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3 years ago

What is the equation of this graphed line?

Mathematics

1 answer:

barxatty [35]3 years ago

4 0

Answer:

$y=-\frac{1}{3}x-5$

Step-by-step explanation:

Given:

The two points on the line are:

$(x_1,y_1)=(-6,-3)\\(x_2,y_2)=(6,-7)$

Now, for a line with two points on it, the slope of the line is given as:

$m=\frac{y_2-y_1}{x_2-x_1}$

For the points $(x_1,y_1)=(-6,-3)\ and\ (x_2,y_2)=(6,-7)$ , slope is:

$m=\frac{-7-(-3)}{6-(-6)}\\m=\frac{-7+3}{6+6}\\m=\frac{-4}{12}=-\frac{1}{3}$

Now, for a line with slope 'm' and a point $(x_1,y_1)$ on it is given as:

$y-y_1=m(x-x_1)$

Plug in all the values and determine the equation of the line. This gives,

$y-(-3)=-\frac{1}{3}(x-(-6))\\\\y+3=-\frac{1}{3}(x+6)\\\\y+3=-\frac{1}{3}x-\frac{1}{3}\times 6\\\\y+3=-\frac{1}{3}x-2\\\\y=-\frac{1}{3}x-2-3\\\\y=-\frac{1}{3}x-5$

Therefore, the equation of the line is:

$y=-\frac{1}{3}x-5$

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Which set of ordered pairs represents a function?

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{(-1,0),(-8, 9), (7,0), (1,3)}

Step-by-step explanation:

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3 years ago

About 5% of the population has a particular genetic mutation. 300 people are randomly selected.

xz_007 [3.2K]

The standard deviation for the number of people with the genetic mutation is 3.77

<h3>How to determine the standard deviation?</h3>

The given parameters are:

Sample size, n = 300

Proportion that has the particular genetic mutation, p = 5%

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation = √np(1 - p)

Substitute the known values in the above equation

Standard deviation = √300 * 5% * (1 - 5%)

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Standard deviation = 3.77

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2 years ago

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Answer:

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Step-by-step explanation:

You can observe the sides of both triangles to see if this property holds

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Now check the length of the corresponding side DE

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3 years ago

Write any 4 laws of exponents.<br>

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$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Write any 4 laws, or properties, of exponents.</em>

<em />

<em> </em> $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

$\Large\text{Law number 1:-}$

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$\Large\text{It states that:-}$

When we multiply together numbers with the same base,

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$\Large\text{Law number 2:-}$

$\Large\text{$a^m:a^n=a^{m-n}$}$

$\Large\text{It states that:-}$

When we divide numbers with the same base, we

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$\Large\text{Law number 3:-}$

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$\Large\text{It states that:-}$

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And then last but not least,

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$\Large\text{It states that:-}$

If we have a number with a negative exponent, we flip it over.

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

$\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}$

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2 years ago

Read 2 more answers

If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal

lorasvet [3.4K]

Answer:

The percentage is

$P(x_1 < X < x_2 ) = 51.1 \%$

The probability is $P(Z > 2.5 ) = 0.0062097$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 800$

The variance is $var(x) = 1600 \ kg$

The range consider is $x_1 = 778 \ kg \ x_2 = 834 \ kg$

The value consider in second question is $x = 900 \ kg$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{var (x)}$

substituting value

$\sigma = \sqrt{1600}$

$\sigma = 40$

The percentage of a cucumber give the crop amount between 778 and 834 kg is mathematically represented as

$P(x_1 < X < x_2 ) = P( \frac{x_1 - \mu }{\sigma} < \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma } )$

Generally $\frac{X - \mu }{ \sigma } = Z (standardized \ value \ of \ X)$

$P(x_1 < X < x_2 ) = P( \frac{778 - 800 }{40} < Z< \frac{834 - 800 }{40 } )$

$P(x_1 < X < x_2 ) = P(z_2 < 0.85) - P(z_1 < -0.55)$

From the z-table the value for $P(z_1 < 0.85) = 0.80234$

and $P(z_1 < -0.55) = 0.29116$

$P(x_1 < X < x_2 ) = 0.80234 - 0.29116$

$P(x_1 < X < x_2 ) = 0.51118$

The percentage is

$P(x_1 < X < x_2 ) = 51.1 \%$

The probability of cucumber give the crop exceed 900 kg is mathematically represented as

$P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x - \mu }{\sigma } )$

substituting values

$P(X > x ) = P( \frac{X - \mu }{\sigma } >\frac{900 - 800 }{40 } )$

$P(X > x ) = P(Z >2.5 )$

From the z-table the value for $P(Z > 2.5 ) = 0.0062097$

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3 years ago