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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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Paul and Charlene are 420 miles apart. They start toward each other with Paul driving 16 mph faster than Charlene. They meet in

Thepotemich [5.8K]

Answer:

34 mph.

Step-by-step explanation:

Let x be speed of Charlene, then speed of Paul will be x+16 as we are given that Paul is driving 16 mph faster than Charlene.

Let y be distance covered by Charlene, then distance covered by Paul will be 420-y.

Now we will use formula $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$ . Upon using our given information we will get two equation and two unknowns as:

$x+16=\frac{420-y}{5}...(1)$

$x=\frac{y}{5}...(2)$

Upon substituting $x=\frac{y}{5}$ in 1st equation we will get,

$\frac{y}{5}+16=\frac{420-y}{5}$

Upon multiplying both sides of our equation by 5 we will get,

$5(\frac{y}{5}+16)=420-y$

$5\times\frac{y}{5}+5\times 16=420-y$

$y+80=420-y$

$y+80+y=420-y+y$

$2y+80=420$

$2y=420-80$

$2y=340$

$y=\frac{340}{2}$

$y=170$

Upon substituting y=170 in 2nd equation we will get,

$x=\frac{170}{5}$

$x=34$

Therefore, Charlene's speed is 34 miles per hour.

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3 years ago

5+2 root 3 / 7+4 root 3 =a-6root3

STALIN [3.7K]

Answer:

Step-by-step explanation:

$\dfrac{5+2\sqrt3}{7+4\sqrt3}\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{5+2\sqrt3}{7+4\sqrt3}\cdot\dfrac{7-4\sqrt3}{7-4\sqrt3}=\dfrac{(5+2\sqrt3)(7-4\sqrt3)}{7^2-(4\sqrt3)^2}\qquad\text{use FOIL}\\\\=\dfrac{(5)(7)+(5)(-4\sqrt3)+(2\sqrt3)(7)+(2\sqrt3)(-4\sqrt3)}{49-4^2(\sqrt3)^2}\\\\=\dfrac{35-20\sqrt3+14\sqrt3-8(3)}{49-(16)(3)}=\dfrac{(35-24)+(-20\sqrt3+14\sqrt3)}{49-48}\\\\=\dfrac{11-6\sqrt3}{1}=11-6\sqrt3$

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3 years ago

Which inequality is true 1.5 > 2 1/2, 1/2 > 0.5, -2.5 > -1.5, -3 1/2 > - 4.5

yawa3891 [41]

Answer: D

Step-by-step explanation:

(A. 1.5 > 2 1/2

(B. 1/2 > 0.5

(C. -2.5 > -1.5

(D. -3 1/2 > - 4.5

Step 1: Convert everything to decimals or fractions so its easier to see and make it less likely to get the question wrong

Method #1: Fractions

1.5= 1 1/2

0.5= 1/2

-2.5= - 2 1/2

-1.5= - 1 1/2

-4.5= -4 1/2

Now we have:

(A. 1 1/2 > 2 1/2 --> This is wrong because 1 1/2 is supposed to be less than 2 1/2.

(B. 1/2 > 1/2 This is also wrong. 1/2 is equal to 1/2; they are obviously the same.

(C. -2 1/2 > -1 1/2 This is wrong because, in negative numbers, its sort of backwards. For example, -2 is actually less than -1 because its farther away from 0. But if they were normal positive numbers, 2 would be bigger. But here, -2 1/2 is less than -1 1/2.

(D. -3 1/2 > - 4 1/2 This is correct. -3 1/2 is closer to 0 than -4 1/2, so it has to be bigger.

Solving the problem this way gets me to: Answer= D

Method #2: Decimals (remember: same numbers, different way of writing them!!!)

(A. 1.5 > 2.5 False. 1.5 is less than 2.5

(B. 0.5 > 0.5 False. 0.5 is equal to 0.5

(C. -2.5 > -1.5 False. -2.5 is farther away from 0 so its actually smaller.

(D. -3.5 > - 4.5 True. -3.5 is closer to 0.

Doing it this way also leads me to Answer= D.

Hope this helps :)) Also can i please have brainiest? I worked pretty hard on this :D

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Dive your answer by three so 9.60/3 = 3.20 or £3.20

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3 years ago

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Hello, I'll try to make this as easy to understand as possible, anyways, let's begin:

First, we know that 3 is a bigger number than 2 1/2, and since it's negative, it means they lost weight, therefore...

Jenna lost more weight than Sarah.

Hope this helped! c:

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3 years ago