Answer:
1. Sine θ = 1/3
2. Cos θ = 2√2 / 3
3. Tan θ = √2 / 4
4. Cosec θ = 3
5. Sec θ = 3√2 / 4
6. Cot θ = 2√2
Step-by-step explanation:
We'll begin by determining the adjacent. This can be obtained as follow:
Hypothenus (Hypo) = 9
Opposite (Opp) = 3
Adjacent (Adj) =?
Hypo² = Adj² + Opp²
9² = Adj² + 3²
81 = Adj² + 9
81 – 9 = Adj²
72 = Adj²
Take the square root of both side
Adj = √72
Adj = 6√2
Finally, we shall determine six trigonometric functions of the angle θ. This Can be obtained as follow:
1. Determination of Sine θ
Hypothenus = 9
Opposite = 3
Sine θ =?
Sine θ = Opposite / Hypothenus
Sine θ = 3/9
Sine θ = 1/3
2. Determination of Cos θ
Adjacent = 6√2
Hypothenus = 9
Cos θ =?
Cos θ = Adjacent / Hypothenus
Cos θ = 6√2 / 9
Cos θ = 2√2 / 3
3. Determination of Tan θ
Opposite = 3
Adjacent = 6√2
Tan θ =?
Tan θ = Opposite / Adjacent
Tan θ = 3 / 6√2
Tan θ = 1 / 2√2
Rationalise
(1 / 2√2) × (2√2 /2√2)
= 2√2 / 4×2
Tan θ = √2 / 4
4. Determination of Cosec θ
Sine θ = 1/3
Cosec θ =?
Cosec θ = 1 / Sine θ
Cosec θ = 1 ÷ 1/3
Cosec θ = 1 × 3/1
Cosec θ = 3
5. Determination of sec θ
Cos θ = 2√2 / 3
Sec θ =?
Sec θ = 1 / Cos θ
Sec θ = 1 ÷ 2√2 / 3
Sec θ = 1 × 3 / 2√2
Sec θ = 3 / 2√2
Rationalise
= (3 / 2√2) × (2√2 / 2√2)
= 3 × 2√2 / 4×2
Sec θ = 3√2 / 4
6. Determination of Cot θ
Tan θ = √2 / 4
Cot θ =?
Cot θ = 1 / Tan θ
Cot θ = 1 ÷ √2 / 4
Cot θ = 1 × 4 / √2
Cot θ = 4 / √2
Rationalise
= (4 / √2) × (√2 / √2)
= 4√2 / 2
Cot θ = 2√2
Could someone please help me out
Answer:
It's 108
You add the sides 48 and 24 and then subtract it from 180. That how you get your answer.
a bowling ball with a diameter of 10.9
Answer:
34.226
Step-by-step explanation:
10.9 ÷ 2 = 5.45
C = 2πr
2 × 5.45 × 3.14
34.226
To the nearest tenth, what percentage of people were in the 41 - 50 age group and favored the Do-It-Yourself books?
A. 9.2%
B 20.4%
C. 45.1%
D. 57.1%
HELPP ASAP
Answer: it should be 9.2%
Step-by-step explanation:
The percentage of people in the [tex]41 - 50[/tex] age group and favored the Do-It-Yourself books will be [tex]9.2\%[/tex] .
What is Percentage ?Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, [tex]"\%"[/tex] .
Percentage [tex]=\frac{Obtained\ Number}{Total\ Number} *100[/tex]
We have,
Total number of people [tex]=750[/tex]
Number of people in the [tex]41 - 50[/tex] age group [tex]=268[/tex]
Number of people in the [tex]41 - 50[/tex] age group and favored the Do-It-Yourself books [tex]=69[/tex]
So,
Percentage of favored the Do-It-Yourself books in the [tex]41 - 50[/tex] age group [tex]=\frac{Do-It-yourself\ 41-50\ age}{Total\ Number\ people} *100[/tex]
[tex]=\frac{69}{750} *100[/tex]
[tex]=9.2\%[/tex]
So, the percentage of people is [tex]9.2\%[/tex] .
Hence, we can say that the percentage of people in the [tex]41 - 50[/tex] age group and favored the Do-It-Yourself books will be [tex]9.2\%[/tex] .
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Find the area of the shaded region to the nearest tenth.
Answer:
Shaded region is 18.3 units²
Step-by-step explanation:
First find the area of the white triangle. The base and height of this triangle are both 8. Thus, the area of the triangle is (1/2)(base)(height), or 32 units.
Next, find the area of the whole circle. It is πr², which in this case comes
out to π(8 units)² = 64π units². Realize that (1/4) of this, or 16π units², is the area of the quarter circle that contains the triangle.
To find the shaded area, take the area of the quarter circle (16 π units²) and subtract the area of the triangle (32 units²).
16π units² - 32 units² = 18.3 units²
Shaded region is 18.3 units²
Simplify the expression. Write your answer as a power.
Answer:
either 2^8/3^8 or 256/6561
Step-by-step explanation:
looked it up on Symbolab
Hi :) I'm working with rational and irrational numbers. There's a problem .025 with the 25 repeating. If anyone could lend some help on how to solve an equation like this. It would be greatly appreciated.
Please answer correctly !!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
If I remember correctly it should be 7 for the first one and 5 for the second
Answer:
7 & 5
Step-by-step explanation:
Hope it helps:)!!!!!
This bar graph shows the money earned from the sale of skateboards one Saturday at four stores. What can you tell from the information in this graph? A) Skateaway sold the most skateboards. B) Skating is more popular at Great Skates. At Ben's Boards, skateboards cost the least. D) Skateaway made the most money selling skateboards.
Answer:
its D <3
Step-by-step explanation:
hope this helps :)
Answer:
D) Skateaway made the most money selling skateboards.
I just took the test I got it right.
Stay gold
can you help me please I have been stuck
x = 8 is the solution for which equation?
A. -4 + 8p = 68
B. 4 + 8p = 68
C. 4 + -8p = 68
D. 4 + 8p = -68
Answer:
a. -4 + 8p = 68
8p = 68 + 4 = 72
p = 72/8 = 9
a. is not the answer as the solution is not 8
b. 4 + 8p = 68
8p = 68 - 4 = 64
p = 64/8 = 8
b. is the answer as the solution is 8
c. 4 + -8p = 68
-8p = 68 - 4 = 64
p = 64/-8 = -8
c. is not the answer as the solution is not 8
d. 4 + 8p = -68
8p = -68 -4 = -72
p = -72/8 = -9
d. is not the answer as the solution is not 8
b. is the answer
hope this answer helps you..
please mark as brainliest.. thank you!
Determine the intercepts of the line.
Answer:
-8,-6
Step-by-step explanation:
4. Ann bought four pens and three exercise books for a total of sh 17 while peter bought five
similar pens and two exercise books for a total of sh.16 find the cost of a pen and an exercise
book.
Answer:
pen = 2 book = 3
Step-by-step explanation:
p= pens
b=books
4p +3b =17
5p+2b=16
Multiply the first by 5
Multiply the second by -4
Add both (p variable will ce cancelled)
20p +15b = 85
-20p -8b = -64
7b = 21
b=3 (book =3)
Lets plug this in one of the equations
4p + 3x3 = 17
4p +9 0 19
4p = 8
p= 2 (pencil = 2)
Which function has the same range as
f(x)= -2sqrt (x-3)+8
Answer:
Answer: : g(x)=-sqrt(x+3)+8
Step-by-step explanation:
The function has the same range is the third one:
g(x)=-sqrt(x+3)+8
The range of this function is:
x+3>=0
sqrt(x+3)>=sqrt(0)
sqrt(x+3)>=0
Multiplying the equation by -1:
-1[ sqrt(x+3)>=0]
- sqrt(x+3)<=0
Adding 8 both sides of the equation:
- sqrt(x+3)+8<=0+8
- sqrt(x+3)+8<=8
g(x)<=8
Then Range g(x)= (-Infinite, 8]
Answer: Third option: g(x)=-sqrt(x+3)+8
Which of the following expressions is not equal to X^3?
A. X^5 . X^-4 .X^2
B. X^-2 .X^9 .x^-4
C.x^0 . x^10 . x^-7
D. x. x^7 . x^-4
Answer:
D. x. x^7 . x^-4
Step-by-step explanation:
A. X^5 . X^-4 .X^2=X^(5-4+2)= X^3
B. X^-2 .X^9 .x^-4=X^(-2+9-4)= X^3
C.x^0 . x^10 . x^-7=X^(0+10-7)= X^3
D. x. x^7 . x^-4=X^(1+7-4)= X^4
Triangle ABC is similar to triangle FGH.
A) 24 cm
B) 9 cm
C) 15.75 cm
D) 28 cm
Answer:
C
Step-by-step explanation:
8x - 22 = 230 -10x Find what x is
Answer:
x = 14
Step-by-step explanation:
Here's your solution
=> 8x - 22 = 230 - 10x
=> 8x + 10x = 230 + 22
=> 18x = 252
=> x = 252/18
=> x = 14
hope it helps. 【●●】
Given the side lengths, determine whether the triangle is acute, obtuse, right, or not a triangle: 8,15,23
Answer:
hablas español? O no??, no se tu pregunta pique no se ingles perdón
Answer:
Obtuse angled triangle
Step-by-step explanation:
If a, b and c are the sides of a triangle with c the largest side
• If a² + b² = c² ⇒ right triangle
• If a² + b² > c² ⇒ acute angled
• If a² + b² < c² ⇒ obtuse angled
Here a = 8, b = 15, c = 23
a² + b² = 8² + 15² = 64 + 225 = 289
c² = 23² = 529
Since a² + b² < c² then obtuse angled triangle
Due tonight.. *no links*
HELP PLEASE I HAVE BEEN STUCK FOR HOURS THIS IS DUE- I'll mark brainliest. In parallelogram WXYZ, diagonal WY is drawn, M and N are points on WX and YZ respectively, and WY intersects MN at E. If m<Z= 60°, m<WYX= 84°, and m<NEY= 102°, find m<ZNM. l'll mark brainliest, I'm not sure how to do this problem and I'm stressed-
Answer:
m<ZNM = 138 degrees
Step-by-step explanation:
Answer:
138°Step-by-step explanation:
We can observe that:
∠ZWY ≅ ∠XYW as alternate interior anglesm∠ZWY = m∠XYW = 84°m∠WEN = 180° - m∠NEY = 180° - 102° = 78°, as straight angle is 180°m∠WZN = 60° - givenConsider sum of interior angles in quadrilateral WENZ:
m∠ZWY + m∠WEN + m∠WZN + m∠ZNM = 360°Substitute values and find the missing angle:
m∠ZNM = 360° - (84° + 78° + 60°) = 138°A. X=1
B. X=2
C. X=3
D. X=4
E. X=5
F. X=6
Answer:
1.) 5
2.) 6
3.) 2
4.) 2
5.) 2
6.) 5
A large bacterium measures 750 micrometers in diameter. One micrometer = 10 − 6 meters. How would you express the diameter of the bacterium in meters using scientific notation? A. 7 . 5 × 10 − 8 B. 750 × 10 − 6 C. 75 × 10 − 5 D. 7 . 5 × 10 − 4
Answer:
7.5 * 10^-4
Step-by-step explanation:
To express this, we will have to multiply 750 by the conversion unit
we have this as;
750 * 10^-6
750 = 7.5 * 10^2
so we have;
7.5 * 10^2 * 10^-6
= 7.5 * 10^(-6+2)
= 7.5 * 10^-4
The diameter of the bacterium in meters using scientific notation is 7.50 × 10^-4
Length of the bacterium = 750 micrometersOne micrometer = 10^-6How to write scientific notationMove the decimal point in between the first and second numberCount the number of digits after the decimal pointDiameter of the bacterium in scientific notation = 7.50 × 10²
Recall one micrometer = 10^-6
So
7.50 × 10² × 10^-6
= 7.50 × 10^(2-6)
= 7.50 × 10^-4
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Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. How fast was the wind blowing that day?
4 mph
7 mph
10 mph
12 mph
Answer:it’s 4 mph
Step-by-step explanation:
Answer: 4mph
Step-by-step explanation:
Edge 2021
A high school drama club is selling tickets for a fundraiser event. Based on data from past events, the number of tickets sold can be modeled by a linear function Q(x) = −40x + 640, where x is the price, in dollars, of each ticket. The revenue R can be determined by multiplying the ticket price x by the number of tickets sold. Write a quadratic function R that correctly represents this model.
The quadratic function R that correctly represents the revenue model is given by R(x) = -40x² + 640x.
To find the quadratic function R that represents the revenue, we need to multiply the ticket price x by the number of tickets sold Q(x).
Given that the number of tickets sold Q(x) is given by the linear function Q(x) = -40x + 640, the revenue R can be calculated as:
R(x) = x * Q(x)
Substitute the expression for Q(x) into the revenue equation:
R(x) = x * (-40x + 640)
Now, we'll expand the expression:
R(x) = -40x² + 640x
Thus, the quadratic function R that correctly represents the revenue model is given by R(x) = -40x² + 640x.
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Jamal works at the recreation center 40 hours a week during the school year. He earns $8.75 an hour for 8 hours a day. Bi-weekly, he works 80 hours. Calculate his bi-weekly taxes below.
Answer:
40x8.75=$350, 80-40=40x8=$320 350+320=$670
Answer:
670
Step-by-step explanation:
Pls help meee。I’m so confused TwT
Find the distance between points l and m then find the distance between points l and n which distance is greater howmuch
Answer:
Following are the responses to the given question.
Step-by-step explanation:
In this question, the points values are missing which is why its solution can be defined as follows:
Let
[tex]l= (7,-1) \\\\m=(-2, 4)\\\\n =(6,5)\\\\[/tex]
Formula:
[tex]d=\sqrt{((x_2-x_1)^2+(y_2-y_1)^2)}[/tex]
For d1:
[tex]x_1=7, y_1=-1, x_2=-2, y_2=4\\\\[/tex]
[tex]d=\sqrt{((-2-7)^2+(4+1)^2)}[/tex]
[tex]=\sqrt{((-2-7)^2+(4+1)^2)}\\\\=\sqrt{((-9)^2+(5)^2)}\\\\=\sqrt{(81+25)}\\\\=\sqrt{(106)}\\\\=10.29[/tex]
For d2:
[tex]x_1=7, y_1=-1, x_2=6, y_2=5\\\\[/tex]
[tex]d=\sqrt{((6-7)^2+(5+1)^2)}[/tex]
[tex]=\sqrt{((-1)^2+(6)^2)}\\\\=\sqrt{(1+36)}\\\\=\sqrt{(37)}\\\\=6.08[/tex]
The first distance value is greater than the second distance value.
PLSSSS Plsssss help quick
Answer:
(x, y) (1,5.5) , (2,5.75) (3,5.83) (4,5.875) (5,5.9)
Step-by-step explanation:
The x values lie on the horizontal line and the y values lie on the vertical line.
In order to find the value of y you must substitute the value of x in the equation given and you must plot you graph using the answers you got which I wrote for you.
NOTE:if there's anything you don't understand let me know.
50 PTS!!!!Which statements must be true to model a data set using a normal distribution?
The population mean must be greater than the sample mean.
The sample size, n, must be at least 30.
The standard deviation of the population must be less than 30.
The sample must be randomly selected.
The sample mean must equal the population mean.
-There are multiple answers
Answer:
Normal distributions are symmetric around their mean. The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0. Normal distributions are denser in the center and less dense in the tails.
Step-by-step explanation:
Extra Answered question:
How do you determine if a distribution is normal?
Answer: In order to be considered a normal distribution, a data set (when graphed) must follow a bell-shaped symmetrical curve centered around the mean. It must also adhere to the empirical rule that indicates the percentage of the data set that falls within (plus or minus) 1, 2 and 3 standard deviations of the mean.
I hope this is what your looking for :)
Answer:
I don't the right answers but I know these answers are incorrect:
The sample mean must equal the population mean.
The standard deviation of the population must be less than 30.
Step-by-step explanation:
Select the correct answer.
Members of a student council are designing a school float for a parade. They decide to poll 10% of the student body to get feedback about the
theme they have chosen.
What would most likely happen if they decided to randomly sample 5% of the student body instead?
Answer: The sample portion would less closely model the population proportion
Answer:
Answer is that is will less closely model to the total population.
Step-by-step explanation:
This is because there are less numbers to be chosen and will be harder to find a proper medium and mean.
Kayla has 16 cups of trail mix that she wants to give to her friends. She decides to divide it into cup portions. How many portions can she make?
[?] portions
Answer:
16
Step-by-step explanation: