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3 years ago

Solve for p. 2(p + 1) = 18

Mathematics

1 answer:

n200080 [17]3 years ago

7 0

Answer:

p = 8

Step-by-step explanation:

Subtract 18 from behind the equal sign to cancel it out. This leaves you with 2(p+1)- 18= 0.

Next you'll need to pull out the terms to work with the beginning of the problem. 2(p+1)- 18= 0 would turn into 2p - 16 = 2(p - 8).

This would leave you with 2= 0, but that's not true so continue on to the variable.

So p - 8= 0 making the answer p = 8

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2 years ago

What is the thirty-second term of the arithmetic sequence -12, -7, -2, 3, ... ? Show your work.

anzhelika [568]

The thirty-second term is 143

Further explanation:

As it is already given that the given sequence is an arithmetic sequence

We have to find the common difference first

So,

$a_1=-12\\a_2=-7\\a_3=-2\\a_4=3$

$d=a_2-a_1=-7-(-12)=-7+12=5\\a_3-a_2=-2-(-7)=-2+7=5$

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The explicit formula for arithmetic sequence is:

$a_n=a_1+(n-1)d\\Here,\\a_n\ is\ nth\ term\\a_1\ is\ first\ term\\d\ is\ common\ difference$

Putting the values in the formula

$a_n=-12+(n-1)(5)\\a_n=-12+5n-5\\a_n=-17+5n$

Putting n=32 in explicit formula

$a_{32}=-17+5(32)\\=-17+160\\=143$

The thirty-second term is 143

Keywords: Common difference, Arithmetic Sequence

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2 years ago

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A. The formula (mathematical function) for the monthly revenue, R, earned by Alec, R(s, n) = <u>$18.20s + $5n</u>.

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<h3>What is a function?</h3>

A function is an expression, rule, or law defining the relationship between an independent variable and a dependent variable.

Functions are used to define physical relationships between variables.

<h3>Data and Calculations:</h3>

Cost monthly subscription = $28.20 per box

Number of normal potatoes in each box = 16

Cost of additional luxury potatoes = $5 per potato

If the monthly revenue function, R, is given as R(s, n) where:

s = number of monthly subscribers

n = total number of luxury potatoes ordered

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1 year ago