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jeka57 [31]
3 years ago
10

Rectangle ABCD with length 24 feet and width 20 feet is dilated by a scale factor of 4/3. What is the area of rectangle A'B'C'D'

?​
Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
6 0

multiply the length and with by the scale factor:

24 x 4/3 = 32 feet

20 x 4/3 = 26 2/3 feet

Area is length x width:

32 x 26 2/3 = 853 1/3 square feet.

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\bf \textit{zeros at } \begin{cases} x = -3\implies &x+3=0\\ x = -1\implies &x+1=0\\ x = 4\implies &x-4=0 \end{cases}\qquad \implies (x+3)(x+1)(x-4)=\stackrel{y}{0} \\\\\\ (x^2+4x+3)(x-4)=0\implies x^3~~\begin{matrix}+ 4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+3x~~\begin{matrix} -4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-16x-12=0 \\\\\\ x^3-13x-12=0

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\bf x^3-13x-12=y\implies \stackrel{x = -2}{(-2)^3-13(-2)-12}=y \\\\\\ -8+26-22=y \implies 6=y

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\bf 4(x^3-13x-12)=y\implies \stackrel{x = -2}{4[~~(-2)^3-13(-2)-12~~]}=y \\\\\\ 4[~~-8+26-22~~]=y\implies 4[6]=y\implies 24=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 4x^3-52x-48=y~\hfill

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