please help me out with these questions. Its trigonometry.
Find the value of the lettered angles
In case the pic's not clear;
[tex] \cos \alpha = \sin(50 + \alpha ) [/tex]
Answers
Answer: i) θ = 30°, 60°, 210°, & 240°
ii) θ = 20° & 200°
Step-by-step explanation:
i) sin (2θ) = cos 30°
[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]
To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above. θ = 30°, 60°, 210°, 240°
If you need ALL of the solutions (more than one rotation), add 180n to the solutions. θ = 30° + 180n & 60° + 180n
*********************************************************************************************
ii) cos α = sin (50 + α)
Use the Identity: cos α = sin (90 - α)
Use Transitive Property to get: sin (50° + α) = sin (90° - α)
50° + α = 90° - α
50° + 2α = 90°
2α = 40°
α = 20°
To find all solutions for one rotation, add 360/2 = 180 to the solution above.
α = 20°, 200°
If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n
Related Questions
Write the equation of the line in slope intercept form that passes through the points (4,-2) and (2,-1)
Answers
Answer:
y + 2 = (-1/2)(x - 4)
Step-by-step explanation:
Let's move from (2, -1) to (4, -2) and measure the changes in x and y. x increases by 2 units from 2 to 4, and y decreases by 1 unit from -1 to -2. Thus, the slope of the line connecting the two points is m = rise / run =
-1
--- = (-1/2).
2
Using the point-slope formula, we get:
y + 2 = (-1/2)(x - 4)
easy math please help!
Answers
Answer:
[tex]\boxed{ \sf 41.81}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(?)=\frac{2}{3}[/tex]
[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]
[tex]\sf ?= 41.81031489...[/tex]
Answer:
[tex]\boxed{41.81}[/tex]
Step-by-step explanation:
∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.
The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).
However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.
Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.
Which of the following statement is incorrect?
4
A.3/4<4/5
B.5/6>0.83
C.2/3>0.66
D.1/3>0.3
درا
Answers
Answer:
None,
they are all correct.
Step-by-step explanation:
A)
3/4 - 75%
4/5 - 80%
3/4 < 4/5
B)
5 ÷ 6 = .83333333333
5/6 > .83
C)
2 ÷ 3 = .666666666
2/3 > .66
D)
1 ÷ 3 = .33333333333
1/3 > .3
Thus,
all of the given statements are correct.
Hope this helps :)
According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017 . Data for the sale of randomly selected 40 homes sold in Greene County, Ohio, in showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in . Round your answer to four decimal places.
P-value =
Answers
Answer:
t= 1.89736659
Step-by-step explanation:
Write a system of equations in x and y describing the situation. Do not solve the system.
Keiko has a total of $5500, which she has invested in two accounts. The larger account is $700 greater than the smaller account. (Let x be the amount of money in the
larger account and y be the amount of money in the smaller account.)
Choose a system of equations describing the situation,
X+ y + 5500 = 0
x+y=5500
X= y + 700
X-y+ 700 = 0
O
2x = 5500
2x + 2y = 5500
x-y=700
x- y = 700
Answers
X is larger acct
Y is smaller acct
Larger acct equals amount in smaller account plus $700.
round 235,674 to the nearest thousand
Answers
Answer:
236,000
Step-by-step explanation:
When rounding to thousands, if the hundred is 500 or over, you round up. If it is less, round down.
Answer:
Hey! The answer is 236,000.... steps will be below!
Step-by-step explanation:
Since there is 5,674 it is more closer to 6,000 than 5,000
So we change the number to 236,000
ANSWER TO YOUR QUESTION: 236,000
Hope this helps! :)
⭐️Have a wonderful day!⭐️
a beetle sets out on a journey. on the first day it crawls 1m in a straight line. on the second day it makes a right-angled turn (in either direction) and crawls 2m in a straight line. on the third day it makes a right-angled turn (in either direction) and crawls 3m in a straight line. this continues each day with the beetle making a right-angled turn ( in either direction and crawling 1m further than it did the day before. what is the least number of days before the beetle could find itself stopped at its starting point?
Answers
Answer:
7
Step-by-step explanation:
The signed sum of sequential odd numbers must be zero, as must the signed sum of sequential even numbers.
The minimum number of sequential even numbers that have a sum of 0 is 3: 2+4-6 = 0.
The minimum number of sequential odd numbers with a sum of zero is 4: 1-3-5+7=0.
Since we start with an odd number, we can get these sets of numbers in 7 days. The attached diagram shows one possible route.
Penyelesaian
0.02 m: 3 cm: 4.6 cm = 2 cm : 3 cm: 4.6 cm
= 2 : 3 : 4.6
20 : 30 : 46
10 : 15
23
Latih Diri 4.1a
1. Wakilkan hubungan antara tiga kuantiti berikut dalam bentuk a : b:c.
(a) 2 minggu kepada 16 hari kepada 1 minggu
(b) 0.1 kg kepada 50 g kepada 0.25 kg
(c) 4 minit kepada 120 saat kepada 1.6 jam
(d 3 m kepada 480 cm kepada 6 400 mm
2. Tahir membayar RM5.60 untuk sepinggan nasi beriani, RM1.20 untuk segelas teh
dan 30 sen untuk sekeping kuih. Wakilkan hubungan harga bagi nasi beriani, teh dan
kuih dalam bentuk a:b:c.
76
BAB 4
Answers
Answer:
a:b:c
1a) 14:16:7
b) 2:1:5
c) 2:1:48
d) 15:24:32
2) 56:12:3
Step-by-step explanation:
Untuk membentuk nisbah tiga kuantiti, pertama-tama kita menukar masing-masing menjadi unit yang sama.
a) 2 minggu hingga 16 hari hingga 1 minggu
Menukar semuanya menjadi bilangan hari, kerana ia sangat setanding.
2 minggu = 14 hari
16 hari = 16 hari
1 minggu = 7 hari
2 minggu hingga 16 hari hingga 1 minggu = 14 hari hingga 16 hari hingga 7 hari
14: 16: 7
b) 0.1 kg hingga 50 g hingga 0.25 kg
Menukar semua menjadi gram
= 100 g hingga 50 g hingga 250 g
= 100: 50: 250
Bahagikan dengan 50
= 2 : 1 : 5
c) 4 minit hingga 120 saat hingga 1.6 jam
Menukar semua menjadi beberapa saat
= 240 saat hingga 120 saat hingga (1.6 × 60 × 60) saat
= 240 saat hingga 120 saat hingga 5,760 saat
= 2: 1: 48
d) 3 m hingga 480 cm hingga 6 400 mm
Menukar semua ini menjadi mm
= 3000 mm hingga 4800 mm hingga 6400 mm
Membahagi hingga 200 mm
= 15:24:32
2) RM5.60 hingga RM1.20 hingga 30 sen
Menukar semuanya kepada sen
= 560 sen hingga 120 sen hingga 30 sen
Membahagi hingga 10
= 56: 12: 3
Semoga ini Membantu !!!
English Translation
Solution
0.02 m: 3 cm: 4.6 cm = 2 cm: 3 cm: 4.6 cm = 2: 3: 4.6
20:30:46
10:15:23
Self Training 4.1a
1. Represent the relationship between the following three quantities in the form a: b: c.
(a) 2 weeks to 16 days to 1 week
(b) 0.1 kg to 50 g to 0.25 kg
(c) 4 minutes to 120 seconds to 1.6 hours
(d) 3 m to 480 cm to 6 400 mm
2. Tahir pays RM5.60 for a plate of beriani rice, RM1.20 for a glass of tea and 30 cents for a piece of cake.
Represent the price relationship for beriani rice, tea and cake in the form of a: b: c.
Solution
To form a ratio of three quantities, we first convert each of them to the same units.
a) 2 weeks to 16 days to 1 week
Converting all of it to number of days, as itnis very comparable.
2 weeks = 14 days
16 days = 16 days
1 week = 7 days
2 weeks to 16 days to 1 week
= 14 days to 16 days to 7 days
14 : 16 : 7
b) 0.1 kg to 50 g to 0.25 kg
Converting all into grams
= 100 g to 50 g to 250 g
= 100 : 50 : 250
Divide through by 50
= 2 : 1 : 5
(c) 4 minutes to 120 seconds to 1.6 hours
Converting all into seconds
= 240 seconds to 120 seconds to (1.6×60×60) seconds
= 240 seconds to 120 seconds to 5,760 seconds
= 2:1:48
(d) 3 m to 480 cm to 6 400 mm
Converting all of this to mm
= 3000 mm to 4800 mm to 6400 mm
Dividing through by 200 mm
= 15:24:32
2) RM5.60 to RM1.20 to 30 cents
Converting it all to cents
= 560 cents to 120 cents to 30 cents
Dividing through by 10
= 56:12:3
Hope this Helps!!!
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 3, 1) and point K is at (negative 8, 11). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –6 –5 5 7
Answers
Answer: (-5, 5)
Step-by-step explanation:
J = (-3, 1) K = (-8, 11) ratio 2 : 3 --> 2 + 3 = 5 segments
x-distance from J to K: -8 - (-3) = -5 units
y-distance from J to K: 11 - 1 = 10 units
Divide those distance into 5 segments:
x = -5/5 = -1 unit per segment
y = 10/5 = 2 units per segment
The partition is 2 segments from J:
x = -3 +2(-1) = -5
y = 1 + 2(2) = 5
The partition is located at (-5, 5)
Answer:
5
Step-by-step explanation:
Bernard works for a business that sells and repairs tires. He can repair 24 tires in an 8 hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Answers
Step-by-step explanation:
Unit rate = 24 ÷ 8 = 3 tires
Answer:
Step-by-step explanation:
24 tires/8hours
for f(x)=1/x-5 and g(x)=x^2+2 find the expression for g(x) and substitute the value of g(x) into the function in place of x to find the value of f(g(x))
Answers
Answer:
f(x) = (1/x) - 5
g(x) = x^2 + 2
=> f[g(x)] = [1/(x^2 +2)] - 5
Please help ASAP!!! Thank you so much!!! Just want confirm my answer and it is A) -5. Consider the function f(x)= [tex]x^{3}[/tex] +4[tex]x^{2}[/tex]-25x-50. (x^3+4x^2-25x-50). If there is a remainder of 50 when the function is divided by (x-a) what is the value of a? A) -5 B) -2 C)-3 D)
Answers
Answer:
Correct is A
Step-by-step explanation:
Correct is A , notice that when you perform synthetic division you get that the reminder is 50, please refer to the image I attach to see it.
Solve.
5x – 10 <20
O (-00, 2]
O (-0,2)
O (-00, 6]
O (-0, 6)
Answers
What is the missing segment?
Answers
Answer:
78.
Step-by-step explanation:
12 / (48-12) = 26 / x
12/36 = 26/x
1/3 = 26/x
x = 26*3 = 78.
Write the equation of the line in point-slope form that passes through (1, -4) and has a slope of 1/4.
Answers
Answer:
y + 4 =(1/4)(x - 1)
Step-by-step explanation:
The point slope equation is y - k = m(x - h), where (h, k) is the given point and m is the given slope.
In this particular case we have y + 4 =(1/4)(x - 1)
The radius of a sphere is 11 cm.what is the surface area of the sphere? Round to the nearest tenth.
Answers
Answer:
The answer is
1520.5 cm²Step-by-step explanation:
Surface area of a sphere is given by
S = 4πr²
where r is the radius
From the question r = 11cm
So the surface area of the sphere is
4π(11)²
= 4(121)π
= 484π
= 1520.5308
Which is
1520.5 cm² to the nearest tenth
Hope this helps you
A certain article indicates that in a sample of 1,000 dog owners, 680 said that they take more pictures of their dog than of their significant others or friends, and 490 said that they are more likely to complain to their dog than to a friend. Suppose that it is reasonable to consider this sample as representative of the population of dog owners.
(a) Construct a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends. (Use a table or technology. Round your answers to three decimal places.)
(______),(_________)
(b) Construct a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend. (Use a table or technology. Round your answers to three decimal places.)
(_______),(_______)
Answers
Answer: a) a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).
b) a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).
Step-by-step explanation:
Confidence interval for a population proportion is given by:-
[tex]\hat{p}\pm z(\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]
, where [tex]\hat{p}[/tex] = sample proportion , n= sample size, z= critical z-value.
As per given,
a) n=1000
Sample proportion of dog owners say they take more pictures of their dog than of their significant others or friends =[tex]\hat{p}=\dfrac{680}{1000}=0.68[/tex]
critical value for 90% confidence = 1.645 [By table]
A 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends.
[tex]0.68\pm (1.645)\sqrt{\dfrac{0.68(1-0.68)}{1000}}\\\\\approx0.68\pm0.024=(0.68-0.024,0.68+0.024)=(0.656,0.704)[/tex]
Hence, a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).
b) Sample proportion of dog owners say they are more likely to complain to their dog than to a friend =[tex]\hat{p}=\dfrac{490}{1000}=0.49[/tex]
critical value for 95% confidence = 1.96 [By table]
A 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend:
[tex]0.49\pm (1.96)\sqrt{\dfrac{0.49(1-0.49)}{1000}}\\\\\approx0.49\pm0.031=(0.49-0.031,0.49+0.031)=(0.459,0.521)[/tex]
Hence, a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).
Because of a manufacturing error, 3 cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack. Determine the probability that at least one contain regular soda.
Answers
Answer:
161/184 or 0.875
Step-by-step explanation:
Total number of cans = 24 cans
Total number of diet soda = 3 cans
Total number of regular soda = 21 cans
We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly
We have two ways for this happening
a) two of the cans are regular soda
b) one of the cans is regular , while one is diet
Hence,
Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)
Probability(that two of the cans are regular soda) = 21/24 × 20/23
= 35/46
Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23
= 21/184
Probability (that at least one contain regular soda) = 35/46 + 21/184
We find the Lowest common multiple of the denominators = 184
= 35/46 + 21/184
= (35 × 4) + (21 × 1)/184
= 140 + 21/184
= 161/184
= 0.875
Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875
Of the following points, name all that lie on the same horizontal line? (1,-2) (-1,2) (-2,1) (2,-1)
Answers
Hey there!
If a line is horizontal, the entire line is at the same elevation. On a line, the elevation is the y-value. So, all of the points with the same y-value are on the same horizontal line.
We see that all of these points have different y-values so none of them would be on the same horizontal line.
I hope that this helps! Have a wonderful day!
f(x)=−7x^2 −x and g(x)=9x^2 −4x , find (f−g)(x) and (f−g)(1)
Answers
Answer:
f(x) = -7x² - x
g(x) = 9x² - 4x
To find ( f - g)(x) subtract g(x) from f(x)
That's
( f - g)(x) = - 7x² - x - ( 9x² - 4x)
= -7x² - x - 9x² + 4x
Group like terms
( f - g)(x) = - 7x² - 9x² - x + 4x
( f - g)(x) = - 16x² + 3xTo find (f - g)(1) substitute 1 into ( f - g)(x)
That's
(f - g)(1) = - 16(1) + 3(1)
= -16 + 3
= - 13Hope this helps you
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Answers
Answer:
5
Step-by-step explanation:
A bowl of Halloween candy contains 7 chocolate candies and 3 lemon candies. Tanya will choose one piece of candy at random.
Answers
Find the slope of the line passing through the given points. State whether the line is increasing, decreasing, horizontal, or vertical. (7,3) and (8,7)
Answers
Answer:
slope = 4
The line is increasing
Step-by-step explanation:
slope can be found through the equation [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. So, if we plug these points in, we get [tex]\frac{7-3}{8-7}[/tex], which simplifies to 4. So, the slope is 4.
Since the slope is positive, the line is increasing.
stephano walks 2/5 mile in 1/4 hour. What is stephano's speed in miles?
Answers
Explanation:
V = d/t
V = 2/5 divide by 1/4
V = 2/5 x 4/1
V = 8/5 mi/hr
What is the volume of air that the beach ball will hold?
Answers
Answer:
In order to solve this problem, we need to know the volume of a sphere.
The volume of a sphere is (4/3)pir^3
In this case our r value, or radius, is 30cm.
If we plug in 30cm to the equation like so:
(4/3)pi(30)^3
The answer is 113097 cm^3 of air
Hope you understand
Y= 2/3x – 18 What is the rate of change from -5 to 10? What is the average rate of change from 0 to 3?
Answers
Answer:
this is all i got for the second question.
Step-by-step explanation:
That is, the average rate of change of from 3 to 0 is 1. That is, over the interval [0,3], for every 1 unit change in x, there is a 1 unit change in the value of the function. Here is a graph of the function, the two points used, and the line connecting those two points.
hope this kinda helps
-lvr
What is the simplified form of 144x^36?
O 12x6
O 12x18
O 72x6
072x18
Answers
Answer:
B
Step-by-step explanation:
helPpppppppppPPppppPPPPPPppppppPPPPPPPPPpppppppp
Charli believes that if he flips a coin 650 times, it will land heads up exactly 325 times. What would you tell charli about her prediction?
Answers
Answer:
What I would tell Charli is that his prediction is somewhat right because there is a 50/50 chance of landing the coin on each side because 325 is half of 650.
Step-by-step explanation:
Question 5(Multiple Choice Worth 4 points) (05.05)Based on the graph, what is the initial value of the linear relationship?
Answers
Answer: A) -2
Step-by-step explanation:
The y-intercept (where the graph crosses the y-axis) is the "initial value".
Looking at the given graph, it crosses the y-axis when y = -2
Use identities to find values of the sine and cosine functions of the function for the angle measure
a. theta, given that cos2theta=28/53 and 0theta < theta < 90degrees
b. 2theta, given sin theta= - sqrt 7 over 5 and cos theta > 0
c. 2x, given tan x=2 and cos x<0
Answers
Answer:
Step-by-step explanation:
a) Given cos2theta=28/53 and 0degrees< theta < 90degrees
From cos2theta=28/53
[tex]2\theta = cos^{-1}\frac{28}{53}[/tex]
[tex]2\theta = cos^{-1}0.5283\\ \\2\theta = 58.12\\\\Dividing\ both \ sides\ by \ 2\\\\\frac{2\theta}{2} = \frac{58.12}{2}\\ \\\theta = 29.06^0[/tex]
b) Given
[tex]sin\theta = \frac{-\sqrt{7} }{5} \\\\\theta = sin^{-1} \frac{-\sqrt{7} }{5}\\\\\\\theta = sin^{-1} \frac{-2.6458}{5}\\\\\theta = sin^{-1} -0.5292\\\\\theta = -31.95^0[/tex]
If cos theta [tex]\gneq[/tex] 0, this means we need to look for the quadrant where sin is negative and cos is positive. That will be the fourth quadrant. In the fourth quadrant, theta = 360 - 31.95° = 328.05°
2theta = 2 * 328.05
2theta = 656.1°
c) Given tan x=2 and cos x<0, lets find the angle of x first.
If tan x = 2
x = tan^-1 2
x = 63.4°
Sine cos is less than 0, then we need to find the angle of x where tan is positive and cos is negative. That will be the third quadrant. In the third quadrant, ew value of x = 180+63.4
x = 243.4°
Since we are to find 2x,
2x = 2(243.4)
2x = 486.8°