Solve for x
2(x - 5) = 24

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

Step-by-step explanation:

AC B D

AD B C

A BC D

A BD C

hope it's right

Answer:

Like the other person said there's 40 apples.

Step-by-step explanation:

but is there more to the question or..?

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:

https://brainly.com/question/4079902

#SPJ9

9514 1404 393

Answer:

  (d)  Q(1, −7), S(−2, 3)

Step-by-step explanation:

Reflection across the x-axis negates the y-coordinate:

  (x, y) ⇒ (x, -y) . . . . reflection across the x-axis

Then we have ...

  P(1, 7) ⇒ Q(1, -7)

  R(-2, -3) ⇒ S(-2, 3)

These coordinates match the last choice.

Answer:

-18.75 Meters

Step-by-step explanation:

0.75 x -25 = -18.75 Meters :D

Answer:

I hope this helps!!!

Step-by-step explanation:

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:

One x input cannot have two or more resulting y outputs

Step-by-step explanation:

That's why we use the vertical line test to see if there's two y vales for a corresponding x value, hope that helped

Answer:

 The  decision rule is  

Reject the null hypothesis

   The conclusion is

There sufficient evidence that the true mean disclosure score of all adolescents will exceed 3

Step-by-step explanation:

From the question we are told that  

      The sample is  n  =  224

      The  sample mean is [tex]\= x = 3.38[/tex]

      The standard deviation is  [tex]s = 0.98[/tex]

      The population mean is [tex]\mu = 3[/tex]

       The level of significance  is  [tex]\alpha = 0.05[/tex]

The null hypothesis is  [tex]H_o : \mu = 3[/tex]

The alternative hypothesis is  [tex]H_a : \mu > 3[/tex]

Generally the test statistics is mathematically represented as

          [tex]z = \frac{ \= x - \mu }{ \frac{s}{ \sqrt{n} } }[/tex]

=>       [tex]z = \frac{ 3.38 - 3 }{ \frac{0.98 }{ \sqrt{224} } }[/tex]

=>       [tex]z = 5.80[/tex]

From the z table  the area under the normal curve to the right corresponding to 5.80  is

        [tex]p-value = 0[/tex]

From the value obtained we that [tex]p-value < \alpha[/tex] , hence  

   The  decision rule is  

Reject the null hypothesis

   The conclusion is

There sufficient evidence that the true mean disclosure score of all adolescents will exceed 3

Answer:

C. x = √61

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to solve for the missing length.

Step 2: Identify Variables

Leg a = 6

Leg b = 5

Hypotenuse c = x

Step 3: Solve for x

Answer: 61

Step-by-step explanation:

25+36=x

61=x

x=61

Answer:

[tex]f(x) = \frac{x + 1}{4}[/tex]

Step-by-step explanation:

To inverse the function switch the places of x and y like this:

x = 4y - 1

Now, solve for y:

[tex]x + 1 = 4y\\\frac{x + 1}{4} = y[/tex]

It's that easy!

I hope this helps!!

- Kay :)

Answer:

I think that it would be 9 because it is less than ten and can be divided equally by 3.

Step-by-step explanation:

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

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:

There is nothing here?

Step-by-step explanation:

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) 11

2) 15

Step-by-step explanation:

The bars on the sides of the numbers represent the absolute value/magnitude of the number, so you will need to remove the negative symbol if it is present in front of the number (if it is already a positive number, leave it as it is).

Example:

[tex]|-3+2| = |-1|[/tex]

[tex]= 1[/tex]

Hope this helps :)

Answer:

32x^2+68x+21

Step-by-step explanation:

Answer:

32x^2+68x+21

Step-by-step explanation:

This is right just did this!!

Answer:

140

Step-by-step explanation:

300-20=280

280 divided by 2

140

Answer:

140 is your answer

Step-by-step explanation:

Let the parts be 2x, 3x and 5x.

Sum= 25000

Therefore,2x+3x+5x=25000

10x=25000

x=25000/10

x=2500

Therefore, parts:-

1. 2×2500=5000

2. 3×2500=7500

3. 5×2500=12500

Answer:

5000, 7500, 12500

Step-by-step explanation:

[tex]2 + 3 + 5 = 10[/tex]

[tex]25000[/tex] ÷ [tex]10[/tex] = [tex]2500[/tex]

[tex]2500[/tex] × [tex]2 = 5000[/tex]

[tex]2500[/tex] × [tex]3 = 7500[/tex]

[tex]2500[/tex] × [tex]5 = 12500[/tex]

[tex]\therefore[/tex] [tex]25000[/tex] will split into [tex]5000[/tex], [tex]7500[/tex], and [tex]12500[/tex].

To check if the answer is correct, you can add the values up and see if they sum up to [tex]25000[/tex]:

[tex]5000 + 7500 + 12500 = 25000[/tex]

Hope this helps :)

Answer:

false right

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

3x² + 8 = 83

3x² = 83 - 8

3x² = 75

x² = 75/3

x² = 25

x = √25

x = 5

-TheUnknownScientist

Answer:

x =5

Step-by-step explanation:

3x²+8=83

3x²=83-8

3x²=75

x²=75

3

x²=25

x=√25

x=5

hope it help u.

Answer:

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

Step-by-step explanation:

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: