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svet-max [94.6K]
3 years ago
5

Daniel and William have some marbles. Daniel finds that 2/5 of the marbles he has is 4/5 the number marbles William has. William

s. has 195 marbles how many marbles does Daniel have
Mathematics
2 answers:
Bogdan [553]3 years ago
5 0

Answer:

Daniel has 390 marbles.

Step-by-step explanation:

W = 195

2/5D = 4/5W

2/5D = 4/5(195)

2/5D = 156

D = 390

fgiga [73]3 years ago
4 0
If William has 195 marbles, let's find 4/5 of that.

195 * 4/5 = 156

156 is 2/5 of the marbles Daniel has.

Now we must multiply by the reciprocal

156 * 5/2 ( to find all of Daniel's marbles, not just 2/5) = 390 marbles

Daniel has 390 marbles.
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b) . Use composition to show that f(x) and g(x) are inverses of each other.

\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x

Similarly,

\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x

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c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

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∴ f(x) and g(x) are inverses of each other.


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Step-by-step explanation:

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