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3 years ago

Solve the system using substitution. Ex-= 3x+2y = 23 1/2X-4= y

Mathematics

1 answer:

adoni [48]3 years ago

3 0

Answer:

-1 1/2

Step-by-step explanation:

x = 5

y = 4

y2 = -1 1/2

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Please help me answer this question

ratelena [41]

By the definition of the hyperbolic function tanh x, we have proven that $\frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}$

<h3>Hyperbolic functions & Proof of identities </h3>

By definition

$tanh \ x=\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}}$

Then,

$\frac{1-tanh \ x}{1 + tanh \ x}=\frac{1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }{1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }$

$=1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} \div (1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} })$

$=\frac{e^{x} +e^{-x}-(e^{x} -e^{-x})}{e^{x} +e^{-x}} \div (\frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} })$

$=\frac{e^{x} +e^{-x}-e^{x} +e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} }$

$=\frac{e^{-x}+e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{x} }{e^{x} +e^{-x}} }$

$=\frac{2e^{-x}}{e^{x} +e^{-x}} \div \frac{2e^{x} }{e^{x} +e^{-x}} }$

$=\frac{2e^{-x}}{e^{x} +e^{-x}} \times \frac{e^{x} +e^{-x}}{2e^{x}}$

$=\frac{2e^{-x}}{1} \times \frac{1}{2e^{x}}$

$=\frac{2e^{-x}}{2e^{x}}$

$=\frac{e^{-x}}{e^{x}}$
$=e^{-x} \times \frac{1}{e^{x}}$

$= e^{-x} \times e^{-x}$

$= e^{-x+-x}$

$= e^{-x-x}$

$= e^{-2x}$

Hence, we have proven that $\frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}$

Learn more on Proof of Identities here: brainly.com/question/2561079

#SPJ1

6 0

2 years ago

Determine if x + 2 is a factor of p(x) = x ^4 + 3x^ 3 + 4x ^2 - 8 and explain why.

zlopas [31]

X^4+ 3x^3+4x^2-8 | x+2 = x^3+x^2+2x-4
-x^4-2x^3
-----------------------
x^3+4x^2-8
-x^3-2x^2
-------------------------
2x^2-8
-2x^2-4x
--------------
-4x-8
4x+8
----------------------------
/ /

is a factor because (x+2)(x^3+x^2+2x-4)=x^4+3x^3+4x^2-8

4 0

3 years ago

Read 2 more answers

Art Club Flyer

Finger [1]

The area of Erin's circle to the nearest hundredth is 50.24 in².

<h3>What is the area of the circle?
</h3>

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :