Given:
[tex]\sin x=-\dfrac{15}{17}[/tex]
x lies in the III quadrant.
To find:
The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].
Solution:
It is given that x lies in the III quadrant. It means only tan and cot are positive and others are negative.
We know that,
[tex]\sin^2 x+\cos^2 x=1[/tex]
[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]
[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]
[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]
x lies in the III quadrant. So,
[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]
[tex]\cos x=-\dfrac{8}{17}[/tex]
Now,
[tex]\sin 2x=2\sin x\cos x[/tex]
[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]
[tex]\sin 2x=-\dfrac{240}{289}[/tex]
And,
[tex]\cos 2x=1-2\sin^2x[/tex]
[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]
[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]
[tex]\cos 2x=\dfrac{289-450}{289}[/tex]
[tex]\cos 2x=-\dfrac{161}{289}[/tex]
We know that,
[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]
[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]
[tex]\tan 2x=\dfrac{240}{161}[/tex]
Therefore, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].
A rectangular prism has a volume of 175 in'. The height of the prism is 7 in. The base is a square. What is the length of a side of the base? please help
Answer:
a=5cm
Step-by-step explanation:
V=B*H
You will get base if you do this:
B=V:H
B=175:7
B=25
I'm not so good with English, side is probably a,so:
Formula for base: B=a²
Then a=√B
a=√25
a=5cm
I hope this helps.
A CD usually sells for $18.00. If the CD is 10% off, and sales tax is 7%, what is the total price of the CD, including tax?
A. $18.30
B. $17.33
C. $17.46
D. $17.50
Answer:
b
Step-by-step explanation:
Tell whether the angles are complementary or supplementary. Then find the value of $x$ . A ray intersects two other rays forming a right angle. The angles formed after the intersection is x degrees and left parenthesis x minus 20 right parenthesis degrees.
The measure of the value of x is 55°.
We have,
Complementary angles are two angles that add up to 90 degrees.
Supplementary angles are two angles that add up to 180 degrees.
Now,
The ray intersects two other rays forming a right angle.
This means,
It is a complementary angle.
i.e
x + (x - 20) = 90
x + x - 20 = 90
2x = 90 + 20
2x = 110
x = 55°
Thus,
The measure of the value of x is 55°.
Learn mroe about complementary angles here:
https://brainly.com/question/15380971
#SPJ12
if it is exactly 8:00, How long does it take for the hands of the clock to be pointed in the same direction
Answer:
Hey! do not go to brainly for this, sometimes brainly can be no help and people will scam for points, or maybe try to hack you (pt virus) with those links saying the answers there.. I am not saying this for points but go to https://www.varsitytutors.com/basic_geometry-help/how-to-find-the-distance-between-clock-hands for that
Step-by-step explanation:
So don't waste your time on brainly finding answers, you can run out of points fast, some people wont answer at all.
HELP ASAP THIS IS DUE IN A LIVE CLASS DONT GUESS ITS QUESTION 4
Answer:
2 answers
Step-by-step explanation:
factor: 2π(hr+π)
evaluate: 2π(hr+π)
hope that helps
53+2444= ??????? HELP I D K THE ANSWER
Answer:
2497
Step-by-step explanation:
Answer:
2497
Step-by-step explanation:
53 + 2444
= 0053 + 2444
= 2497
Help me so I can go be lazy.
Answer:
1. D. Wiley has to defeat the Hairy Man three times to make him go away.
2. A. Wiley gets out of the tree without being hurt by the Hairy Man.
3. The antagonist in the story "Wiley, His Mother, and the Hairy Man" is:
“Mama is the antagonist because she finally wins the fight against the Hairy Man”.
4. The antagonist in the story "Wiley, His Mother, and the Hairy Man" is:
“Mama is the antagonist because she finally wins the fight against the Hairy Man”.
5. The most important lesson Wiley learns in "Wiley, His Mother, and the Hairy Man" is, 'It is better to be a clever person than a strong one.' Option C.
6. They confront the that their partner/friend giles corey died becasue he was phused over to confessed to witchcraft.
Step-by-step explanation:
1. "Wiley, His Mother, and the Hairy Man" is a musical play that has it depends on an oral established story of the South of the United States.
Wiley is the hero of the play as he is the character that endures the principle struggle, against his adversary the Hairy Man, and furthermore on the grounds that the play is centered around his contention as well as on Wiley's association with his mother.
3. An antagonist is a person who goes against the main force and changes it over a course of time.
In the mentioned story, it is Wiley’s Mama who keeps telling him how to keep changing the hairy man into various forms and then finally wins at her own game.
4. An antagonist is a person who goes against the main force and changes it over a course of time.
In the mentioned story, it is Wiley’s Mama who keeps telling him how to keep changing the hairy man into various forms and then finally wins at her own game.
5. "Wiley, His Mother, and the Hairy Man" is a short story for children with a beautiful message. The story depicts how Wiley deals with a Hairy man who was quite dangerous to be handled alone and who used to steal baby. One day it so happens that, when Hairy man was about to steal a baby, Wiley changed that baby for a pig, thus defeating the Hairy man.
This way Wiley learned a lesson that its always better to be a clever person than a strong one. Wiley's smartness helped him to save the life of a baby.
6. I just learned that last week
help this is khan academy
Answer:
20
Answer:
20
Step by step:
v = l × w × h
v = 2 × 2× 5
v = 4 × 5
v = 20
What is the reference angle of 255°?
Answer:
255 degrees is in quadrant 3. The reference angle in this case is the negative x axis to 255 degrees, which is 255 - 180 = 75 degrees
Step-by-step explanation:
The first five terms in a pattern are shown below. -0.5, -0.25, 0 , 0.25, 0.5, . . . Which equation represents the pattern?
Answer:
x + 0.25
Step-by-step explanation:
In this equation, x is representing an integer ( - 0.5, - 0.75, 0, 0.25) whilst 0.25 is a constant
Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve an inequality to find how many hours she will need to babysit to buy the dress. Interpret the solution.
she will need two more hours to buy the dress
The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units
Answer:
The area of a triangle is 1/2BH, or 1/2 times the base times the height.
If the area = 6, and B and H must both be whole numbers.
The area of the triangle ΔSTU is given by A = 12 units²
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the area of the triangle ΔSTU be represented as A
Now , the area of triangle ΔQTU is 6 square units, and the area of triangle ΔRSU is 6 square units
So , the base of the triangle ΔSTU = 6 units
The height of the triangle ΔSTU = 4 units
So , area of the triangle = ( 1/2 ) x Length x Base
On simplifying , we get
The area of triangle ΔSTU = ( 1/2 ) x 4 x 6
The area of triangle ΔSTU = 12 units²
Therefore , the value of A is 12 units²
Hence , the area of the triangle is 12 units²
To learn more about triangles click :
https://brainly.com/question/16739377
#SPJ3
The complete question is attached below :
The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units?
la suma de los cuadrados de dos numeros
Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Part A: If the product of x and 3 is y, write an equation to represent the relationship between the two variables.
Part B: Explain your work in Part A.
Part C: Create a table of values to display five solutions to the equation. Write the solutions as ordered pairs.
Answer:
Part A: y = 3x
Part B: The relationship of y to x is y is 3 times as much as x.
Part C: (0,0), (1,3), (2,6), (3,9), (4,12)
Step-by-step explanation:
Part A: The product of x and 3 (3 times x) is (equals) y. So we can write this linear equation as y = 3x.
Part B: The linear equation is a representation of the relationship between y and x. Y is equivalent to three times x.
Part C: To create solutions to the linear equation, simply plug in a value of x to output a y.
x = 0 -> y = 3(0) = 0; (0,0)
x = 1 -> y = 3(1) = 3; (1,3)
x = 2 -> y = 3(2) = 6; (2,6)
x = 3 -> y = 3(3) = 9; (3,9)
x = 4 -> y = 3(4) = 12; (4, 12)
Cheers.
Whoever helps me will have a good day and maybe get kissed by your crush
Answer:
16
Step-by-step explanation:
i totally forgot how to write the equation so i did it the long way and i got with 16 shovels of dirt you get 100 pounds
2\0.1 x 10\10 = it would help me a lot
Answer:
The answer is1 thank you
I need help pls I don’t understand it
What is the median of the following data set?
{5, 2, 9, 7,4}
A.5
B.7
C.8
D.9
Answer:
5
Step-by-step explanation:
The median of all the answers equal up to 5.
Pls Help Asap pls T^T
Answer: think its c
Step-by-step explanation:
I believe the answer is 18%
Evaluate:
Σ18/1 (5n– 4) = [? ]
Basically, you are going to evaluate 5n - 4 from n = 1 to n = 18. Don't forget to add as you evaluate.
I will get you started.
Let n = 1 and then n = 2.
5(1) - 4 + 5(2) - 4 + the rest
5 - 4 + 10 - 4 + the rest
1 + 6 + the rest
7 + the rest
Just continue the pattern. You will then let n be 3, 4, 5, etc all the way to 18.
plz give some one answrer
Answer:
x=120 (opp. angles of //gram)
Step-by-step explanation:
Because DA//CB and AB//DC (given)
Therefore ABCD is a parallelogram (opp. sides equal)
Therefore,
∠DAB = ∠DCB (opp. ∠s of //gram)
x = 120
A store gives reward points for every dollar
spent. The number of reward points varies
directly with the total amount spent.
Sofia spends $300 and receives 15 reward
points.
Juan spends $900. He receives reward points
at the same rate as Sofia.
How many more reward points will Juan
receive than Sofia?
Please help me I give u 14 points please only correct answers ,!!!
Please answer this quick
I'm sorry but i can't really see the picture
Answer:
1/4
Step-by-step explanation:
Form and solve an equation for .
5x - 7
23
Answer:
x = 6
Step-by-step explanation:
5x - 7 and 23 are vertical angles and are congruent , then
5x - 7 = 23 ( add 7 to both sides )
5x = 30 ( divide both sides by 5 )
x = 6
Helppppp please it’s timed
Answer:
Estimated population of New Hampshire is
A. 35,000
A recent survey of 800 seventh graders from across the state shows 4 out there of 10 like to play paper football. How many students said they like to play paper football?
Answer:
320
Step-by-step explanation:
800 = 10
x = 4
800 x 4 = 10 x
3200= 10x
x = 320
can someone please help me.
Answer:
y=70° x=11
Step-by-step explanation:
.............ur welcome...........
Is this right? Please help me
Answer: Thats correct
Plz help!! 10 points
Answer:
The answer is the second option. x = -5.873 , x = 1.873
Step-by-step explanation:
1. add 11 to both sides of the equation
x^2 + 4x = 11
2. find a value that is equal to the square of half of b
(b/2)^2 = (2)^2
3. add the term to each side of the equation
x^2 + 4x + (2)^2 = 11 + (2)^2
4. simplify the equation
x^2 + 4x + 4 = 15
5. factor the perfect trinomial square into
(x + 2)^2 • (x + 2)^2 = 15
6. solve the equation for x
x = 1.873 , x = -5.873
HOPE THIS HELPS!!
☆☆ plz mark as brainliest ☆☆
What is the following difference?
11 inverse 45 -4 inverse 5