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Leokris [45]
3 years ago
7

If m 2 n, which inequalities must be true? Check all that apply.

Mathematics
2 answers:
anzhelika [568]3 years ago
8 0

Answer:

(a)\ m+ 2.1 > n + 2.1

(b).\ m - (-4) > n - (-4)

(c)\ 9 +m> 6 + n

Step-by-step explanation:

Given

m > n

Required

Select true inequalities

(a)\ m+ 2.1 > n + 2.1

Subtract 2.1 from both sides

m > n

This is true

(b).\ m - (-4) > n - (-4)

Open brackets

m + 4 > n + 4

Subtract 4 from both sides

m > n

(c)\ 9 +m> 6 + n

m> -9+6 + n

m> n-3

This is also true

shutvik [7]3 years ago
4 0

Answer:

A,B,D

Step-by-step explanation:

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\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}

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\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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