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2 years ago

x,y, and z to the nearest tenth .(hint: use altitude and leg rules) PLEASE HELP FAST !!! please solve and show steps

Mathematics

1 answer:

madreJ [45]2 years ago

7 0

Use the Pythagorean theorem to find z:

z = √(6^2 + 9^2)

z= √(36 + 81)

z = √117

z = 3√13 = 10.8

Use leg rule to find x:

x/6 = 6/9

Cross multiply:

9x = 36

Divide both sides by 9:

x = 36/9

x = 4

Use Pythagorean theorem to find y:

y = √(6^2 + 4^2)

y= √(36 + 16)

y = √52

y = 2√13 = 7.2

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

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

so, both are inverses of each other.

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

And both f(x) and g(x) are symmetry to y=x.

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