Please Help!
Find tan x/2, given sin x = 3/5, with 90° < Θ < 180°

Answers

Answer 1

we know the angle is between 90° and 180°, 90° < θ < 180°, that means the angle is in the II Quadrant, where the sine is positive and the cosine is negative, with that info, let's find check a few things

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2 - 3^2}=a\implies \pm\sqrt{16}=a\implies \pm 4 = a\implies \stackrel{II~Quadrant}{-4=a} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}} \\\\\\ tan\left(\cfrac{\theta}{2}\right)\implies \cfrac{sin(\theta)}{1+cos(\theta)}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{1-\frac{4}{5}}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{\frac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{5}{1}\implies 3[/tex]


Related Questions

A rectangular room has a length of 16 ft and a diagonal of 22 ft. What is the approximate
width of the room?

Answers

Answer:

no

Step-by-step explanation:

Answer: 15.09967ft

Step-by-step explanation: w=d2﹣l2=222﹣162≈ hope this helps ^^

(50 POINTS! PLEASE HELP!) Alang has a bag that contains pineapple chews, strawberry chews, and lime chews.
He performs an experiment. Alang randomly removes a chew from the bag, records
the result, and returns the chew to the bag. Alang performs the experiment 26 times.
The results are shown below:
A pineapple chew was selected 20 times.
A strawberry chew was selected 4 times.
A lime chew was selected 2 times.
Based on these results, express the probability that the next chew Alang removes
from the bag will be lime chew as a fraction in simplest form.

Answers

Answer:

1/13

Step-by-step explanation:

Probability (lime chew) :

No. of times lime chew was selected / Number of times experiment was conducted2/261/13

The probability that the next chew Alang removes from the bag will be lime chew is 1/13.

What is probability?

The likelihood or chance of an event occurring is quantified by probability. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.

For instance, there is only one outcome (rolling a "6") that result in the desired event, hence the chance of rolling a "6" on a fair six-sided die is 1/6. (rolling a "6"). , there is a 1/6 chance of rolling any other number.

By dividing the number of times a lime chew was chosen by the total number of trials, the likelihood of choosing a lime chew could be computed (26).

The likelihood of choosing a lime chew is; 2/26, which reduces to 1/13 in basic form.

Therefore, 1/13 is the probability.

To know more about probability visit:

brainly.com/question/13604758

#SPJ2

Pls help urgent i will marke the brainlist

Answers

Answer:

Yes, because 8n + 4 = 4(2n + 1) because of the distributive property. And about the 4 = 52 - 8n, that is also equivalent to the rest of them because of the associative property.

OR

You could just solve the math and show that they are equivalent.


In the figure below, QRT and SRV are complementary.
What is the value of x?

Answers

[tex]\bold{ANSWER:}[/tex]
x = 40

[tex]\bold{SOLUTION:}[/tex]

can anyone help plssss??

Answers

Answer:

42 degrees

Step-by-step explanation:

48+90=138

180-138=42

What is the value of this expression?

48−{(18+12)÷6}×2


8

14

38

86

Answers

The answer is-38Step-by-step explanation:48−30÷6×248−5×248−1038

If you complete the square in the quadratic equation ​, you get the quadratic formula for the solutions x ​_______.

Answers

Answer:

[tex]D. \ \ x=\frac{-b\pm \sqrt{b^{2}-4ac} }{2a}[/tex]

Step-by-step explanation:

ax² + bx + c = 0

[tex]a\left( x^{2}+\frac{b}{a} x+\frac{c}{a} \right) =0[/tex]

[tex]a\left( \left( x+\frac{b}{2a} \right)^{2} -\frac{b^{2}}{4a^2}+\frac{c}{a} \right) =0[/tex]

[tex]a\left( \left( x+\frac{b}{2a} \right)^{2} -\frac{b^{2}-4ac}{4a^2}\right) =0[/tex]

[tex]a\left( x+\frac{b}{2a} \right)^{2} -\frac{b^{2}-4ac}{4a}=0[/tex]

[tex]a\left( x+\frac{b}{2a} \right)^{2} =\frac{b^{2}-4ac}{4a}[/tex]

[tex]\left( x+\frac{b}{2a} \right)^{2} =\frac{b^{2}-4ac}{4a^2}[/tex]

[tex]x+\frac{b}{2a} =\frac{\pm \sqrt{b^{2}-4ac} }{2a}[/tex]

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac} }{2a}[/tex]

What is the equation of the line written in slope-intercept form that passes through the point (-1, 5) and is parallel to the line y = -2x – 5?

Answers

Answer:

Step-by-step explanation:

y - 5 = -2(x + 1)

y - 5 = -2x - 2

y = -2x + 3

How many fluid ounces are there in 3 pints and 8 fluid ounces?

Answers

Answer:

56

Step-by-step explanation:

((3*2)+1)*8

Answer:

1 pint equals 16 ozs. so the answer in 48

2 There are 40 students in class six. 30% of them are girls. (i) How many are girls? (ii) How many are boys? ​

Answers

Answer:

12 girls

28 boys

Step-by-step explanation:

Multiply 40 by 30/100 to get 12 girls.

Subtract 12 from 40 to get 28 boys.



Jackie is a student of UEW. This year, her age is a multiple of 6. Next year, her age will be a multiple of 5. If Jackie is younger than 40, how old will she be next year? ​

Answers

Using the multiples of 5 and 6, it is found that she will be 25 years old next year.

What are the multiples of 5 and 6?

They are given as follows, considering numbers less than 40:

M(5) = {0, 5, 10, 15, 02, 25, 30, 35}.M(6) = {0, 6, 12, 18, 24, 30, 36}.

This year, her age is a multiple of 6. Next year, her age will be a multiple of 5, hence, her age next year is a multiple of 5, whose predecessor is a multiple of 6, hence the only option is that she will be 25 years old next year.

More can be learned about multiples at https://brainly.com/question/251701

#SPJ1

Laticia randomly selected 25% of the seventh grade students in her school and asked them what their favorite season was. Of the students surveyed, 51 chose summer as their favorite season. Based on this data, approximately how many seventh grade students in the whole school?

Answers

Answer:

1000

Step-by-step explanation:

please find the value of x .​

Answers

Step-by-step explanation:

that was just answered with the last question, where you asked for the help here ...

x = 50°.

If 5 times a certain number is 40, and 9 times the same number is 72, how would you find 59 times that number? A)400 + 72 B)40 + 72 C)40 × 72 D)400 + 720 pls tell answer urgently.​

Answers

Answer:

A) 400 + 72

Step-by-step explanation:

Let the certain number be denoted by x.

⇒ 5x = 40 [Equation 1]

⇒ 9x = 72 [Equation 2]

Multiply Equation 1 by 10 :

⇒ 10(5x) = 40(10)

⇒ 50x = 400 [Equation 3]

Finding the sum of Equation 2 and Equation 3 :

⇒ 50x + 9x = 400 + 72

⇒ 59x = 400 + 72

Hence, 59 times a certain number is represented by : 400 + 72

what is the positive solution of 3x^2-10-8=0?

Answers

Answer:

x=4

Step-by-step explanation:

I'm going to assume the question has a typo and that the question is actually [tex]3x^2 -10x-8=0[/tex].

You can simplify this to:

[tex](3x+2)(x-4)=0[/tex]

This leaves the solutions [tex]x=-\frac{2}{3}[/tex] and x=4

The only positive solution therefore is x=4

Answer:

The answer is 4

Step-by-step explanation:

Use the improved quadratic formula (https://socratic.org/algebra/quadratic-equations-and-functions/quadratic-formula)

D=d^2=b^2-4ac=100+96=196⇒d±14

There are 2 real roots: x=-b/2a±d/2a=10/6±14/6=5/3±7/3

The positive real root is : 12/3=4

You had $21 to spend on eight notebooks. After buying them you had $5. How much did each notebook cost?

Answers

Answer:

each notebook costs $2

Step-by-step explanation:

21-5=16/8=$2

Each notebook cost $2

Write a​ slope-intercept equation for a line that passes through (-3, 5.5) and (0, 5.5)

The​ slope-intercept equation for the line is
​(Use integers or decimals for any numbers in the​ equation.)

Answers

Answer:

y-5.5=0 * (x+3)

Step-by-step explanation:

Need help please and thank you

Answers

Answer:

no thank you

Step-by-step explanation:

lol good day

C is the correct function

Please help need urgent

Answers

Convert the cm to feet for the base and the height:

12/2 = 6 x 3 = 18 feet

9/2 = 4.5 x 3 = 13.5 feet


area = 1/2 x base x height

Area = 1/2 x 18 x 13.5

Area = 121.5 square feet


answer: 121.5 square feet

Davis paid $250 for a sneaker and there is a 33% advertised discount. How much is the discount?

Answers

25 is the discount in this equation

Answer:

152.5

Step-by-step explanation:

I think that might be the answer ( im not that good at math )

2 How many 1.2-kg books can you pack into a suitcase so that the total weight does not exceed 36 kg?​

Answers

Answer:

30 books

Step-by-step explanation:

36 / 1.2 = 30

You can pack 30 books and it will not exceed 36 Kg.

- - -

Side Note:

We don't know how heavy the suitcase is...

Is it impossible, unlikely, likely, or certain that you will blink in the next two minutes?​

Answers

Answer:

you would have to very good at not blinking to but if your not I suggest not to because it will hurt also why not try to test it out ;)

Step-by-step explanation:

once again you can earn free easy points just by answering this simple question :)

Answers

Answer:

D Rotainon.

Step-by-step explanation:

The shape is flipped.

Math help can’t solve please

Answers

Answer:

See below

Step-by-step explanation:

a) 43.8 - 38 = 5.8 yrs

b) SD = 8.9 yrs    5.8 / 8.9 = .6517 SD   below the mean

(A z score merely shows how many standard deviations a score (age) is above or below the mean in SD units)

c) Z =     - .6517     Negative because it is BELOW the mean                                                                                   ( FYI    from z-score table: this is .2578  in percentage )

d) usual       ( it  (-.6517)  is between -2   and + 2  )

Find the value of y…

Answers

Answer:

     y = 94

Step-by-step explanation:

Linear Pair:

The two adjacent angles whose non common arms form a straight line is called linear pair. They add up to 180

2x + 36 = 180 {linear pair}

       2x  = 180 - 36

       2x = 144

        2x = 144°

Sum of all angles of a n-sided polygon = (n-2)*180

                                                                 = ( 6-2)*180

                                                                 = 4 * 180

                                                                  = 720

y + 144 + 111 + 105 + 165 + 101 = 720

                                  y + 626  = 720

                                             y = 720 - 626

                                            [tex]\sf \boxed{y = 94^ \circ}[/tex]

Answer:

94°

Step-by-step explanation:

2x + 36 = 180 (angles on a straight line)

2x = 180 - 36

2x = 144

2x = 144°

Sum of all angles of a n-sided polygon = (n-2)×180 = ( 6-2)×180

= 4 × 180

= 720

y + 144 + 111 + 105 + 165 + 101 = 720

y + 626 = 720

y = 720 - 626

y=94 °

HELP WITH PROB AND STATS

Use the given data to find the best predicted value of the response variable.

Six pairs of data yield r= 0.344 and the regression equation y = 5x + 2. Also, y = 18.3
What is the best predicted value of y for x = 5? Use a = 0.05.

Answers

Sub in x = 5 into the equation y = 5x + 2. If you do that you should get a y-value of about 27.

I need help please ASAP??!!

Answers

Answer:

i got you the answer is .....

Step-by-step explanation:

there you go

need help with my aleks

Answers

Answer:

Below in bold,

Step-by-step explanation:

The angles in a triangle add up to 180 degrees.

So the equation is:

7x + 8 + 4x + x + 4 = 180

12x + 12 = 180  <-------- Required equation

12x = 168

x = 14.

m< L = 14 + 4 = 18 degrees

m< M = 7(14) + 8 = 106 degrees

m< N = 4(14)= 56 degrees

Paul reads on a map that 1 inch represents 7 miles. He measures the distance between two spots to be 8.5 inches. What is the real distance?

Answers

Answer:

59.5 miles

Step-by-step explanation:

1 in = 7 mi

7 x 8.5 = 59.5

The ages of Charlotte and Olivia are in the ratio 6:10. After 10 years, their ratio will become 4:6. Find their ages.

Answers

Answer:

Charlotte's age = 30 years

Olivia's age = 50 years

Step-by-step explanation:

Present ages of Charlotte & Olivia = 6:10.

Then, their present ages are:

Charlotte = 6x

Olivia = 10x

Now, in 10 years, their ratio = 4:6

Then,

Ratio of Charlotte's & Olivia's present age + 10 years each = Ratio of their ages in 10 years

[tex]\frac{6x + 10}{10x + 10} = \frac{4}{6} \\6(6x + 10) = 4 (10x + 10) \: \: \: \: [\mathrm{cross\: multiplication}]\\36x + 60 = 40x + 40\\36x - 40x = 40 - 60\\4x = 20\\\boxed{\bf\:x = 5}[/tex]

So,

Charlotte's present age [tex]= 6x = 6(5) = {\boxed{\bf\:30 \:years}[/tex]

Olivia's present age = [tex]10x = 10(5) = \boxed{\bf\:50 \: years}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

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