part 3. Find the value of the trig function indicated, use Pythagorean theorem to find the third side if you need it.​

Part 3. Find The Value Of The Trig Function Indicated, Use Pythagorean Theorem To Find The Third Side

Answers

Answer 1

Answer:  [tex]\bold{9)\ \sin \theta=\dfrac{1}{3}\qquad 10)\ \sin \theta = \dfrac{4}{5}\qquad 11)\ \cos \theta = \dfrac{\sqrt{11}}{6}\qquad 12)\ \tan \theta = \dfrac{17\sqrt2}{26}}[/tex]

Step-by-step explanation:

Pythagorean Theorem is: a² + b² = c²   , where "c" is the hypotenuse

[tex]9)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{12}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]

Note: 4² + (8√2)² = hypotenuse²   →   hypotenuse = 12

[tex]10)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{16}{20}\quad \rightarrow \large\boxed{\dfrac{4}{5}}[/tex]

Note: 12² + opposite² = 20²   →   opposite = 16

[tex]11)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{\sqrt{11}}{6}\quad =\large\boxed{\dfrac{\sqrt{11}}{6}}[/tex]

Note: adjacent² + 5² = 6²   →   adjacent = √11

[tex]12)\ \tan \theta=\dfrac{\text{side opposite of}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{17}{13\sqrt2}\quad =\large\boxed{\dfrac{17\sqrt2}{26}}[/tex]

Note: adjacent² + 7² = (13√2)²   →   adjacent = 17


Related Questions

i need help pls i would really appreciate it !!

Answers

Answer : a
Sin is opposite/hypotenuse which is 8/10
And this is 4/5
‘A’ will be the answer to your question

Which graph shows a negative correlation?

Answers

Answer:

Option D

Step-by-step explanation:

because the data wasn't place on a table...

if 60% of a number is 90, what is 4/5 of the number

Answers

Answer:

120

Step-by-step explanation:

To solve this, we can first find the value of the number.

Let's name the number x.

We can set up a proportion to solve.

90/60=x/100

Simplify.

9/6=x/100

Cross multiply.

6x=900

Divide both sides by 6.

x=150

The original number is 150.

Let's find 4/5 of that.

4/5*150

Multiply.

600/5

Divide.

120

________________________________

Hey!!!

Solution,

Let the number be X

60% of X=90

or,60/100*X=90

or,3/5*X=90

or,X=90/3/5

or,X=90*5/3

or,X=450/3

X=150

Again,

4/5 of X

=4/5*150

=120

The answer is 120

hope it helps

Good luck on your assignment

_____________________________

So 59 rounded to the nearest ten is​

Answers

Answer:

60

This is because a number 5 or above is rounded up. Lower than 5 is equal to the lower number.

Answer:

60.. hope it helps

Step-by-step explanation:

Check the number in the ones place

It's is 9, which is greater than 5 so we will add 1, to the tens place,

It becomes 60

Another method..

The closest tens multiples to the given number are 50 and 60.

Evidently, it is closer to 60 so when it is rounded off to the nearest ten, it's 60

Which situation is best modeled with a division expression?

finding the number of equal-sized parts into which a number can be split
finding the combined value of several different numbers
finding the distance between two numbers on a number line
finding the total value when several of the same number are grouped together

Answers

Answer: Finding the number of equal-sized parts into which a number can be split

Step-by-step explanation:

Hi, a division expression is the division of 2 numbers that results in a quotient.

The quotient is the number of times that the second number in the division is contained in the first number.

For example 20 ÷ 2 = 10

Number 2 is contained 10 times in the number 10, or in other words, 20 can be split into ten equal-sized parts.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

A

Step-by-step explanation:

for edge

The rati of the number of moons the planet neptune has to the number that saturn has is 4 to 9 saturn has 18 moons how many moons does nepturn have ???

Answers

Answer:

HEY!

Neptune contains 8 moons.

Step-by-step explanation:

18/9) *4 = 8 moons. Hence, Neptune has a total of 8 moons according to the given conditions.

Which expression is equivalent to 81^1/3?
33/3
3133
9313
273/3​

Answers

Answer: 3 3√3

Step-by-step explanation:

81^1/3

=3√81

= 3 3√3

PLEASE HELP!! The table shows the balance of an investment account at the beginning of each year the account was held. Assuming no other deposits have been made to the account, which statement describes the accounts growth.

The table and answers are attached.

Answers

Answer:

C

Step-by-step explanation:

The answer is c because 10.5 also equals up to 1,32300

The statement describes the growth of the account as C. The account grew exponentially at an annual interest rate of 5.00%.

What is an example of a cash account?

Cash accounts

A cash account might be the type of funding account you believe you studied when you consider making an investment. You deposit cash into a coins brokerage account, and you then use the budget to shop for securities.

What type of account is ideal for investment?

A cash account is suitable for the majority of traders. It lets you buy investments with the cash you deposit into the account. A margin account is for investors who want to borrow cash from the broker to buy investments. Margin trading is a riskier sort of investing this is nice proper for advanced traders.

Learn more about Traders at https://brainly.com/question/17727564

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A recent school survey found that 8 out of 10 students plan to go to college after graduating high school. At that rate, how many of the 2540 students at the local high school plan to go to college?

Answers

Answer:

1960

Step-by-step explanation:

8 out of 10 is 80% or 0.8. 0.8 * 2540 = 1960 students.

Answer:2032

Step-by-step explanation:

8 out of 10 is 80% or 0.8 then 2540 times 0.8=2023

During the 2010 baseball​ season, the number of wins for three teams was three consecutive integers. Of these three​ teams, the first team had the most wins. The last team had the least wins. The total number of wins by these three teams was 252. How many wins did each team have in the 2010​ season?

Answers

Answer: 83,84 and 85

Step-by-step explanation:

Let the number of win for the teams be x, x+1 and x+2 respectively. From the question, we are told that the total number of wins by these three teams was 252 for the 2010​ season. Therefore,

x+x+1+x+2 = 252

3x+3 = 252

3x = 252 - 3

3x = 249

x = 249/3

x = 83

This means that the team with least wins has 83 while the second team has 84 and the team with most wins has 85.

If b=5, then 4^1•4^b is equal to?

Answers

Answer:4096

[tex]solution \\ b = 5 \\ {4}^{1} . {4}^{b} \\ = {4}^{1} . {4}^{5} \\ = 4 ^{1 + 5} \\ = {4}^{6} \\ = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \\ = 4096 \\ [/tex]

hope it helps...

Good luck on your assignment

Answer:

[tex] = 4096[/tex]

Step-by-step explanation:

Given that,

[tex]b = 5[/tex]

Let's solve now.

[tex] = {4}^{1} \times {4}^{b} \\ = {4}^{1} \times {4}^{5} \\ = {4}^{6} \\ = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \\ = 16 \times 16 \times 16 \\ = 256 \times 16 \\ = 4096[/tex]

9) A grandmother is nine times older than her grandson. If she is also 56 years older than
him, what is the age of her grandson after 6 years?
a) 7 years
b) 9 years
c) 11 years
d) 13 years

Answers

Answer= 13 years

Solution,

Let the age of grandmother be y

Let the age of grandson be X

according to question,

9x=y ( equation I)

X+56=y( equation ii)

Substituting,

9x=x+56

or,9x-x=56

or,8x=56

or,X=56/8

X=7

Again,

Age of grandson after 6 years

=7 years+6 years

=13 years

Hope it helps

Good luck on your assignment

The age of her grandson after 6 years is 13 years.

What is the algebraic equation?

A mathematical statement in which two expressions are set equal to each other is known as an algebraic equation. A variable, coefficients, and constants are commonly included in an algebraic equation.

How to solve this problem?

Let the age of the grandmother be x and the age of her grandson be y.

Since the grandmother is 9 times older than her grandson, we can write

x = 9y ...(1)

Since the grandmother is 56 years older than her grandson, we can also write

x = y + 56 ...(2)

We have to solve these two algebraic equations.

Equating the L.H.S. of (1) and (2),

9y = y + 56

i.e. 9y - y = 56

i.e. 8y = 56

i.e. y = 56/8 = 7

So, now the age of her grandson is 7 years.

Therefore the age of her grandson after 6 years is 6+7= 13 years.

Know more about algebraic equations here -

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The length of the sides of a triangle from a G.P. The length of the longest side exceeds that of the shortest side by 9cm. The perimeter of the triangle is 61cm. Find the length of each side.​

Answers

Take sides as [tex] a, \: ar, \: ar^2[/tex]

which method can be used to solve 11x13

Answers

Answer:

Simple column method

Step-by-step explanation:

  11

x 13

  33

 110

 143

Answer:

Use the grid method, since it is the most obvious option. But, you may also use the distribution method.

Step-by-step explanation:

Distribution method:

divide 13 into 10 +3

then multiply 11 with 10 and 3 individually.

This can be written as 11(10+3) = 110+33 = 143

Please mark brainiest

Simultaneous equation

Answers

Answer:

x = 5, y = 9.

Step-by-step explanation:

8^x / 2^y = 64

3^4x * (1/9)^(y -1) = 81

From the first equation

2^3x / 2^y = 2^6

2^(3x-y) = 2^6

So 3x - y = 6  ..........(1)

From the second equation:

3^4x * 9^(-(y-1)) =  3^4

3^4x * 3^2(-(y-1)) = 3^4

3^(4x+ 2(1 - y)) = 3^4

So 4x + 2(1 - y) = 4

4x - 2y = 2

2x - y = 1   .............(2)

Subtract: (1) - (2):

x = 5.

and  2(5) - y = 1

so y = 9.

Solving the simultaneous equations we get x is 5  and y is 9 .

Simultaneous equations in algebra are those that concurrently involve two or more variables, such as x and y. Even though they are solved simultaneously, the equations are known as simultaneous equations. Just these equations alone have innumerable answers.

A system of equations, often known as an equation system, is a collection of finite equations for which common solutions are sought.

The two given equations can be simplified as:

[tex]8^x \div 2^y = 64\\\\or,\frac{2^{3x}}{2^y} =2^6\\\\or, 2^{3x-y}=2^6\\\\or, 3x-y = 6[/tex]

And :

[tex]3^{4x} \times (\frac{1}{9})^{y-1}=81\\\\or, 3^{4x} \times 3^{-2(y-1)}=3^4\\\\or, 3^{4x+2-2y}=3^4\\\\or, 4x-2y = 2\\\\or,2x-y=1[/tex]

Now we can solve the two simultaneous equations :

3x - y = 6 and 2x - y = 1

Subtracting the equations we get:

x = 5

and

y = 9

Solving the simultaneous equations we get the value of x as 5 and the value of y as 9 .

To learn more about simultaneous equations visit:

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f(n) = 4(n-1) + 7

fine the first three(3) terms in the sequence show all work​

Answers

........................................

Answer:

f(n) = 4(n-1) + 7

First term

f(1) = 4(1-1) +7 = 0 + 7 = 7

Second term

f(2) = 4(2-1) + 7

= 4(1) + 7 = 4 + 7 =11

Third term

f(3) = 4(3-1) + 7

= 4(2) + 7

= 8 + 7 = 15

Therefore the first three terms of the sequence are 7, 11 and 15.

Hope this helps

Find the upper bonds for the following lengths : a) 40cm measured to the nearest cm
B)82.8cm measured to the nearest tenth of a cm

Answers

Answer: a= 40.5 b= 82.85

Step-by-step explanation:

Which bar diagram represents the equation 5x + 7.5 = 15?
5X
7.5
15
7.5
5X
15
15
5x
7.5
LO
7.5x
15
Mark this and return
Save and Exit
Next​

Answers

Answer:

it would be C i took the test

Step-by-step explanation:

Answer:

The answer would be C because i just took the test and got it right hope this helps.

Step-by-step explanation:

72= 27+ 9s solve the equation

Answers

Answer:

s=5

Step-by-step explanation:

72=27+9s

Subtract 27 from both sides.

72-27=9s+27-27

45=9s

Divide 9 from both sides.

5=s

Ms. Redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented.

A number line going from 0.5 to 5. 0 dots are above 0.5 0 dots are above 1. 2 dots area above 1.5. 1 dot is above 2. 3 dots are above 2.5. 1 dot is above 3. 2 dots are above 3.5. 1 dot is above 4. 0 dots are above 2.5. 0 dots are above 5.

The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph?

A. The median will decrease.
B. The mean will decrease.
C.The median will increase.
D. The mean will increase.

Answers

Let's see if we can recreate the histogram from the description.

Time count

0.5  0

1       0

1.5    2

2      1

2.5   3

3       1

3.5    2

4       1

4.5    0

5       0

The mean is between 2.5 and 3 so that will definitely decrease with a data point that's less that that, as 0.5 is.  

For 10 data points the median is the average of the 5th and 6th when sorted, and those are both 2.5.  When the new point is added the median will be the 6th of 11 points, still 2.5 in this story.

Answer: B  the mean will decrease

Answer:

B

Step-by-step explanation:

This is because the mean will decrease

Part of a book fell out. The first page of this part has number 143. The last page has a number written with the same digits. How many pages are in the part of the book which has fallen out?

Answers

Answer:

142 pages

Step-by-step explanation:

The parameters given are

First page of part of the book available = 143

The last is numbered with the digits 143

Since the book is said to have been split into two parts with, we have that one part of the book starts from the beginning, while the other part continue from the first part stops

Number on the pages on the first part = from 1 to number on the first page on the second part - 1

Hence, the part of the book available is the second part and the number of pages in the first part = 1 to 142 or 142 pages.

in a given year, the rate of flu infection for the general public was 8.3%. And sample of 200 people who receive the flu vaccine, the rate of flu infection was just 3.5%. What conclusion should you draw?​

Answers

Answer:

[tex]\fbox{\begin{minipage}{10em}Option A is correct\end{minipage}}[/tex]

Step-by-step explanation:

Step 1: Define significance level

In this hypothesis testing problem, significance levels α is selected: [tex]0.05[/tex], the associated z-value from Laplace table:

Φ([tex]z[/tex]) = α - [tex]0.5 = 0.05 - 0.5 = -0.45[/tex]

=> [tex]z[/tex] = [tex]-1.645[/tex]

Step 2: Define null hypothesis ([tex]H_{0}[/tex]) and alternative hypothesis ([tex]H_{1}[/tex])

[tex]H_{0}[/tex] : rate of flu infection [tex]p[/tex] = 8.3% or 8.3/100 = 0.083

[tex]H_{1}[/tex] : rate of flu infection [tex]p[/tex] < 8.3% or 8.3/100 = 0.083

Step 3: Apply the formula to check test statistic:

[tex]K = \frac{f - p}{\sqrt{p(1 - p)} } * \sqrt{n}[/tex]

with [tex]f[/tex] is actual sampling percent, [tex]p[/tex] is rate of flu infection of [tex]H_{0}[/tex], [tex]n[/tex] is number of samples.

The null hypothesis will be rejected if [tex]K < z[/tex]

Step 4: Calculate the value of K and compare with [tex]z[/tex]

[tex]K = \frac{(\frac{3.5}{100}) - 0.083}{\sqrt{0.083(1 - 0.083)} } * \sqrt{200} = -2.46[/tex]  

We have [tex]-2.46 < -1.645[/tex]

=>This is good evidence to reject null hypothesis.

=> The actual rate is lower. (As [tex]H_{1}[/tex] states)

Hope this helps!

:)

What is a equivalent expression to $3.79 x 2 = $7.58

Answers

Answer: $7.58/2=$3.79

Step-by-step explanation:

URGENT!! Please help if you can!!
Does this represent a nonlinear function, liner function, or no function at all?

Answers

Answer:

Not a function.

Step-by-step explanation:

It is not a function since it does not pass the vertical line test.

Answer:

not a function

Step-by-step explanation:

you can test it out by sliding your pencil thru the graph and making sure

the function doesn't cross thru the pencil twice

PLEASE HELP ASAP!!!
How is solving addition and subtraction equations similar to and different from solving multiplication and division equations?

Answers

Answer:

Here is what I think:

Addition and Multiplication are very similar. Multiplication is just repeated addition. If you do 3*2 its just adding 3, 2 times to each-other. The same goes for division. Its repeated subtraction. 15/3 If you subtract 3 from 15 how many times can you do it. There are also differences though. Multiplication is usually used to calculate different things though. It can calculate area and volume while addition usually doesn't. Division is used to find how much of something can fit into something. But subtraction usually is only used for subtracting other things. Those are similar things and different things for this.

Complete the following: 2197 is the CUBE root of ______

Answers

The Cube root of 2197 is 13.

I will give you brainliest!!!! Use substitution method to solve the system of equations. y=6x-5 y=x+5

Answers

Answer:

(2,7)

Step-by-step explanation:

y=6x-5

y=x+5

Since they are both equal to y, set them equal to each other

6x-5 = x+5

Subtract x from each side

6x-x-5 = x+5-x

5x-5 = 5

Add 5 to each side

5x-5 +5 = 5+5

5x=10

Divide by 5

5x/5 = 10/5

x=2

y = x+5

y = 2+5

y =7

Answer:

Choice C: (2,7)

Step-by-step explanation:

Using substitution method let y = x + 5

We have x + 5 = 6x - 5

Get let’s get rid of the 6x, so -5x + 5 = -5

Get rid of the 5 by subtracting by 5, so -5x = -10

Divide -5 on both sides and you get x = 2

Input 2 for x in y = x + 5, we get y = 2 + 5, which equals 7.

So (2,7)

Please mark BRAINLIEST!

7. The length of a minute hand of a clock is 3.5cm. Find the angle it turns through if it
sweeps an area of 48 cm. (Taken=22/7)
(3 marks)
Page 2 of 3​

Answers

Answer:

The angle it turns through if it  sweeps an area of 48 cm²   is   448.8°

Step-by-step explanation:

If the length of a minute hand of a clock is 3.5cm, to find the angle it turns through if it  sweeps an area of 48 cm, we will follow the steps below;

area of a sector = Ф/360  ×   πr²

where Ф is the angle,  r is the radius   π is a constant

from the question given, the length of the minute hand is 3.5 cm, this implies that radius r = 3.5

Ф =?   area  of the sector= 48 cm²    π = [tex]\frac{22}{7}[/tex]

we can now go ahead to substitute the values into the formula  and solve Ф

area of a sector = Ф/360  ×   πr²

48   =  Ф/360  ×  [tex]\frac{22}{7}[/tex] × (3.5)²

48 = Ф/360  ×  [tex]\frac{22}{7}[/tex] ×12.25

48 = 269.5Ф / 2520

multiply both-side of the equation by 2520

48×2520 = 269.5Ф

120960 = 269.5Ф

divide both-side of the equation by 269.5

448.8≈Ф

Ф = 448.8°

The angle it turns through if it  sweeps an area of 48 cm²   is   448.8°

5. A car uses 10 litres of petrol in 75 km. How far will it go on 8 litres?​

Answers

Answer:

60km

Step-by-step explanation:

75/10=x/8

Solve For X

75*8=600,   600/10=60

THEREFORE

75/10=60/8

You could ALSO Divide 75 by 10, get 7.5, and multiply THAT by 8, as the car is assumed to have constant gas usage

Answer:

60km

Step-by-step explanation:

Let x represent the required distance.

Since the quantity of petrol is directly proportional to the distance:

x : 75 = 8 : 10

i.e.      [tex]\frac{x}{75}[/tex] = [tex]\frac{8}{10}[/tex]

           x = [tex]\frac{75 * 8}{10}[/tex]

           x = 60

∴ The distance is 60 km.

Hope this helps!!!

Write down the solution for 5x - 12 = x - 8. Write down your answer in the form x =

Answers

Answer:

x= 1

Step-by-step explanation:

5x - 12 = x - 8

Subtract x from each side

5x -12 -x = x-8-x

4x -12 = -8

Add 12 to each side

4x-12+12 = -8+12

4x = 4

Divide each side by 4

4x/4 = 4/4

x = 1

Answer:
x = 1

Steps:
5x - 12 = x - 8
-x -x

4x - 12 = -8
+12 +12

4x = 4
/4 /4

x = 1
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