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3 years ago

URGENT PLEASE

Mathematics

1 answer:

iragen [17]3 years ago

4 0

$\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=7.2\\ b=6.7\\ c=4.5\\ s=\frac{7.2+6.7+4.5}{2}\\[0.5em] \qquad 9.2 \end{cases} \\\\\\ A\sqrt{9.2(9.2-7.2)(9.2-6.7)(9.2-4.5)}\implies A=\sqrt{9.2(2)(2.5)(4.7)} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 14.704~\hfill$

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Find f(g(x)) and g(f(x)) 1. F(x) = X²-3x+1 g(x)=5x-7

Mariana [72]

We are given the following functions

$\begin{gathered} f(x)=x^2-3x+1 \\ g(x)=5x-7 \end{gathered}$

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Substitute x = 5x - 1 into the function f(x) and simplify

$\begin{gathered} f(g(x))=(5x-7)^2-3(5x-7)+1 \\ f(g(x))=(25x^2-2\cdot5x\cdot7+49)^{}-15x+21+1 \\ f(g(x))=25x^2-70x+49^{}-15x+22 \\ f(g(x))=25x^2-70x-15x+49+22 \\ f(g(x))=25x^2-85x+71 \end{gathered}$

Now let us find g(f(x))

Substitute x = x² - 3x + 1 into the function g(x) and simplify

$\begin{gathered} g(f(x))=5(x^2-3x+1)-7 \\ g(f(x))=5x^2-15x+5-7 \\ g(f(x))=5x^2-15x-2 \end{gathered}$

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1 year ago

You bought a car for $50,000. Each year it depreciates in value by 7.5%.

sweet-ann [11.9K]

Answer:

y= 50,000(1-.075)^x

Step-by-step explanation:

The first year of depreciation is calculated by:

50,000 - (0.075)*(50,000) = 46,250

This can also be written as:

(50,000)*(1 - 0.075) [Pull out the 50,000]

The second year will depreciate starting with the $46,250 value at the end of the first year:

46,250 - (0.075)*(46,250) = 42,781

This may be written as:

(46,250)(1 - 0.075) = 42,781

The 46,250 was derived from the first year depreciation calculation, so we can substitute that instead of the 46,250:

((50,000)*(1 - 0.075))(1 - 0.075) = 42,781

This reduces to:

(50,000)*(1 - 0.075)^2 = 42,781. Note that the term (1-0.075) is now raised to the 2nd power. This power represents the 2nd year. Each succeeding year would be raised by one additional power, so that we can write a depreciated value after x years will be:

(50,000)*(1 - 0.075)^x

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2 years ago

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Aleksandr [31]

Answer:

scale factor = $\frac{1}{3}$