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puteri [66]
2 years ago
15

Simplify 3k - (2m + 5K) - m

Mathematics
2 answers:
Bingel [31]2 years ago
4 0

Answer:

-3m-2k

Step-by-step explanation:

<em>Given to simplify : 3k - (2m + 5K) - m</em>

<em>Solution :</em>

<em />\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b

-\left(2m+5k\right)=-2m-5k

=3k-2m-5k-m

\mathrm{Group\;like\;terms}

=-2m-m+3k-5k

\mathrm{Group\;like\;terms}

=-3m+3k-5k

\mathrm{Group\;like\;terms}

=-3m-2k

[RevyBreeze]

Luda [366]2 years ago
3 0
<h3>hello!</h3>

Use the distributive property:-

-(2m+5k) = -2m-5k \checkmark

\rule{270}{1}

Let's simplify this expression by combining like terms:-

\bigstar The like terms are:-

3k, -5k

and

-2m, -m

\bigstar{ Combine Like terms:-

3k-5k=-2k

-2m-m=-3m

Hence, we have:-

\bigstar{\boxed{\pmb{-2k-3m}}

<h3>note:-</h3>

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

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Answer:  see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = \frac{\sqrt3}{2}

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

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Proof LHS → RHS:

LHS                          cos 165

Double-Angle:        cos (2 · 165) = 2 cos² 165 - 1

                             ⇒ cos 330 = 2 cos² 165 - 1

                             ⇒ 2 cos² 165  = cos 330 + 1

Given:                        2 \cos^2 165  = \dfrac{\sqrt3}{2} + 1

                              \rightarrow 2 \cos^2 165  = \dfrac{\sqrt3}{2} + \dfrac{2}{2}

Divide by 2:               \cos^2 165  = \dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \dfrac{2\sqrt3+4}{8}

Square root:             \sqrt{\cos^2 165}  = \sqrt{\dfrac{4+2\sqrt3}{8}}

Scratchwork:            \cos^2 165  = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2

                             \rightarrow \cos 165  = \pm \dfrac{\sqrt3+1}{2\sqrt2}

             Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

                             \rightarrow \cos 165  = - \dfrac{\sqrt3+1}{2\sqrt2}

LHS = RHS \checkmark

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