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2 years ago

Find the slope of the line passing through each pair of points. (9,4) and (5,-3).

Mathematics

1 answer:

rjkz [21]2 years ago

3 0

Answer:

$m=\frac{7}{4}$

General Formulas and Concepts:

Order of Operations: BPEMDAS
Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

(9, 4)

(5, -3)

Step 2: Find slope m

Substitute: $m=\frac{-3-4}{5-9}$
Subtract: $m=\frac{-7}{-4}$
Simplify: $m=\frac{7}{4}$

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Step-by-step explanation:

Since we have given that

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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,

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

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.

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

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