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4 years ago

#1 Determine if AB is tangent to the circle centered at point C. Explain your reasoning. * PLZ HELP

Mathematics

1 answer:

Hatshy [7]4 years ago

7 0

AB is a tangent to the circle

Solution:

Given data:

AB = 21, AC = 20 and BC = 29

To prove BC² = AB² + AC²:

BC² = 29²

BC² = 841

AB² + AC² = 21² + 20²

= 441 + 400

AB² + AC² = 841

So, BC² = AB² + AC².

Therefore by Pythagoras theorem, angle A is right angle.

Therefore AB is a tangent to the circle.

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Answer:

$\dfrac{1}{4}$

Step-by-step explanation:

Given information:

Total number of pupils = 20
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We can assume that 3 pupils play the flute <u>only</u> as we have also been told that 6 pupils play both instruments.

To calculate the probability that a randomly chosen pupil plays neither instrument, first determine how many pupils do not play an instrument by subtracting the number of pupils who do play an instrument from the total number of pupils:

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To calculate probability:

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Therefore:

$\implies \textsf{Probability of a pupil playing neither instrument} = \dfrac{5}{20}=\dfrac{1}{4}$

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

A fraction greater than one is an improper fraction.

$9\frac{3}{6}$ when converted into an improper fraction is

$9\frac{3}{6} =9+\frac{3}{6} \\\\=\frac{9*6}{6}+ \frac{3}{6}\\\\ =\frac{54}{6}+ \frac{3}{6}=\frac{57}{6}\\\\ =\boxed{\frac{19}{2}. }$

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$3\frac{4}{6}=3+\frac{4}{6}\\\\=\frac{3*6}{6}+ \frac{4}{\\\\6}\\\\=\frac{18}{6}+\frac{4}{6}=\frac{22}{6}\\\\=\boxed{\frac{11}{3}. }$

Thus fractions $9\frac{3}{6}$ and $3\frac{4}{6}$ when converted to fractions greater than one are $\frac{19}{2}$ and $\frac{11}{3}$ respectively.

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