what is the value of 6/15 ÷ 2/3? write your answer in simplest form​

First,

tan(θ) = sin(θ) / cos(θ)

and given that 90° < θ < 180°, meaning θ lies in the second quadrant, we know that cos(θ) < 0. (We also then know the sign of sin(θ), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < θ/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(θ/2) > 0 and sin(θ/2) > 0.

Now recall the half-angle identities,

cos²(θ/2) = (1 + cos(θ)) / 2

sin²(θ/2) = (1 - cos(θ)) / 2

and taking the positive square roots, we have

cos(θ/2) = √[(1 + cos(θ)) / 2]

sin(θ/2) = √[(1 - cos(θ)) / 2]

Then

tan(θ/2) = sin(θ/2) / cos(θ/2) = √[(1 - cos(θ)) / (1 + cos(θ))]

Notice how we don't need sin(θ) ?

Now, recall the Pythagorean identity:

cos²(θ) + sin²(θ) = 1

Dividing both sides by cos²(θ) gives

1 + tan²(θ) = 1/cos²(θ)

We know cos(θ) is negative, so solve for cos²(θ) and take the negative square root.

cos²(θ) = 1/(1 + tan²(θ))

cos(θ) = - 1/√[1 + tan²(θ)]

Plug in tan(θ) = - 12/5 and solve for cos(θ) :

cos(θ) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(θ/2) and tan(θ/2) :

sin(θ/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(θ/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

Answer: I would go towards B

Step-by-step explanation:

122/8 = 15.25

This is more towards 15, so put the dot in the middle of 14 and 16

Answer:

There is nothing here?

Step-by-step explanation:

Answer:

99.7%

Step-by-step explanation:

99.7% of boys fall between 61.5 and 76.5

The percentage of the boys that are between 61.5 and 76.5 inches tall is 99.73%

The given parameters are:

Start by calculating the z score for x = 61.5 and 76.5 using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So, we have:

[tex]z_1 = \frac{61.5 - 69}{2.5} = -3[/tex]

[tex]z_2 = \frac{76.5 - 69}{2.5} = 3[/tex]

The percentage is then represented as:

Percentage = P(-3 < x < 3)

Using the z table of probabilities, we have:

Percentage = 0.9973

Express as percentage

Percentage = 99.73%

Hence, 99.73% of the boys are between 61.5 and 76.5 inches tall

Read more about normal distribution at:

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Answer:

11. the first one 12. the last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

11 - the first option

12-the second option

Answer:

I hope this helps!!!

Step-by-step explanation:

Answer:

$5825000

Step-by-step explanation:

You just take 23.3% of the 25 million dollars silly.

Answer:

80 ppl have gray T-shirts

Step-by-step explanation:

Hope this helps!      :3

Plz mark as brainliest!

Answer:

Step-by-step explanation:

7x + 6 + 5

six and five both are regular numbers but the 7x is not like term

7x + 11

Answer:

$3.50

Step-by-step explanation:

14 is double 7

So the price should be double

1.75 x 2 = 3.5

(Assuming there's no base fee and the charge is purely for minutes)

Answer:

1 /3

≈0.333

Step-by-step explanation:

The representation which the arrow point out 0.666...

A number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.

given:

2/3+1 1/6-1/2

Taking LCM

=2*2/3*2+1 1/6-1*3/2*3

=4/6+7/6-3/6

=8/6

=2/3

=0.666...

So, the number that represent 0.666... is  not shown it should be a representation which the arrow point out 0.666...

Learn more about number line here:

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Answer:

C, if someone else gets the same answer as me then its right

Step-by-step explanation:

Answer:

Subsitute the known point: (-1,3)

y>-5x^4+ 7x^3 +8.

3> -5(-1)^4 + 7(-1)^3 + 8

3> -5(1) + 7(-1) + 8

3> -5 - 7 + 8

3 > -4

True

3 Is greater than -4.

Answer:

True

Step-by-step explanation:

Just got it right on edge!

Answer:

10

Step-by-step explanation:

5 x 2 = 10

Let's put it this way. 5 two times. 5 and 5. 5 + 5

Add them. you get 10.

Answer:

10, bro if you in college like the question says i feel bad for you. other wise you in 2nd grade.

Step-by-step explanation:

Step-by-step explanation:

AC B D

AD B C

A BC D

A BD C

hope it's right

Answer:

false right

Step-by-step explanation:

Answer:

Like the other person said there's 40 apples.

Step-by-step explanation:

but is there more to the question or..?

Correct question is;

Type the correct answer in the box bellow: If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is ...........

Answer:

x = 35°

Step-by-step explanation:

We are told that;

cos x = sin(20 + x)°

and 0° < x < 90°

From trigonometric identities, we know that;

cos x = sin (90 - x)

Applying to our question gives;

sin (90 - x) = sin (20 + x)°

Comparing both sides, we have;

90 - x = 20 + x

Rearranging;

90 - 20 = x + x

70 = 2x

x = 70/2

x = 35°

Answer:

-18.75 Meters

Step-by-step explanation:

0.75 x -25 = -18.75 Meters :D

Answer:

7/4 and 3

Step-by-step explanation:

It's a positive slope (sloping up and to the right).

If its sloping from quadrant 3 to 1, it's positive

Answer:

117

Step-by-step explanation:

Answer:

117

Step-by-step explanation:

2+2=4

45+68=113

113+4=117

Answer:

90 games

Step-by-step explanation:

Of the 120 games the football team played, they won 75% of them.

Remember that in mathematics, "of" almost always means to multiply. Here, that means we must multiply 75% by 120:

75% * 120

Remember also that % just means divided by 100, so 75% = 75 / 100. So:

75% * 120 = (75/100) * 120 = 9000/100 = 90 games

5 ln(x - 2) + 8 ln(x + 3) - 3 ln(x + 8)

ln(x - 2)⁵ + ln(x + 3)⁸ - ln(x + 8)³

since [tex]a\log_cb=\log_cb^a[/tex] (for any base c)

ln((x - 2)⁵ (x + 3)⁸ / (x + 8)³)

since [tex]\log_c(a)+\log_c(b)=\log_c(ab)[/tex] and [tex]\log_c(a)-\log_c(b)=\log_c\frac ab[/tex] (also for any base c)

Answer:

Step-by-step explanation:

Let the length of the string be x: