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2 years ago

Calculate the slope of the line that passes through (12,15) and (10, 21). Reduce answer to lowest terms if

Mathematics

1 answer:

gulaghasi [49]2 years ago

3 0

Answer:

-3

Step-by-step explanation:

Slope is rise divided by run. Y2-Y1 Divided by X2-X1

You get 6 divided by -2

-3

You might be interested in

Am I correct on 12?

lukranit [14]

Yes, HL would be correct.

This states that if two hypotenuses are congruent (they have the same one)

and if one pair of legs are congruent,

the figure is congruent.

I hope this helps!
~cupcake

7 0

3 years ago

Please help i beg i never get these right

Anuta_ua [19.1K]

Answer:

$\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}$

Step-by-step explanation:

Given

$\sin(105^o)$

Required

Solve

Using sine rule, we have:

$\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)$

This gives:

$\sin(105^o) = \sin(60 + 45)$

So, we have:

$\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)$

In radical forms, we have:

$\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}$

$\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}$

Take LCM

$\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}$

Rewrite as:

$\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}$

Hence:

$\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}$

3 0

2 years ago

The half-life of a certain substance is 20 years. How much of a 100 gram sample will be left after 20 years?

cluponka [151]

$\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( \frac{1}{2} \right)^{\frac{20}{20}}\implies A=100\left( \frac{1}{2} \right)^1\implies A=50$