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3 years ago

Triangle ABC is equilateral. Find the length of CD .

Mathematics

2 answers:

lilavasa [31]3 years ago

7 0

Answer:

CD = 5.20 units to the nearest hundredth.

Step-by-step explanation:

Triangle BCD is a right angled triangle with m < C = 60 degrees (because triangle ABC is equilateral).

tan 60 = 9/CD

CD = 9 / tan 60

= 5.196.

goldenfox [79]3 years ago

4 0

Answer:

The answer to your question is: CD = 5.2 units

Step-by-step explanation:

ΔABC is equilateral, then its angles are 60°, 90° and 30°

∠C = 60°

sin 60° = 6 / hypotenuse

hypotenuse = BC = 9 / sin 60

BC = 6.9

tan 60 = 9/ CD

CD = 9 / tan 60

CD = 5.2 u

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

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musickatia [10]

Answer:

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Step-by-step explanation:

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3 years ago

What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16

blsea [12.9K]

Answer:

Step-by-step explanation:

$Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================$

$\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}$

$\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}$

$4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D$

8 0

3 years ago

How is a rational number converted to its decimal form?

luda_lava [24]

Answer:

Answer to first question is:

You can convert all fractions to decimals. The decimal forms of rational numbers either end or repeat a pattern. If the fraction is a mixed number, change it to an improper fraction. Divide the numerator by the denominator. If the division doesn't come out evenly, round the decimal off.

Answer to second question is: 0.222222

Answer to third question is: Yes

Step-by-step explanation:

Well the way I think of it is:

3/9 as a fraction is 1/3... so 1 divided by 3 equals 0.333333 repeating. You can even write it as:

0.3 with the fraction bar over it because it keeps repeating.

This goes for 2/9. All you have to do is do 2 divided by 9 and you get 0.222222 repeating. You can even write it as:

0.2 with the fraction bar over it because it keeps repeating.

Hope this helps, have a good day. c;

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3 years ago