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amid [387]
3 years ago
8

Chanel is renting a digital video recorder from a cable supplier for a start up fee of $45 plus $5 per month. She has a budget o

f $250. What is the maximum number of months she can rent the digital video recorder?
Mathematics
1 answer:
Norma-Jean [14]3 years ago
5 0
Fixed Cost = $45
Monthly Cost = $5

----------------------------------------
Define x:
----------------------------------------
Let x be the number of months she can rent.

----------------------------------------
Construct Inequality:
----------------------------------------
45 + 5x ≤ 250

----------------------------------------
Solve x :
----------------------------------------
45 + 5x ≤ 250
5x ≤ 250 - 45
5x ≤ 205
x≤ 41

--------------------------------------------------------------------------------
Answer: She can rent for a maximum of 41 months.
--------------------------------------------------------------------------------
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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

The common difference is 5.

And first term is -12

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

Learn more about arithmetic sequence at:

  • brainly.com/question/10879401
  • brainly.com/question/10940255

#LearnwithBrainly

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What is the perimeter of the triangle?
Dennis_Churaev [7]
Answer:

The perimeter will be 30

Step-by-step explanation:

Perimeter = all side lengths added

Step 1. Determine the length of the triangle

Answer: 5

Step 2. Determine the width of the triangle

Answer: 12

Step 3. Determine the diagonal line across the triangle

Answer + explanation:

For it to figure it out, we must use this method called Pythagorean Theorem

Pythagorean Theorem: a^2 + b^2 = c^2

Where a = 12 b = 5 and c = the diagonal line

12^2 + 5^2 = c^2

144 + 25 = c^2

c^2 = 169

c = 13

The diagonal line measures 13 units

Step 4. Add all of the dimensions we just reviewed

Answer:

Length = 5

Width = 12

Diagonal line = 13

5 + 12 + 13 = perimeter

perimeter = 30

Therefore, the perimeter is 30


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