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3 years ago

Use substitution to solve the linear system of equations

Mathematics

1 answer:

xenn [34]3 years ago

4 0

we are given

system of equations

$y=4x$

$3x+5y=-46$

we can plug first equation into second equation

we get

$3x+5(4x)=-46$

Simplify left side

$3x+20x=-46$

$23x=-46$

Divide both sides by 23

and we get

$x=-2$

now, we can find y-value

$y=4*-2$

$y=-8$

so, our solution is

$(x,y)=(-2,-8)$ .............Answer

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Sebastian observed the number of minutes his dormmates spent on social media sites while they were at the library. He reported h

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4 years ago

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Prove that the circumcenter of a triangle is equidistant from its vertices.

ruslelena [56]

Answer:

Step-by-step explanation:

The circumcenter is equidistant from the three vertices of the triangle. From the figure shown, we will prove DA = DB = DC. 2) DA = DB, DC = DB(If a point is on the perp. bisector of a segment, it is equidistant from each endpoint of the segment.)

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3 years ago

Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if c

Vlad [161]

Answer:

The t-statistic that Jacob calculates is $t = -2.71$

Step-by-step explanation:

Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population.

At the null hypothesis, we test if the mean is of 8 hours, that is:

$H_0: \mu = 8$

At the alternative hypothesis, we test if the mean is different of 8 hours, that is:

$H_1: \mu \neq 8$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

8 is tested at the null hypothesis:

This means that $\mu = 8$

From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.

This means that $n = 101, X = 7.3, s = 2.6$

What is the t-statistic that Jacob calculates?

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}$

$t = -2.71$

The t-statistic that Jacob calculates is $t = -2.71$

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3 years ago

Help<br> This is big<br> Plsss

Sauron [17]

Answer:

The answer for this would be:

Sin P = Opp/Hyp

Sin P = 55/73

Answer = 55/73

<h2>Please mark my answer as brainliest for further answers :)</h2>

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3 years ago

Which category best describes this group of shapes?

Effectus [21]

Answer:

I think it's parallelograms.....

Step-by-step explanation:

Parallelograms; a four-sided plane rectilinear figure with opposite sides parallel.

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3 years ago