dfrac{6}{10}\\\\6.\\8\dfrac{1}{6}-3\dfrac{5}{6}=7\dfrac{6+1}{6}-3\dfrac{5}{6}=7\dfrac{7}{6}-3\dfrac{5}{6}=(7-3)+\dfrac{7-5}{6}=4\dfrac{2}{6}=4\dfrac{2:2}{6:2}=\boxed{4\dfrac{1}{3}}

9.\\7\dfrac{1}{6}-2\dfrac{5}{6}=6\dfrac{6+1}{6}-2\dfrac{5}{6}=6\dfrac{7}{6}-2\dfrac{5}{6}=(6-2)+\dfrac{7-5}{6}=4\dfrac{2}{6}=\boxed{4\dfrac{1}{3}}\\\\10.\\9\dfrac{3}{12}-4\dfrac{7}{12}=8\dfrac{12+3}{12}-4\dfrac{7}{12}=8\dfrac{15}{12}-4\dfrac{7}{12}=(8-4)+\dfrac{15-7}{12}=4\dfrac{8}{12}\\\\=4\dfrac{8:4}{12:4}=\boxed{4\dfrac{2}{3}}

5 0
3 years ago
As an assistant in pet store, one of your responsibilities is to fill the aquariums with water. One 50-gallon aquarium is 36 inc
Fynjy0 [20]

Answer:

Eleven thousand five hundred and twenty

Step-by-step explanation:

E2021

6 0
3 years ago
The cube of a positive number divided by the square of the same positive number
meriva
So, an example of this situation would be 3³÷3². When you divide like this, you simply would subtract 2 from 3 and that would be the new exponent. In this case, the exponent would be 1, so the expression is actually equal to whatever the positive number is. In another way, if you have 3×3×3 and you divide it by 3×3, you would have one three left, so that's your answer. Hope this helps!
3 0
3 years ago
2. Solve for the values of x by factoring.
Vikki [24]

Answer:

x = - 3, x = - 6

Step-by-step explanation:

{x}^{2}  + 9x + 18 = 0 \\  \\  {x}^{2}  + 6x + 3x + 18 = 0 \\  \\ x(x + 6) + 3(x + 6) = 0 \\  \\ (x + 6)(x + 3) = 0 \\\\ x + 3 = 0 \:  \: or \:  \: x + 6 = 0 \\  \\ x =  - 3, \:  \: or \:  \: x =  - 6 \\  \\

7 0
3 years ago
Read 2 more answers
What is the approximate area of the circle shown below?
creativ13 [48]
Area = pi * radius²
Area = 3.14159 * 9²
Area = 3.14159 * 81
Area = <span> <span> <span> 254.46879 </span> </span> </span>
answer is D


4 0
4 years ago
Read 2 more answers
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