Algebra 1. i just need help with understanding multiple step equations like...

Mathematics

2 answers:

Lapatulllka [165]3 years ago

4 0

$72+4-14d=36 \\\\ 76-14d=36 \\\\ 14d=36-76 \\\\ -14d=-40 \ |:(-2) \\\\ 7d=20 \\\\ \boxed{d=\frac{20}{7}}$

11111nata11111 [884]3 years ago

4 0

$72+4-14d=36\\
-14d=-40\\
d=\frac{40}{14}=\frac{20}{7}$

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I don't need you to work it out, just theorem(s) i need to reach the answer :)

VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

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3 years ago

Use the slope formula to determine the slope of the line that passes through the points R (1, 2) and S (5, 7)

Citrus2011 [14]

M = (y2-y1)/(x2 -x1)
m = (7 -2)/(5 - 1)
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answer: slope m = 5/4

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2 years ago

Lines c and d are parallel lines cut by transversal p.

lilavasa [31]

Answer:

Option (B).

Step-by-step explanation: