Recall that
cos²(x) + sin²(x) = 1
for all x, so that
sin(x) = ± √(1 - cos²(x))
Given that cos(θ) = 4/9 > 0, and
tan(θ) = sin(θ) / cos(θ) < 0
it follows that sin(θ) < 0, so
sin(θ) = - √(1 - cos²(θ)) = - √(1 - (4/9)²) = - √(65)/9
The value of sinθ is √(65)/9.
What is a sine function?The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.
Since cos(theta) = 4/9 and tan(theta) < 0, we know that theta is in the second quadrant of the unit circle, where cosine is positive and sine is positive.
We can use the Pythagorean identity to find sin(theta):
sin²(theta) + cos²(theta) = 1
Substituting in the given value of cos(theta), we get:
sin²(theta) + (4/9)² = 1
sin²(theta) + 16/81 = 1
sin²(theta) = 1 - 16/81
sin²(theta) = 65/81
Taking the square root of both sides, we get:
sin(theta) = ± sqrt(65)/9
Since theta is in the second quadrant where sine is positive, we can take the positive root:
sin(theta) = sqrt(65)/9
Therefore, sin(theta) = sqrt(65)/9.
To learn more about the sine function;
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Tommy is using a bucket to collect nuts from a nut tree. He then dumps the bucket into a barrel for shipping of the nuts. He notices that 1 over 4 bucket of nuts fills 2 over 3 of the barrel.
Part A: Write and solve an equation to find the amount of nuts that will fill the entire barrel. Show your work. (8 points)
Part B: Explain your answer in words. (2 points)
Answer:
3/8 bucketStep-by-step explanation:
Given that 1/4 bucket of nuts fills 2/3 of the barrel
PART A
To find the amount of nuts that fills entire basket we can put this as:
1/4 bucket → 2/3 barrelx bucket → 1 barrelUse cross-multiplication to find the value of x:
x×2/3 = 1×1/4x = 1/4 ÷ 2/3x = 1/4×3/2x = 3/8 bucketPART B
Using the bucket to barrel ratio to solve the problem. Having the number of required buckets as x and considering full barrel as 1 helps to find the value of x.Solve the following equation for the value for x.
7(0.3x - 0.9) = 6x-0.6 (18 +4x)
Help please I don’t get it
Answer:
[tex]12+\frac{1}{4}\cdot12[/tex] [tex],[/tex] [tex]12\left(1+\frac{1}{4}\right)[/tex] [tex]and[/tex] [tex]12\cdot\frac{5}{4}[/tex]
Step-by-step explanation:
[tex]--------------------------------------------[/tex]
[tex]\frac{1}{4}[/tex] [tex]of[/tex] [tex]12[/tex] [tex]is[/tex] [tex]3[/tex]
[tex]12+3[/tex] = [tex]15[/tex]
[tex]--------------------------------------------[/tex]
[tex]12+\frac{1}{4}[/tex] = [tex]12.25[/tex] ✘
[tex]12\cdot\frac{1}{4}[/tex] = [tex]3[/tex] ✘
[tex]12+\frac{1}{4}\cdot12[/tex] = [tex]15[/tex] ✔
[tex]12\left(1+\frac{1}{4}\right)[/tex] = [tex]15[/tex] ✔
[tex]12\cdot\frac{3}{4}[/tex] = [tex]9[/tex] ✘
[tex]12\cdot\frac{5}{4}[/tex] = [tex]15[/tex] ✔
[tex]--------------------------------------------[/tex]
Sorry that it took long, really wanted to work hard on this one.
[tex]--------------------------------------------[/tex]
Hope this helps! <3
[tex]--------------------------------------------[/tex]
can u pls help me with this question
Answer:
i believe the answer is b
Step-by-step explanation:
unit means one
Is 9.78778777... a rational or irrational number?
Answer:
rational
Step-by-step explanation:
Use the elimination method to solve the following system. 6x – 7y = –8 –x – 4y = –9
(–6, –3)
(0, 4)
(–3, 8)
(1, 2)
-45 + s = -105, s = ?
Answer:
s = - 60
Step-by-step explanation:
-45 + s = -105
s = -105 + 45
s = - 60
4(x - 1) + 5x = 6x - 16
Please help me solve the equation
Answer:
x=−4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
4(x−1)+5x=6x−16
(4)(x)+(4)(−1)+5x=6x+−16(Distribute)
4x+−4+5x=6x+−16
(4x+5x)+(−4)=6x−16(Combine Like Terms)
9x+−4=6x−16
9x−4=6x−16
Step 2: Subtract 6x from both sides.
9x−4−6x=6x−16−6x
3x−4=−16
Step 3: Add 4 to both sides.
3x−4+4=−16+4
3x=−12
Step 4: Divide both sides by 3.
3x/3=-12/3
x=-4
Answer:
4x-4+5x=6x-16, 9x-4=6x-16, 3x=-12, x=-4
Step-by-step explanation:
Perform the following operation
and express the answer in
scientific notation.
4.0x105 x 3.0x103
[ ? ]x10!?)
Answer:
Step-by-step explanation:
first step, multiply 4 and 3
4x3=12 , we write is 1.2x10
10^5 x10^3=10^8
4 x10^5 x 3 x 10^3= 1.2x10^9
The required answer is 1.20 x 10⁹ in scientific notation.
What is scientific notation?Scientific notation is a method of writing extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, it is written in scientific notation.
Here,
To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. Applying this rule, we get:
= (4.0 x 10⁵) x (3.0 x 10³)
= (4.0 x 3.0) x (10³ x 10⁵)
= 12.0 x 10⁵⁺³
= 12.0 x 10⁸
However, the answer is not yet in proper scientific notation form because the coefficient 12.0 is not between 1 and 10. To express the answer in scientific notation, we need to adjust the coefficient and exponent so that the coefficient is between 1 and 10. We can do this by dividing the coefficient by 10 and increasing the exponent by 1. Doing this, we get:
12.0 x 10⁸ = 1.20 x 10⁹
Therefore, the answer is 1.20 x 10⁹ in scientific notation.
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"simplify 3/5+(-1/4) ÷ 7/10" How can you answer this question. and what's the answer, can you help me out please
Answer:
s
Step-by-step explanation:
Answer:
17/70
Step-by-step explanation:
First use PEMDAS which is the order to solve questions like these.
Parenthesis
Exponents
Multiplication
Division
Addition
and Subtraction
There is one parenthesis which has a (-1/4) so let's start with that, we know that when there is a negative and a positive sign the negative out rules the positive
3/5-1/4 divided by 7/10 (Sorry I don't have the division sign on my device)
There are no exponents or multiplication but there is division
-1/4 divided by 7/10 is -5/14
3/5-5/14 is 17/70
Thus, our answer is 17/70
what is the value of d+3
Answer:
you need to explain
Step-by-step explanation:
Whats h to the power of itself
Answer:
h squared (h^2)
Step-by-step explanation:
h to the power of its self is just h squared
Fernando loves to make music playlists. He likes to keep the same ratio of country songs to rock songs. On his summer playlist, he has 100 country songs and 24 rock songs. On his road trip playlist, Fernando has 25 country songs.
How many rock songs are on Fernando's road trip playlist?
Answer:
There are 6 rock songs on Fernando's road trip playlist.
Step-by-step explanation:
Given that he keeps the ratio same
This means that the ratios for both summer playlist and trip playlist will be the same
Let
c1 be the country songs in summer playlist
r1 be the rock songs in trip playlist
Similarly,
c2,r2 will be the country and rock songs in trip playlist
Both will be equal so
[tex]\frac{c_1}{r_1} = \frac{c_2}{r_2}[/tex]
Putting the values
[tex]\frac{100}{24} = \frac{25}{r_2}\\100r_2 = 25*24\\100r_2 = 600r_2 = \frac{600}{100}\\r_2 = 6[/tex]
Hence,
There are 6 rock songs on Fernando's road trip playlist.
Answer:
6 songs
Step-by-step explanation:
need help with this one
Answer:
triangle 2.854e55
Step-by-step explanation:
help need done quick pls.
Help help help help help help pls
Answer:
a.) 36
b.) 18
c.) 27
Step-by-step explanation:
need help with this solve or r
Answer:
C
------ = r
2pi
Step-by-step explanation:
Divide both sides by 2pi. We get:
C
------ = r
2pi
At a bake sale, as student spent $11.00 buying 3 brownies and 5 cookies. His friend spent $3.95 buying 1 brownie and 2 cookies. What is the price of a brownie?
Answer:
$[tex]$2.25[/tex]
Step-by-step explanation:
Let [tex]b =[/tex] the cost of one brownie, [tex]c =[/tex] cost of one cookie
[tex]3b + 5c = 11[/tex]
[tex]b+2c = 3.95[/tex]
Times [tex]3[/tex] on both sides on the second equation above to get the following:
[tex]3b + 6c = 11.85[/tex]
[tex]3b+6c - (3b+5c) = 11.85-11[/tex]
[tex]3b+6c-3b-5c = 0.85[/tex]
[tex]c = 0.85[/tex]
To find the value of [tex]b[/tex], use substitution:
[tex]b+2c = 3.95[/tex]
[tex]b = 3.95-2c[/tex]
[tex]= 3.95 - 2\times0.85[/tex]
[tex]= 2.25[/tex]
[tex]\therefore[/tex] the cost of a brownie is $[tex]$2.25[/tex]
Hope this helps :)
Vocabulary Is every relation also a function? Use the drop-down menus to show and explain your answer.
Choose...
; A
Choose...
is a special type of
Choose...
where each input maps to exactly one output. In a
Choose...
, an input can have one or more outputs.
Answer:
19
Step-by-step explanation:
9+10 is not 21 it is 19.
If 2 tens make a 20 and 1 number is gone, 20-1=19
Help
w(a)=a-1; find w(0)
Answer:
Step-by-step explanation:
w(0) = 0-1
w(0) = 0-1
w(0) = -1
Since w(0), this basically means that a = 0.
So, plug 0 into anywhere a is.
The value of the function w(a) = a - 1 at a = 0 will be negative 1.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
w(a) = a - 1
The value of the function at a = 0 will be
w(0) = 0 - 1
w(0) = - 1
The value of the function w(a) = a - 1 at a = 0 will be negative 1.
More about the value of expression link is given below.
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is 3x+y=12 linear or nonlinear
Answer: It is linear
Can someone help me please
Answer:
31.42 m
Step-by-step explanation:
circumference = (pi)d
circumference = 3.14159 * 10 m
circumference = 31.4159 m
Answer: 31.42 m
Answer: circumference =31.42m
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
can u pls help me with this question
and the equations to choose from are
y=k+x
y=k
y=kx
y=kx
Step-by-step explanation:
That's the formula for direct variation relationships!
The other two answers are nonsense and don't mean anything.
Solve the equation.
W+3/3 = - 4
Answer:
W=−5
r=3
hope this helps!!
In the diagram below, what is the ratio of unshaded parts to shaded parts?
4 shaded triangles and 12 unshaded triangles.
4 unshaded to 9 shaded
9 unshaded to 4 shaded
3 unshaded to 1 shaded
1 unshaded to 3 shaded
Answer:
The answer is D.
Step-by-step explanation:
I hope this helps :D
PLEASE HELP!! I will mark brainliest
Answer:
the top one and bottom one
Step-by-step explanation:
Answer:
first and sixth
Step-by-step explanation:
they match
I need help, if is right I mark you as brainliest.
A. He made a division error.
B. He combined the variable terms incorrectly.
C. He combined the constants incorrectly.
D. He distributed -5 incorrectly.
Answer:
D. He distributed -5 incorrectly.
Step-by-step explanation:
Last option is the correct answer.
Answer:
Parker: D. He distributed -5 incorrectly.
Step-by-step explanation:
Find - square root 36
A.+6
B.-6
C.6
D.18
Help the I
Answer:
A.
Step-by-step explanation:
Seventh grade
M.1 Add, subtract, multiply, and divide money amounts: word problems HGN
You have prizes to reveal
A high-tech company came out with two new MP3 players this week. It costs $465 for the
model with more memory or $107 for the one with less memory. What is the price
difference?
Submit
Answer:
C. NUMBER OF DOWNLOADED SONGS
Step-by-step explanation:
Among the following, the independent quantity in the function:
amount of remaining MP3 player memory as a function of downloaded songs is
The remaining memory will depend on the number of songs downloaded. So, the number of downloaded songs is considered as the independent variable while the remaining memory is the dependent variable.
Answer:
Easy, 358
Step-by-step explanation:
because 2 new mp3 players are $465 and have new storage.
While 1 new mp3 player is $107 but it has less storage.
So we subtract because it's asking us the difference between the price of the $465 and the $107.
465
- 107
--------
358