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4 years ago

What is the next term for the given arithmetic sequence? -3, -2.25, -1.5, -0.75, ...

Mathematics

2 answers:

Allisa [31]4 years ago

6 0

<h2>Option B is the correct answer.</h2>

Step-by-step explanation:

Arithmetic progression have a first term and common difference.

Here first term, a = -3

Common difference, d = -2.25 - (-3) = -2.25 + 3 = 0.75

The n th term of an arithmetic progression is given by a + (n-1) d

Here we need to find fifth term, that is n = 5

Fifth term = a + (n-1) d = -3 + (5-1) x 0.75

Fifth term = a + (n-1) d = -3 + 4 x 0.75

Fifth term = a + (n-1) d = -3 + 3 = 0

So next term for the given arithmetic sequence = 0

Option B is the correct answer.

wel4 years ago

4 0

The next term in the arithmetic sequence is 0 since its adding 0.75 every time.

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If f(x)=4x^2+1 and g(x) =x^2-5 find (f-g)(x)

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Answer:

$\huge\boxed{(f-g)(x)=3x^2+6}$

Step-by-step explanation:

$(f-g)(x)=f(x)(x)\\\\\text{substitute}\ f(x)=4x^2+1\ \text{and}\ g(x)=x^2-5\\\\(f-g)(x)=(4x^2+1)-(x^2-5)=4x^2+1-x^2-(-5)=4x^2+1-x^2+5\\\\\text{combine like terms}\\\\(f-g)(x)=(4x^2-x^2)+(1+5)=3x^2+6$

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4 years ago

Which expressions are completely factored? Select each correct answer. 30a6−24a2=3a2(10a4−8) 16a5−20a3=4a3(4a2−5) 12a3+8a=4(3a3+

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When factoring an expression, we need to identify the Greatest Common Factor of the expression (GCF). By definition, GCF is the product of prime factors involved with its Lowest Exponent.

We need to divide each term by the GCF to get the expression inside the parenthesis.

$30a^6-24a^2\\ GCF\; is \; 6a^2\\ \\ 30a^6-24a^2=6a^2(\frac{3a^6}{6a^2} -\frac{24a^2}{6a^2} )=6a^2(5a^4-4)\\ ---------------------\\ \\ 16a^5-20a^3\\ GCF \; is \; 4a^3\\ \\ 16a^5-20a^3=4a^3(\frac{16a^5}{4a^3} -\frac{20a^3}{4a^3})=4a^3(4a^2-5) \\ ---------------------\\ \\ 12a^3+8a\\ GCF \; is \; 4a\\ \\ 12a^3+8a=4a(\frac{12a^3}{4a}+\frac{8a}{4a})=4a(3a^2+2)\\ ---------------------\\ 24a^4+18\\GCF \; is \; 6\\\\24a^4+18=6(\frac{24a^4}{6} +\frac{18}{6})=6(4a^4+3) \\ ---------------------$

Conclusion:

From above we can conclude that the below expressions are factored completely

$16a^5-20a^3=4a^3(4a^2-5)\\ \\ 24a^4+18=6(4a^4+3)$

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3 years ago

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<h3>What are population and sample?</h3>

It is defined as the group of data having the same entity which is related to some problems. The sample is a subset of the population, it is a part of the population.

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Thus, the answers are Sample population and the Sample Size is Large Enough.

Learn more about the population and sample here:

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2 years ago

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m_a_m_a [10]

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3 years ago

D. 61 <br><br> Just checking <br> I tend to 2nd guess a lot

pochemuha

You're correct: the logical OR operator is true whenever one of the two options is true.

So, the sales of shoes OR socks is given by the 52 and 9%, which together evaluates to $52+9=61$

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4 years ago

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