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Leaders please answer this question
No. 8. a
Answers
Answer:
[tex] \frac{1}{ \sqrt{2} } [/tex]
Step-by-step explanation:
Given
[tex]theta = 22 \frac{1}{2} = \frac{45}{2} [/tex]
[tex]2 \times theta = \frac{45}{2} \times 2 = 45[/tex]
Sin2theta=sin45⁰=1/√2
[tex] \frac{1}{ \sqrt{2} } [/tex]
is your answer
Answer:
[tex]\sf \dfrac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
[tex]\sf If\:\theta=\left(22\dfrac12\right)^{\circ}[/tex]
[tex]\sf \implies2\theta=2\cdot\left(22\dfrac12\right)^{\circ}=45^{\circ}[/tex]
[tex]\sf Therefore\:\sin2\theta=\sin(45)^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]
Proof
If a right triangle has an interior angle of 45°, then the third interior angle will also be 45° (since the sum of the interior angles of a triangle is 180°).
This means that the two legs of the right triangle are equal in length.
Using Pythagoras' Theorem, we can state that the hypotenuse of a right triangle with two legs of equal length will be √2 times the length of a leg.
Let a = b = 1
⇒ 1² + 1² = c²
⇒ c = √2
The sine trig ratio is:
[tex]\mathsf{\sin(\theta)=\dfrac{O}{H}}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse[tex]\implies \sf \sin(45^{\circ})=\dfrac{1}{\sqrt{2} }[/tex]
[tex]\implies \sf \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies \sf \sin(45^{\circ})=\dfrac{\sqrt{2}}{2}[/tex]
Related Questions
On a circle of radius 10 feet, what angle would subtend an arc of length 6 feet?
Answers
Answer:
34.38 (rounding to the nearest hundredth)
Step-by-step explanation:
I have my work linked below, but I used to arc length formula and plugged in all known numbers. Then solved for x which will be the angle you are looking for. Hope this helps!
On a circle of radius 10 feet, 34.37° angle would subtend an arc of length 6 feet.
How to find the length of an arc?The length of an arc formula is represented as follows
The length of arc = Ф / 360 × 2πr
where
Ф = angle, r = radius
It is given that circle of a radius of 10 feet,
The length of arc = 6 ft
Therefore,
6 = Ф / 360 × 2 × 3.14159 × 10
6 = 62.8318Ф / 360
360 x 6 = 62.8318Ф
Ф = 360 x 6 / 62.8318
Ф = 34.3784
Ф ≈ 34.37°
Learn more about the length of the arc ;
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The numbers of hours mary works over a period of 8 days are 8, 7, 8, 8, 8, 7, 6, and 8. find the mean, median, mode, and range of the data set.
Answers
Answer:
Mode=8
This is because it occurs the most
Median
=8+8/2
=16/2
=8
Therefore, the median is 8
Mean= £x/n
=6+7+7+8+8+8+8+8/8
=60/8
=15/2
=7.5
Step-by-step explanation:
Please mark me brainliest if correct
The mean, median, mode, and range of the data set will be 7.5, 8, 8, and 2, respectively.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
The quantities of hours mary works over a time of 8 days are 8, 7, 8, 8, 8, 7, 6, and 8.
Arrange the data in increasing order, then we have
6, 7, 7, 8, 8, 8, 8, 8
The mean of the data is given as,
Mean = (6 + 7 + 7 + 8 + 8 + 8 + 8 + 8) / 8
Mean = 60 / 8
Mean = 7.5
The median of the data is given as,
Median = {[8 / 2 + (8 + 2)/ 2] / 2}
Median = (4th + 5th) / 2
Median = (8 + 8) / 2
Median = 16 / 2
Median = 8
The mode of the data is given as,
Mode = Frequency of the number
Mode = 8
The range of the data set is given as,
Range = 8 - 6
Range = 2
The mean, median, mode, and range of the data set will be 7.5, 8, 8, and 2, respectively.
More about the statistics link is given below.
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What are the prime numbers between 2010 and 2020
Answers
Answer: 99%
Step-by-step explanation:
please show your work and no links
and please do the one that are blank
Answers
Answer:
its blury
Step-by-step explanation:
Solve each pair of simulation equation. Multiply one equation by suitable numbers before adding/substracting to eliminate.
A) 2x+ 3y =11
x+ y = 4
B) 4x + 3y =-12
2x - y = 4
Answers
Answer:
A) x = 4, y = 3.
B. x = 0, y = -4.
Step-by-step explanation:
A) 2x+ 3y =11 .........(a)
x+ y = 4.......(b)
Multiply equation (b) by 2:
2x + 2y = 8
Subtract this from equation (a):
y = 11-8 = 3.
Substitute y = 3 into equation (a):
2x + 3*1 = 11
2x = 11 - 3 = 8
x = 4.
B) 4x+ 3y = -12
2x - y= 4
Multiply second equation by 2:
4x - 2y = 8
Subtract this from first equation:
3y - (-2y) = -12 - 8
5y = -20.
y = -4.
Substitute y = -4 into equation 1:
4x + 3*(-4) = -12
4x = -12 + 12 = 0
x = 0.
find the percentage profit in each case cost price 20 selling price 25
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
for profit percentage
p% =(sp-cp/cp)×100%
=(25-20/20)×100%
=25%
The profit percentage is 25%
Select each correct answer.
f(x) is a polynomial function.
f(x) is an exponential function.
g(x) is a polynomial function.
g(x) is an exponential function.
The output values of f(x) will remain greater than those of g(x) as the input values continue to increase.
The output values of g(x) will surpass those of f(x) as the input values continue to increase.
Answers
Answer:
f(x) is a polynomial function.g(x) is an exponential function.The output values of g(x) will surpass those of f(x) as the input values continue to increase.Explanation:
f(x) has a function of x³g(x) has a function of [tex]\sf 3^X[/tex]False statements:
The output values of f(x) will remain greater than those of g(x) as the input values continue to increase.f(x) is an exponential function - as crosses x-axis, exponential never crosses x-axisg(x) is a polynomial function - as has no valid power.Answer:
By examining the table of ordered pairs, notice that the function f(x) is the cube of [tex]x[/tex]. Therefore, [tex]f(x)=x^3[/tex]
By examining the table of ordered pairs, notice that as [tex]x[/tex] increases by a constant value, the value of the function g(x) increases by the common ratio of 3. Therefore, [tex]g(x)=3^x[/tex]
From the table, both functions equal 27 when [tex]x=3[/tex], therefore, the point of intersection of the two functions is (3, 27).
As x increases past [tex]x=3[/tex], g(x) increases quicker than f(x) since g(x) is an exponential function and f(x) is a cubic polynomial.
So the following statements are true:
f(x) is a polynomial functiong(x) is an exponential functionThe output values of g(x) will surpass those of f(x) as the input values continue to increase.Please refer to the attached graph of both functions with plotted ordered pairs.
6. Complete a glide translation (x-2, y) and then reflect over x axis. What would be the new ordered pairs for P'and S'?
Answers
The glide translation and the reflection over x-axis are illustrations of transformation
The new ordered pairs for P'and S'are (x - 2, -y)
How to determine the new ordered pairs?The given parameters are:
Glide translation (x-2, y)
Reflection over x axis
Assume the coordinates of point P and S are (x,y)
When translated, the new points would be:
(x-2, y)
The rule of reflection over the x-axis is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex](x - 2,y) \to (x - 2,-y)[/tex]
Hence, the new ordered pairs for P'and S'are (x - 2, -y)
Read more about transformation at:
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10y 5 +30y 3 −15y
Factor out the gcf then simplify the polynomial
Answers
10y⁵ + 30y³ - 15y =
5y * 2y⁴ + 5y * 6y² + 5y * (-3) =
5y (2y⁴ + 6y² - 3)
Question 1 of 5
What is the spread of the data?
..
. .
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Age of female U.S. Olympic swimmers (years)
A. 15 to 32 years
B. 14 to 33 years
O C. 24 to 32 years
D. 15 to 24 years
Answers
The lowest is 14 and the highest is 33.
The graph below represents data that was collected by students on the number of
social media posts they made the previous day.
What was the mean number of posts made?
Answers
Answer:
4
Step-by-step explanation:
To calculate the mean or average, add all the data point up and whatever the amount of data point there are is supposed to be divided by the sum of the data points. So in this case, 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. This is the sum of the data points. Now we have to divide by the amount of data points which is 7 (0 obviously has no value whatsoever). 28 divided by 7 is 4. The average/mean of the number of post made is therefore 4.
Hope this helps,
IShowSpeed's Right Hand Enthusiast
Please help :)))))))))))
Answers
Answer:
Your answer is C and D
Step-by-step explanation:
Answer:
D. y = -x - 1
Step-by-step explanation:
We are using slope-intercept form for this problem.
Since this line is going from upper left to bottom right we know it will have a negative slope.
The line intersects the y-axis at -1, so the b value is -1.
The equation for this line is D. y = -x - 1
is 69 less then a right angle
Answers
Answer:
yes it is less then a right angle
Step-by-step explanation:
? need in a day or 2 please! Is worth 23 points and brainiest!
Answers
Step by step explanation:
The area of a triangle is Area= base x height divided by 2.
Solve for the base:
Base= 2* area/ height and plug in the data:
Base= 2* 600/20
Final answer:
Base: 60 feet.
Answer:
60 feet
Step-by-step explanation:
The easiest way to do this is to go answer by answer with the triangle area formula :)
Formula: A=hb/2
H = height
B: base
Now lets solve this :)
Choice 1: 50 feet
50 x 20 = 1000
1000/2 = 500
Choice 2: 40 feet
Since 40 feet is smaller than the 50, we know this will not be correct :)
Choice 3: 120 feet
120 x 20 = 2400
2400/2 = 1200
Choice 4: 60 feet
60 x 20 = 1200
1200/2 = 600
The correct answer is 4, 60 feet :)
Have an amazing day!!
Please rate and mark brainliest!!
Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for it.
A sphere has a diameter of 3.8 centimeters.
The volume of the sphere is about
cm3
HELP ME PLS
Answers
Answer:
Step-by-step explanation:
Remark
You are given the diameter but the formula uses the radius. So your first job is find the radius. Then you use this value in the formula to find the volume. Substitute
Givens
pi = 3.14
d = 3.8
r = d/2
r = 3.8/2 = 1.9
Formula
V = (4/3) * pi * r^3
Solution
V = (4/3) * 3.14 * 1.9^3
V = 4/3 * 3.14 * 6.859
V = 28.7163
why is a parallelogram not always a rectangle
Answers
Answer:
A parallelogram by definition has 2 pairs of parallel sides.
A parallelogram could be:
____________
| |
|___________|
A rectangle in euclidean geometry has 4 right angles.
For example:
________________
| |
|_______________|
However, a parallelogram may have 2 pairs parallel sides but not 4 right angles.
For example:
______________
\ \
\______________\
Therefore, A parallelogram is not always a rectangle.
Hope this helps!!!
Please mark me as brainliest!!!
The ratio of the measures of the sides of a triangle is 2:11:15. If the perimeter of the triangle is 168 inches, find the length of the longest side.
Answers
Answer: 90
Step-by-step explanation:
Let the sides have lengths 2n, 11n, and 15n.
Since the perimeter is 168, 2n+11n+15n=168, meaning that n=6.
So, the longest side is 15(6)=90 inches.
Which symbol would correctly compare the values shown be
1-8|?|8
Answers
Answer:
=
Step-by-step explanation:
|-8|?|8|
8 ? 8
8 = 8
Hope this helps :)
Please solve for the value of 3
Answers
Answer:
P = 45
Step-by-step explanation:
180 - 90 = 90
90 / 2 = 45
P = 45
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
What’s the answer to the blank
Answers
Answer:
13.93
Step-by-step explanation:
find the mean
11.60 + 16.25 ÷ 2 = 13.93
Help me on this question please!
Answers
Answer:
1/5
Step-by-step explanation:
Arrange the numbers from smallest to largest...the median is the one in the middle of the list
-12/4 - 2.5 1/5 18/5 10 the middle is 1/5
If the simple interest on $5,000 for 4 years is $1,800, then what is the interest rate?
Answers
Answer:
9%
Step-by-step explanation:
Can some please explain and solve how to do these unit rate equations?
Answers
Find an angle between 0 degrees and 360 degrees that is coterminal with 950 degrees
Answers
Answer:
40 degrees
Step-by-step explanation:
(to find coterminal angles to a given angle, we add 360 degrees to the given angle or subject 360 degrees from the given angle any angle any number of time).
-1400 degrees is negative angl, so to get the coterminal angle between 0 degrees and 360 degrees ( the smallest positive coterminal angle), we must add multiples of 360 degrees until we get a possitive coterminal angle:
-1400 degrees+(360 degrees*4)
=-1400 degrees+1440
=40 degrees
so the answer is 40 degrees
A garden store bought a fountain at a cost of $995.66 and marked it up 100%. Later on, the store marked it down 25%. What was the discount price?
$
Answers
Answer:
$1493.49
Step-by-step explanation:
The original cost was doubled initially.
$995.66 x 2 = 1991.32
1991.32 x 0.75 (25% discount) = $1493.49
A baby weighs 7 pounds at birth. the table shows the baby's weigh after each month of its birth, up to the sixth month
Answers
Find a linear equation with two variables that, together with the
equation 10x + 5y = 1, would comprise a system
with one solution
Answers
Answer:
y = x
Step-by-step explanation:
Any equation that describes a different line will be part of a system with exactly one solution. There are an infinite number of possible equations.
Perhaps one of the simplest is ...
y = x
_____
Together with the given equation, this has the solution ...
x = y = 1/15
The space shuttle carries c pounds of cargo, and each piece of cargo weighs 212.66 pounds. Which of the following expressions represents the number of pieces of cargo?
Answers
Answer:
The answer would be B. c ÷ 158.14
Step-by-step explanation:
i just took this test :) the question was:
The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds. Which of the following expressions represents the number of pieces of cargo The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds? Which of the following expressions represents the number of pieces of cargo?
A. c × 158.14
B. c ÷ 158.14
C. c - 158.14
D. c + 158.14
please help with this question
Answers
Answer:
your answer is 1,-2
Step-by-step explanation:
The value of a vase n years after it was
made is given by this formula:
value in pounds (£) = 500 x 1.28"
=
a) What was the original value of the
vase?
b) By what percentage does the value of
the vase increase each year?
Answers
The answers are
a)640-500
b) + 28%