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1 year ago

The triangle below is equilateral. Find the length of side xx in simplest radical form with a rational denominator.

Mathematics

1 answer:

mylen [45]1 year ago

6 0

The length of side x in simplest radical form with a rational denominator is 8√3

<h3>How to find the length of side x in simplest radical form with a rational denominator?</h3>

The given parameters are:

Triangle type = Equilateral triangle

Height (h) = 12

Missing side length = x

The missing side length, x is calculated using the following sine ratio

sin(60) = Height/Missing side length

This gives

sin(60) = 12/x

Make x the subject of the formula

So, we have

x = 12/sin(60)

Evaluate the quotient

So, we have

x = 12/(√3/2)

This gives

x = 24/√3

Rationalize

x = 24/√3 * √3/√3

Evaluate

x = 8√3

Hence, the length of side x in simplest radical form with a rational denominator is 8√3

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Ebony earned scores of 72 70, 81, 99, and 88 on five math tests. Determine her

Minchanka [31]

Let it be x

$\boxed{\sf Average=\dfrac{Sum\:of\:terms}{No\:of\:terms}}$

$\\ \sf\longmapsto \dfrac{72+70+81+99+88+x}{6}=83$

$\\ \sf\longmapsto \dfrac{410+x}{6}=83$

$\\ \sf\longmapsto 410+x=498$

$\\ \sf\longmapsto x=498-410$

$\\ \sf\longmapsto x=88$

6 0

3 years ago

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probabili

svlad2 [7]

Critical probability is the essentially cut-off value. The critical probability when the confidence level of 58% is 0.79.

<h3>What is the critical probability?</h3>

Critical probability is the essentially cut-off value that defines the region where the test statistic is unlikely to lie.

As it is given that the confidence level is 58%. therefore, in order to calculate the critical probability, we need to calculate the margin of error within a set of data, and it is given by the formula

$\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}$

where the value of the α is expressed as,

$\alpha= 1 -\dfrac{\rm Confidence\ interval}{100}$

Now, as the confidence interval is given to us, therefore, the value of the alpha can be written as,

$\alpha= 1 -\dfrac{\rm 58\%}{100} = 0.42$

Further, the critical probability, assuming a confidence level of 58% is,

$\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\\\\\rm Critical\ Probability, (P*) = 1-\dfrac{0.42}{2} = 0.79$

Hence, the critical probability is 0.79.

Learn more about Critical Probability:

brainly.com/question/5625386

6 0

2 years ago

A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. how soon did the second train overta

Finger [1]

<span>1st train DATA:
rate = 50 mph ; time = x hrs ; distance = rt = 50x miles

2nd train DATA:
rate = 55 mph ; time = (x-(1/2)) hrs ; distance = rt = 55(x-(1/2)) miles

Equation:
distance = distance
50x = 55(x-(1/2)
50x = 55x - (55/2)
-5x = -55/2
x = 11/2
x = 5 1/2 hrs (time at which the 2nd train overtakes the 1st train)
Hope this helps!</span>

8 0

3 years ago

Read 2 more answers

HELP ME PLZ

nadezda [96]

Answer:

BD does bisect the angle created by ABC, however it does not bisect segment AC. So it really depends on what you are determining the bisection to be.

Step-by-step explanation:

We can tell that it is bisecting the angle since it creates two congruent angles.

We can tell that it does not bisect the segment as AD and CD are not the same length.

5 0

3 years ago