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In-s [12.5K]
3 years ago
14

Which statement about proportional relationships is false? A proportional relationship must graph as a line. A graph of a propor

tional relationship must pass through (0, 0). Each point (or pair) in a proportional relationship must share the same ratio. Each point (or pair) in a proportional relationship must share the same difference.
Mathematics
2 answers:
kogti [31]3 years ago
8 0

Answer: It's D

Step-by-step explanation:

natka813 [3]3 years ago
4 0

Answer:

<u><em>D:</em></u> Each point (or pair) in a proportional relationship must share the same difference.

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Calculate the total area of the shaded region.
LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill

\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}

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2 years ago
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Black_prince [1.1K]
15x = 7x + 8x

x^2+15x=-56\\\\ x^2+15x+56=0\\\\ x^2+7x+8x+56=0\\\\x(x+7)+8(x+7)=0\\\\ (x+7)(x+8)=0 \\\\ x=-7 \ or \ x=-8
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\frac{d}{dx}(tan^{3}x) = \frac{d}{dx}(tanx)^{3}
= 3(tanx)^{2} \cdot sec^{2}x

\therefore \frac{d}{dx}(tan^{3}x) = 3tan^{2}x \cdot sec^{2}x
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Step-by-step explanation:

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