The angle \theta_1θ
1

theta, start subscript, 1, end subscript is located in Quadrant \text{IV}IVstart text, I, V, end text, and \cos(\theta_1)=\dfrac{9}{19}cos(θ
1

)=
19
9

cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 9, divided by, 19, end fraction .
What is the value of \sin(\theta_1)sin(θ
1

)sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Express your answer exactly.
\sin(\theta_1)=sin(θ
1

)=sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals

Answers

Answer 1

I guess that we know that the angle θ is in the fourth quadrant, and we know that:

cos(θ) = 9/19

now we want to find the value of sin(θ).

To do it, we can remember that for a point (x, y), such that we can define an angle β between the positive x-axis and a ray that connects the origin with the point (x, y), we can write the relations:

tan(β) = x/y

sin(β) = y/√(x^2 + y^2)

cos(β) = x/√(x^2 + y^2)

Because the angle is in the fourth quadrant, we know that:

x > 0

y < 0.

And we also know that:

cos(θ) = 9/19

then we have:

x = 9

√(x^2 + y^2) = √(9^2 + y^2) = √(81 + y^2) = 19

Solving the above equation we can find the value of y, that we need to remember, is negative:

√(81 + y^2) = 19

81 + y^2 = 19^2

y^2 = 19^2 - 81 = 280

y = √280 = -16.7

Now that we know the value of y, we can replace that in the sine equation to get:

sin(θ) = -16.7/19 = -0.879

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Related Questions

nolan uses 7 inches of string to make each bracelet. if nolan makes 3 bracelets, how many inches of string will he use?

Answers

Answer:

21 inches

Step-by-step explanation:

We can write a ratio to solve

7 inches        x inches

-------------  = -------------------

1 bracelet      3 bracelets

Using cross products

7*3 = 1x

21 = x

21 inches

Answer:

21 inches

Step-by-step

This can be solved two ways: addition or multiplication.

Addition: Since there are three bracelets you could add 7 three times

                 7+7+7

             = 14+7

             = 21

Multiplication: Simply multiply 7 x 3= 21

Anyone good at Ks3 maths

Answers

Answer:

[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 56 \times 3 \frac{1}{2} }} \\ = { \tt{196 \: miles}}[/tex]

Which sentence can represent the inequality 2.4 (6.2 minus x) greater-than negative 4.5?
Two and four tenths times six and two tenths minus a number is larger than negative four and five tenths.
Two and four tenths multiplied by the difference of six and two tenths and a number is more than negative four and five tenths.
The difference of six and two tenths and a number multiplied by two and four tenths is not less than negative four and five tenths.
The product of six and two tenths minus a number and two and four tenths is at minimum negative four and five tenths.

Answers

Answer: Choice B

Two and four tenths multiplied by the difference of six and two tenths and a number is more than negative four and five tenths.

======================================================

Explanation:

2.4 = 2 + 0.4

2.4 = 2 and 4/10

2.4 = 2 and 4 tenths

2.4 = two and four tenths

-------------------

Through similar reasoning,

6.2 = six and two tenths

And also,

-4.5 = negative four and five tenths

---------------------

Notice how 6.2 - x translates into "difference of six and two tenths and a number"

We then multiply that by 2.4, aka two and four tenths.

So that's how we get the phrasing "Two and four tenths multiplied by the difference of six and two tenths and a number"

All of this is greater than -4.5 aka negative four and five tenths.

This points us to Choice B as the final answer.

Answer:

Answer: Choice B

Step-by-step explanation:

Edgunity

A 12-foot ladder is leaning against the side of a building. The bottom of the ladder is 5 feet from the wall. How many feet above the ground does the ladder touch the wall?

A. 119−−−√ feet
A. square root of 119 feet,

B. 7 feet
B. 7 feet

C. 13 feet
C. 13 feet

D. 134−−−√ feet

Answers

Answer:

Option A, √119

Step-by-step explanation:

Let the height be x foot

12^2=5^2+x^2

or, x = ±√119

since distance can't be negative, so it's x = √119

Answered by GAUTHMATH

If m angle GEF is thirteen less than five times m angle DEG and m angle DEF = 149º, find m angle GEF. ​

Answers

def=149

gef=5x-13

deg=x

5x-13+x=149

6x=162

x=27

plug the x back in

5(27)-13=122

The value of <GEF is 122

what is angle?

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle. Let us read about the different parts of an angle.

Parts of an Angle

There are two main parts related to an angle - the arms and the vertex.

Arms of the Angle

The two rays which join at a common point to form the angle are called the arms of the angle. Observe the figure given below which shows that OA and OB are the arms of the angle AOB.

<DEF=149

let <DEG be x

So,<GEF = 5x-13

Now

5x-13+x=149

6x=162

x=27

Hence, <GEF = 5(27)-13= 122

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Sue read 12 more than twice as many pages is tom did last week if sue read 90 pages how many did tom read

Answers

Answer: 39 pages

Step-by-step explanation:

x = the amount of pages Tom read

[tex]2x+12=90\\2x=78\\\frac{2x}{2}=\frac{78}{2}\\x=39[/tex]

If Sue read 90 pages, which is 12 more than twice the amount, subtract 12 from 90, then divide the result by 2, boom, you got your answer. Which should be 39

On a pie chart, a category representing 20% of the whole should correspond to a central angle of 20°.

Answers

Answer:

No! 20% does not correspond to a central angle 20°.

Step-by-step explanation:

The central angle for pie chart is 360°.

So, a category represents 20% is 20%(360) for central angle.

Let's simplify it to get the angle,

[tex]\frac{20}{100} * 360[/tex]

Simplify it,

72°

So, 20% does not correspond to a central angle 20°.

Resuelve el siguiente problema un buzo en una laguna decendio 8m en una hora.Si cada hora bojo la misma cantidad de metros, ¿cuantos metros bojo en 4 horas

Answers

Answer:

X = 32 meters.

Step-by-step explanation:

Let the unknown distance be X.

Given the following data;

Distance = 8 meters per hourTime = 4 hours

To find how many meters he would cover in four hours;

1 hour = 8 meters

4 hours = X meters

Cross-multiplying, we have;

X = 8 * 4

X = 32 meters.

please help me divide this fractions, showboat work.
O_O​

Answers

solution given;

36:5/5

38:86/69

To divide fractions, you basically just multiply the first fraction by the reciprocal of the second. To find the reciprocal, you just flip the numerator and the denominator.

For number 36, you have 2/3÷8/15. To solve this, you just multiply 2/3 by 15/8.

2/3×15/8 is 30/24, which is 5/4 or 1 1/4.

To answer the second problem, you have to convert the mixed numbers to improper fractions.

7 1/6 as an improper fraction is 43/6. 5 3/4 as an improper fraction is 23/4.

Do the same procedure; 43/6×4/23 is 86/69 or 1 17/69.

Use the graph to find the factorization of x2 - 5x + 4.
10
y = x2.5x + 4
-10
10
10
O A. (x + 2)(x - 2)
B. (x - 1)(x-4)
O C. (x + 2)(x+4)
O D. (x + 1)(x + 4)

Answers

Answer: B. (x - 1) (x - 4)

Concept:

Here, we need to know the idea of zeros.

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

By definition, the factored form of quadratic equations is basically their zeros.

STEP ONE: Find the zeros / x-intercept of the graph

The grid number is 2 per grid as 5 grids are 10 units.

The first intercept is between the y-axis and the first grid.

2 / 2 = 1

The second intercept is on the second grid.

2 × 2 = 4

STEP TWO: Plug the zeros into factorization form

Factor form = (x - x₁) (x - x₂)

x₁ = (1, 0)

x₂ = (4, 0)

Factorization of x² - 5x + 4 = (x - 1) (x - 4)

Hope this helps!! :)

Please let me know if you have any questions

-3 , 1 , 5 , 9 , 13
find the 11th term of this sequence
show your working​

Answers

Answer:

a₁₁ = 37

Step-by-step explanation:

There is a common difference between consecutive terms, that is

1 - (- 3) = 5 - 1 = 9 - 5 = 13 - 9 = 4

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 4 , then

a₁₁ = - 3 + (10 × 4) = - 3 + 40 = 37

Solve the equation 3(2x+9)=30

Answers

Answer:

x=1/2

Step-by-step explanation:

3(2x+9) = 30

Multiply out the 3

6x + 27 = 30

Subtract 27 on both sides

6x = 3

Divide by 6 on both sides

x = 1/2

Answer:

x=1/2

Step-by-step explanation

Please help ASAP!!!
What is m

Answers

Answer:

∡A  =115°

as for your question ... m is asking for the  "m" (measure) of angle A

Step-by-step explanation:

Answer:

∠ A = 118°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

3x + 13 + x - 8 + x = 180, that is

5x + 5 = 180 ( subtract 5 from both sides )

5x = 175 ( divide both sides by 5 )

x = 35

Then

∠ A = 3x + 13 = 3(35) + 13 = 105 + 13 = 118°

find the area of the shaded region,(π=3.14).

plx help me​

Answers

Answer:

115.395 cm2

Step-by-step explanation:

The radius of the whole figure: 14 : 2 = 7 (cm)

The area of the whole figure: 7 x 7 x 3.14 = 153.86 (cm2)

The area of the unshaded region:  3.5 x 3.5 x 3.14 = 38.465 (cm2)

The area of the shaded region: 153.86 - 38.465 =  115.395 (cm2)

Answer: 115.395 cm2.

Hope it helps!

A number cube is rolled 14 times and the results are recorded in the table.

What, in simplest form, is the experimental probability that the number cube shows 4?
A. 0
B. 1/6
C. 2/7
D. 5/14

Answers

Answer:

b

Step-by-step explanation:

The experimental probability that the number cube shows 4 is 2/7.

What is an experimental probability?

Experimental probability is a probability that is determined on the basis of a series of experiments.

Given that, a number cube is rolled 14 times, we need to determine the experimental probability that the number cube shows 4,

The formula to calculate the experimental probability is:

P(E) = Number of times an event occurs/Total number of times the experiment is conducted

P(E) = 4/14 = 2/7

Hence, the experimental probability that the number cube shows 4 is 2/7.

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A chef got 7 bags of onions. The red onions came in bags of 8 and the yellow onions came in bags of 3. If the chef got a total of 41 onions, how many bags of each type of onion did he get?

Answers

Answer:

[tex]\#\text{ of 8-onion bags: }4,\\\#\text{ of 3-onion bags: }3[/tex]

Step-by-step explanation:

Let [tex]a[/tex] be the number of bags with 8 onions and let [tex]b[/tex] be the number of bags with 3 onions. We have the following system of equations:

[tex]\begin{cases}a+b=7,\\8a+3b=41\end{cases}[/tex]

Subtracting [tex]b[/tex] from both sides of the first equation, we get [tex]a=7-b[/tex]. Substitute this into the second equation:

[tex]8(7-b)+3b=41,\\56-8b+3b=41,\\56-5b=41,\\-5b=-15,\\b=\boxed{3}[/tex]

Therefore, the number of 8-onion bags is:

[tex]a=7-b,\\a=7-3,\\a=\boxed{4}[/tex]

Thus, the chef got 4 8-onion bags and 3 3-onion bags.

The range of cells in column D and rows 1 to 10 is represented as:

1:10 D1:D10 D:D

Answers

Answer:

how?

Step-by-step explanation:

I didnt get question

The following are the dimensions of a triangle, 6 cm, 8 cm, and 12 cm.

Is this a right triangle?? Use the Pythagorean theorem and the basic law of exponents to prove whether this is a RIGHT triangle.

Show your work and POST your answer.

Answers

Answer:

Perimeter of original triangle: 6+8+10=24 cm

Perimeter of new triangle: 3+4+5=12 cm (You get 3, 4, and 5 from dividing 6, 8. and 10 by 2.)

Ratio of original to new is 24 to 12, simplified to 2 to 1.  

The ratio of the perimeter is the ratio of the corresponding sides, as the original measurements are two times the length of the new measurements.

Area of original triangle: (6x8)/2=24 cm^2

Area of new triangle: (3x4)/2=6 cm^2

Ratio of original to new is 24 to 6, simplified to 4 to 1.

help please summer school sucks!!!

Answers

Answer:

X =30

Step-by-step explanation:

= 60+90

=150

angle sum property

x+150=180

x=180- 150

x= 30

Answer:

Step-by-step explanation:

90 + 60 = 150

(right angles = 90)

There is 180 degrees in a triangle, therefore,

180 - 150 = 30

Therefore, x = 30

p.s. Are you good at history?

p.p.s I dont like summer school either =)

Suppose the line y = 2.8333x - 22.4967 describes the relation between the​ club-head speed​ (in miles per​ hour), x and the distance a golf ball travels​ (in yards), y.

(a) Predict the distance a golf ball will travel if the club-head speed is 100 mph.

(b) Suppose the observed distance a golf ball traveled when the club-head speed was 100 mph was 265 yards. What is the residual?

(c) The golf ball will travel 260.8 yards. (Round to the nearest tenth as needed.)

(d) The residual is:_________ (Round to the nearest tenth as needed.)

Answers

Answer:

c) The golf ball will travel 260.8 yards.

d) Hence the residual is 4.2 yards.

Step-by-step explanation:

c) y' = 2.8333x - 22.4967

Now the golf ball will travel [tex]= 2.8333\times100 - 22.4967[/tex]= 260.8 yards

here y'= 260.8 yards.

d) The residual is : y - y' = 265 - 260.8 = 4.2 yards.

Answer:

a)  [tex]y=260.8333~yd[/tex]

b) [tex]\Delta d=4.1667~yd[/tex]

c) [tex]y=260~yd[/tex]

d) [tex]\Delta y'=0.8333~yd[/tex]

Step-by-step explanation:

Given:

equation of line, [tex]y=2.8333x-22.4967[/tex]

x = club-head speed​ (in miles per​ hour)

y = the distance a golf ball travels​ (in yards)

a)

x = 100 mph

Then the distance travelled by the ball:

(put the given value of x in the above eq.)

[tex]y=2.8333\times 100-22.4967[/tex]

[tex]y=260.8333~yd[/tex]

b)

If the observed distance in the above case comes out to be 265 yards then the residual value will be:

[tex]\Delta d=265-260.8333[/tex]

[tex]\Delta d=4.1667~yd[/tex]

c)

From the calculated value when rounding it to the nearest tenth:

[tex]y=260~yd[/tex]

d)

The residual on rounding the calculated value to the nearest tenth:

[tex]\Delta y'=260.8333-260[/tex]

[tex]\Delta y'=0.8333~yd[/tex]

The probability that Dan buys a sandwich is 0.2.
The probability that Dan gets the bus is 0.9.
Assuming the events are independent, what is the probability that Dan buys a sandwich
and gets the bus?

Answers

Answer:

0.18

Step-by-step explanation:

Find the probability that both independent events occur by multiplying the individual probabilities by each other:

0.2(0.9)

= 0.18

So, the probability is 0.18

Linear equation: -1
2
(6x + 10) = 13

Step 1: –3x – 5 = 13

Step 2: –3x = 18

Step 3: x = –6

Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?

Answers

Answer:

see below

Step-by-step explanation:

-1/2 * (6x + 10) = 13

Distribute -1/2

–3x – 5 = 13

Add 5 to each side

-3x-5+5 = 13+5

–3x = 18

Divide each side by -3

-3x/-3 = 18/-3

x = -6

Edwin hiked to a famous point with a beautiful view. It took 2 hours and 55 minutes to hike to the viewpoint and 25 minutes to hike back. Edwin spent 25 minutes enjoying the view at the top. He finished the hike at 11:45 A.M. What time did Edwin start the hike to the viewpoint?

Answers

Answer:

= 8:00 A.M.

Step-by-step explanation:

▪You first find the total time taken which will be :

2 hrs 55 min + 25 min

= 3 hrs 20 min + 25 min

= 3 hrs 45min

▪ Beginning time = Arrival time - Time taken

= 11:45 - 3:45

= 8:00 am

¿

What are the features of the quadratic function ƒ(x) = x2 + 10x + 21?

Answers

Answer:

B is the answer

Step-by-step explanation:

The intercept is at x = 0 then y = 21 or (0,21) so A and D drop out.

The vertex (-5, -4) satisfies the equation but (-4,-5) does not so C drops out leaving B.

Answer:

B.

Step-by-step explanation:

B.

Can someone help me pls

Answers

Answer:

Step-by-step explanation:

Look at the photo

What is the value of X?​

Answers

Answer:

x=2

Step-by-step explanation:

A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.

For two secant lines that intersect outside of the circle, such as the ones here, we can say that

CE * DE = BE * AE

Therefore, we need to then define these lines.

CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x

We then have

(x+4) * (5+x) = (x+1) * (12+x)

expand

5x + x² + 20 + 4x = 12x+x²+12+x

x²+9x + 20 = x²+13x+12

Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get

-4x + 8 = 0

subtract 8 from both sides to isolate the x and its coefficient

-4x = -8

divide both sides by -4 to isolate the x

x = 2

Answer: A

Explanation: I just took a test on it

Which of the following is the correct factorization of the polynomial below?
x3 + 10x2 + 25x
A. x(x + 5)(x - 5)
B. (x2 + 2x - 5)(x-10)
C. (x2 + 5x - 2)(x-10)
D. x(x + 5)2

Answers

Answer:

x(x+5)^2

Step-by-step explanation:

x^3 + 10x^2 + 25x

Factor out x

x(x^2+10x+25)

What 2 numbers multiply to 25 and add to 10

5*5 = 25

5+5 =10

x(x+5)(x+5)

x(x+5)^2

Answer:

D

Step-by-step explanation:

Given

x³ + 10x² + 25x ← factor out x from each term

= x(x² + 10x + 25) ← perfect square

= x(x + 5)²

Brooke and Lamont ran a half marathon Brooke finished in 1 hour 50 minutes Lamont finished in 100 minutes who had the faster time​

Answers

Answer:

Brooke = 1 hr 50 min

Lamont = 100 min = 1 hr 40 min

Because 60 min = 1 hr

Lamont was faster

Hope this helped

What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5)=g(8)=−9. (Do not include "c=" in your answer.)

Answers

Answer:

[tex]\displaystyle c = \frac{20}{3}[/tex]

Step-by-step explanation:

According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.

We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.

So, differentiate the function. We can take the derivative of both sides with respect to x:

[tex]\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right][/tex]

Differentiate:

[tex]g'(x) = -21x^2+182x-280[/tex]

Let g'(x) = 0:

[tex]0 = -21x^2+182x-280[/tex]

Solve for x. First, divide everything by negative seven:

[tex]0=3x^2-26x+40[/tex]

Factor:

[tex]0=(x-2)(3x-20)[/tex]

Zero Product Property:

[tex]x-2=0 \text{ or } 3x-20=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=2 \text{ or } x = \frac{20}{3}[/tex]

Since the first solution is not within our interval, we can ignore it.

Therefore:

[tex]\displaystyle c = \frac{20}{3}[/tex]

i know it’s kinda all hard to see. i have many more questions like this and i can’t do graphs to save my life.. pls help !!

Answers

Answer: D

Step-by-step explanation:

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