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elena55 [62]
4 years ago
15

Solve inequality 5-3(4x-5)<32

Mathematics
1 answer:
irga5000 [103]4 years ago
6 0

Answer: x > -1

Step-by-step explanation:

1) Subtract 5 from both sides

-3(4x - 5) < 27

2) Divide both sides by -3 (Remember to change the inequality sign to face the other way, because you have multiplied/divided by a negative number)

4x - 5 > -9

3) Add 5 to both sides

4x > -4

4) Divide by 4 on both sides

x > -1

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The graph represents the function g(x). Suppose that f(x) = -x. Which is true when comparing the range of f(x) to g(x)?
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Step-by-step explanation

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What the function?<br> y = 2.5x + 8
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Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that
Helga [31]

Answer:

\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n

Step-by-step explanation:

Rn(x) →0

f(x) = 10/x

a = -2

Taylor series for the function <em>f </em>at the number a is:

f(x) =  \sum^\infty_{n=0} \frac{f^{(n)}(a)}{n!} (x - a)^n

f(x) = f(a) + \frac{f'(a)}{1!}(x-a)+\frac{f"(a)}{2!} (x-a)^2 + ... ............ equation (1)

Now we will find the function <em>f </em> and all derivatives of the function <em>f</em> at a = -2

f(x) = 10/x            f(-2) = 10/-2

f'(x) = -10/x²         f'(-2) = -10/(-2)²

f"(x) = -10.2/x³      f"(-2) = -10.2/(-2)³

f"'(x) = -10.2.3/x⁴     f'"(-2) = -10.2.3/(-2)⁴

f""(x) = -10.2.3.4/x⁵    f""(-2) = -10.2.3.4/(-2)⁵

∴ The Taylor series for the function <em>f</em> at a = -4 means that we substitute the value of each function into equation (1)

So, we get \sum^\infty_{n=0} - \frac{10(x+2)^n}{2^{n+1}} Or \sum^\infty_{n=0} -5 (\frac{x+2}{2})^n

4 0
3 years ago
If the 15th term of the arithmetic sequence is 12, and the 14th term is 21, find the common difference of the sequence.
Oksi-84 [34.3K]

Answer:

9

Step-by-step explanation:

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3 years ago
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