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3 years ago

Suppose that the functions s and t are defined for all real numbers x as follows.

Mathematics

1 answer:

PolarNik [594]3 years ago

8 0

Answer:

(s-t)(-1) = -1

(s+t)(-1) = -7

Step-by-step explanation:

Given the following set of functions

s(x)=2x-2

t(x)=3x

(s-t)(x) = s(t) - t(x)

(s-t)(x) = 2x - 2 - 3x

(s-t)(x) = -x -2

(s-t)(-1) = -(-1) - 2

(s-t)(-1) = 1-2

(s-t)(-1) = -1

(s+t)(x) = s(t) + t(x)

(s+t)(x) = 2x - 2 + 3x

(s+t)(x) = 5x -2

(s+t)(-1) = 5(-1) - 2

(s+t)(-1) = -5-2

(s+t)(-1) = -7

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Step-by-step explanation:

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Can someone give me the answers and step by step instructions please??

professor190 [17]

Answer:

$-1,4,-7,10,...$ neither

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Step-by-step explanation:

Given:

sequences: $-1,4,-7,10,...$

$192,24,3,\frac{3}{8},...$

$-25,-18,-11,-4,...$

To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them

Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

For $-1,4,-7,10,...$ :

$4-(-1)=5\\-7-4=-11\\10-(-7)=17\\So,\,\,4-(-1)\neq -7-4\neq 10-(-7)$

Hence,the given sequence does not form an arithmetic progression.

$\frac{4}{-1}=-4\\\frac{-7}{4}=\frac{-7}{4}\\\frac{10}{-7}=\frac{-10}{7}\\So,\,\,\frac{4}{-1}\neq \frac{-7}{4}\neq \frac{10}{-7}$

Hence,the given sequence does not form a geometric progression.

So, $-1,4,-7,10,...$ is neither an arithmetic progression nor a geometric progression.

For $192,24,3,\frac{3}{8},...$ :

$\frac{24}{192}=\frac{1}{8}\\\frac{3}{24}=\frac{1}{8}\\\frac{\frac{3}{8}}{3}=\frac{1}{8}\\So,\,\,\frac{24}{192}=\frac{3}{24}=\frac{\frac{3}{8}}{3}$

As ratio of the consecutive terms is same, the sequence forms a geometric progression.

For $-25,-18,-11,-4,...$ :

$-18-(-25)=-18+25=7\\-11-(-18)=-11+18=7\\-4-(-11)=-4+11=7\\So,\,\,-18-(-25)=-11-(-18)=-4-(-11)$

As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

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3 years ago

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valkas [14]

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3 years ago

A triangle has sides with lengths of 6 inches, 13 inches, and 17 inches. Is it a right triangle?

Tems11 [23]

Answer:

Nope

Step-by-step explanation:

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2 years ago

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Answer:

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