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mihalych1998 [28]
3 years ago
13

The owner of a video game store creates the expression −2x^2 + 24x + 174 to represent the store's weekly profit in dollars, wher

e x represents the price of a new video game. Choose the equivalent expression that reveals the video game price that produces the highest weekly profit, and use it to determine the price.
−2(x^2 − 12x) + 174; x = $12
−2(x^2 − 12x − 87); x = $87
−2(x − 6)2 + 246; x = $246
−2(x − 6)2 + 246; x = $6
Mathematics
1 answer:
coldgirl [10]3 years ago
6 0
The answer is the second one
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Find the sum of the first 20 terms of an arithmetic progression of which the third term is 55 and the last term is -98
ryzh [129]

The sum of first 20 arithmetic series S_{20}=\frac{-3475}{16}

Given:

Arithmetic series for 3rd term is 55

Arithmetic series for 7th term is -98

To find:

The sum of first 20 Arithmetic series

<u>Step by Step Explanation: </u>

Solution:

Formula for calculating arithmetic series

Arithmetic series=a+(n-1) d

Arithmetic series for 3rd term a_{3}=a_{1}+(3-1) d

a_{1}+2 d=55

Arithmetic series for 19th term is

a_{19}=a_{1}+(19-1) d=-98

a_{19}+18 d=-98

Subtracting equation 2 from 1

\left[a_{19}+18 d=-98\right]+\left[a_{1}+2 d=55\right]

16d=-98-55

16d=-153

d=\frac{-153}{16}

Also we knowa_{1}+2 d=55

a_{1}+2(-153 / 16)=55

a_{1}+(-153 / 8)=55

a_{1}=55+(153 / 8)

a_{1}=440+153 / 8

a_{1}=553 / 8

First 20 terms of an AP  

a_{n=} a_{1}+(n-1) d

a_{20}=553 / 8+19(-153 / 16)

a_{20}=553 / 8+19(-153 / 16)

a_{20}=\{553 * 2 / 8 * 2\}-2907 / 16

a_{20}=[1106 / 16]-[2907 / 16]

a_{20}=-1801 / 16

Sum of 20 Arithmetic series is

S_{n}=n\left(a_{1}+a_{n}\right) / 2

Substitute the known values in the above equation we get

S_{20}=\left[\frac{20\left(\left(\frac{558}{8}\right)+\left(\frac{-1801}{16}\right)\right)}{2}\right]

S_{20}=\left[\frac{\left.20\left(\frac{1106}{16}\right)+\left(\frac{-1801}{16}\right)\right)}{2}\right]

S_{20}=10 \frac{(-695 / 16)}{2}

S_{20}=5\left[\frac{-695}{16}\right]

S_{20}=\frac{-3475}{16}

Result:

Thus the sum of first 20 terms in an arithmetic series is S_{20}=\frac{-3475}{16}

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3 years ago
Find AB: <br><br> Need help ASAP
jek_recluse [69]

Answer: 29

Step-by-step explanation: 66 - 37 = 29

ur welcome :)

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11ft 8in + 2ft 9in =14ft 5in
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Step-by-step explanation:

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(2x2 - 3x + 7) - (-3x2 + 4x - 7) <br>what is the combine terms​
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Answer:

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Step-by-step explanation:

(2*2-3x+7) - (-3*2+4x-7)

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