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3 years ago

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

Mathematics

1 answer:

Vilka [71]3 years ago

3 0

Answer:

(3, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define systems

3x + y = 10

y = x - 2

Step 2: Solve for x

Substitute: 3x + (x - 2) = 10
Combine like terms: 4x - 2 = 10
Isolate x term: 4x = 12
Isolate x: x = 3

Step 3: Solve for y

Define original equation: y = x - 2
Substitute in x: y = 3 - 2
Subtract: y = 1

And we have our answer!

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Ksju [112]

The answer to this equation is 77.. x=77

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3 years ago

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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

some numbers added to -11 is 37.divide this number by -12.then multiply by -8.what is the final number?

LUCKY_DIMON [66]

Since some number added to -11 is 37, we must do 37- (-11), which is 48. Then we check our work and find that 48+-11 is indeed 37. Now we divide 48 by -12, which is -4, multiply by -8 and get a final answer of 32.

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3 years ago

If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades?

nataly862011 [7]

Answer:

The probability of getting exactly 2 of the cards are spades out of 6 cards will be 0.315

Step-by-step explanation:

6 cards are drawn at random from a standard deck of 52 cards.

The number ways 6 cards can be drawn from a deck of 52 cards will be,

$=\ ^{52}\text{C}_6=20358520$

In a deck of 52 cards, 13 cards are of spades. So drawing 2 spades out of 13 is,

$=\ ^{13}\text{C}_2=78$

As exactly 2 must be spades, so the remaining 4 cards must be drawn from other 39 cards of other suits. This can be done in,

$=\ ^{39}\text{C}_4=82251$

The probability of getting exactly 2 of the cards are spades out of 6 cards will be,

$=\dfrac{\ ^{13}\text{C}_2\times ^{39}\text{C}_4}{\ ^{52}\text{C}_6}=\dfrac{78\times 82251}{20358520}=0.315$

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3 years ago

What is the difference between formal and informal geometry

shutvik [7]

Answer:

There is a sub-field of geometry called formal geometry which is related to algebraic geometry and deals with topics such as formal schemes , topological rings , the comparison theorem in algebraic geometry , the Grothendieck existence theorem.

Informal geometry have the topics of definitions, measurements, and constructions of geometric shapes and figures. No attention to formal proofs is given. Subtopics include points, lines, angles, triangles, quadrilaterals, circles, area, and perimeter.

Step-by-step explanation:

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4 years ago