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LekaFEV [45]
3 years ago
5

Simplify 3 × 3x² × y × 4z × x × y × z

Mathematics
2 answers:
geniusboy [140]3 years ago
6 0

Answer : 36x³z²y²

<h3>Firstly, you have to know these:</h3>

<em>a³ × a² = </em>a^{3+2} = a^{5}<em />

<em>a³ × b³ = (ab)³</em>

<em>a × b = ab</em>

<em>a × b × c = abc</em>

<em>a³ × a² × b = </em>a^{5}b<em />

<h3>Simplfy 3 × 3x² × y × 4z × x × y × z</h3>

rewrite like this => 3 × 3x² × x × 4z × z × y × y => you can understand better. I didn't change any number. I only change number's places

3 × 3x² × x × 4z × z × y × y <em>===></em> 9x³ × 4z × z × y × y

3 × 3x² × x × 4z × z × y × y <em>===> </em>3 × 3x² × x × 4z² × y × y

3 × 3x² × x × 4z × z × y × y <em>===> </em>3 × 3x² × x × 4z × z × y²

So;

3 × 3x² × x × 4z × z × y × y = 9x³ × 4z² × y²

9x³ × 4z² × y² = 36x³z²y²

<u><em></em></u>

Hope this helps ^-^

lesantik [10]3 years ago
5 0

this should be correct if not then idk

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Answer:

AB = 27.2

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Step-by-step explanation:

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

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\implies \sf \cos(30^{\circ})=\dfrac{29}{BC}

\implies \sf BC=\dfrac{29}{\cos(30^{\circ})}

\implies \sf BC=\dfrac{58\sqrt{3}}{3}=33.5\:(nearest\:tenth)

\implies \sf \tan(30^{\circ})=\dfrac{BD}{29}

\implies \sf BD=29\tan(30^{\circ})

\implies \sf BD=\dfrac{29\sqrt{3}}{3}

\implies \sf \sin(38^{\circ})=\dfrac{BD}{AB}

\implies \sf AB=\dfrac{\dfrac{29\sqrt{3}}{3}}{\sin(38^{\circ})}

\implies \sf AB=27.2\:(nearest\:tenth)

\implies \sf \tan(38^{\circ})=\dfrac{BD}{AD}

\implies \sf AD=\dfrac{\dfrac{29\sqrt{3}}{3}}{\tan(38^{\circ})}

\implies \sf AD=21.4\:(nearest\:tenth)

\implies \sf AC=AD+DC=21.4+29=50.4

The interior angles of a triangle sum to 180°

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⇒ ∠A = 180° - 90° - 52°

⇒ ∠A = 38°

⇒ ∠ABC + 38° + 30° = 180°

⇒ ∠ABC = 180° - 38° - 30°

⇒ ∠ABC = 112°

**I have checked the measures using a graphing programme - see attached**

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