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AveGali [126]
3 years ago
7

Please help!! Over several years, Stephon gathered data about his age and the time it took him to run two laps on the school tra

ck. The scatter plot shows the data he gathered and the line of best fit. The equation of the line of best fit is y = -2.1x + 565.6. Based on the line of best fit, approximately how long will it take Stephon to run two laps on the track when he is 192 months old?

Mathematics
1 answer:
AVprozaik [17]3 years ago
3 0

Answer:

Time taken by Stephen = 162 seconds

Step-by-step explanation:

Stephan gathered data which fits in the line of best fit,

y = -2.1x + 565.6

Where x represents the age (in months)

And y represents the time (in seconds) taken by Stephen to run two laps on the track.

Time taken to run 2 laps at the age of 192 months,

By substituting x = 192 months,

y = -2.1(192) + 565.6

  = -403.2 + 565.6

  = 162.4 seconds

  ≈ 162 seconds

Therefore, time taken by Stephen to cover 2 laps was 162 seconds when he was 192 months old.

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10 subtracted from the quotient of a number and -3 is at least -1​
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<em><u>10 subtracted from the quotient of a number and -3 is at least -1​ is:</u></em>

\left(\frac{x}{-3}\right)-10\ge \:-1\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-27\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-27]\end{bmatrix}

<em><u>Solution:</u></em>

<em><u>Given statement is:</u></em>

10 subtracted from the quotient of a number and -3 is at least -1​

Quotient means reuslt of dividing two numbers

Let the number be "x"

quotient of a number and -3 = \frac{x}{-3}

Therefore,

10 subtracted from \frac{x}{-3} is at least -1

at least means "less than or equal to"

<em><u>Which is translated into algebraic expression as:</u></em>

(\frac{x}{-3}) - 10\geq -1

<em><u>Solve the above inequality</u></em>

\left(\frac{x}{-3}\right)-10\ge \:-1\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\\\\frac{x}{-3}-10+10\ge \:-1+10\\\\\mathrm{Simplify}\\\\\frac{x}{-3}\ge \:9\\\\Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)

When we multiply or divide by negative number. we have to flip the inequality sign

\frac{x\left(-1\right)}{-3}\le \:9\left(-1\right)\\\\\mathrm{Simplify}\\\\\frac{x}{3}\le \:-9\\\\\mathrm{Multiply\:both\:sides\:by\:}3\\\\\frac{3x}{3}\le \:3\left(-9\right)\\\\\mathrm{Simplify}\\\\x\le \:-27

Thus the solution of inequality is found

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