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Alecsey [184]
3 years ago
12

How to set the answer up

Mathematics
1 answer:
Korolek [52]3 years ago
3 0

Let s and g represents the numbers of suits and gowns produced.

The number of zippers used is 2s+g.

The number of buttons used is 5s+8g.

In order to use all of the available zippers and buttons, we must have ...

  • 2s + g = 171
  • 5s + 8g = 576

Cramer's rule tells you the solution to the system

  • ax +by = c
  • dx +ey = f

Is given by

  • x = (bf-ey)/(bd-ea)
  • y = (cd-fa)/(bd-ea)

Using this rule on the equations for zippers and buttons, we have

... s = (1·576 -8·171)/(1·5 -8·2) = -792/-11 = 72

... g = (171·5 -2·576)/-11 = -297/-11 = 27

72 suits and 27 gowns can be made from available zippers and buttons.

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So, since we have a cubic equation with 4 terms, the first thing we should try is factoring by grouping, so:

12x^3+2x^2-30x+5 =0 \implies \\ 2x^2(6x+1)-5(6x+1)=0 \implies \\ (2x^2-5)(6x+1) = 0

Now that we've factored our equation, we can use ZPP and break it up:

2x^2-5 = 0 \implies \\ 2x^2=5 \implies\\ x^2=\frac{5}{2} \implies\\ x=\pm\frac{\sqrt{5}}{\sqrt{2}}=\pm\frac{\sqrt{10}}{2} \\ \\ 6x+1 =0 \implies \\ 6x=-1 \implies\\ x=\frac{-1}{6}

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Ms. drake invests $1000 at a simple interest rate of 8.5% for 2 years. how much interest will she earn in this time?
PilotLPTM [1.2K]

Ms. Drake will earn \$ 170 in this time from the investment of \$ 1000 at a simple interest with rate of interest 8.5\%

<h3>What is the definition of simple interest?</h3>

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Formula for finding simple interest is \frac{principal \times rate \ of \ interest \times time}{100}

Given principal of Ms. Drake is \$1000

Rate of interest is 8.5 \%

Time is 2 years.

Interest =\frac{1000 \times 8.5 \times 2}{100}

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Therefore, Ms. Drake will earn \$ 170 in this time.

To learn more about simple interest from the given link

brainly.com/question/7639734

#SPJ4

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