Answer:
This identity holds as long as [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].
For the proof, make use of the fact that:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] (definition of tangents,) and
[tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] (Pythagorean identity,) which is equivalent to [tex]1 - \cos^{2}(\theta) = \sin^{2}(\theta)[/tex].
Step-by-step explanation:
Assume that [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex]. This requirement ensures that the [tex]\tan(\theta)[/tex] on the left-hand side takes a finite value. Doing so also ensures that the denominator [tex]\sqrt{1 - \sin^2(\theta)}[/tex] on the right-hand side is non-zero.
Make use of the fact that [tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] to rewrite the left-hand side:
[tex]\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}[/tex].
Apply the Pythagorean identity [tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex] and [tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] to rewrite this fraction:
[tex]\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}[/tex].
Hence, [tex]\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}[/tex].
A segment has endpoints A and C. What are two names for the segment?
Answer:
Ac CA is your answer
Step-by-step explanation:
MARK ME AS BRAINLIEST
AC and CA
Step-by-step explanation:
[tex]line \: which \: has \: endpoint \: \\ \\ A \: and \: C \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ it \: shows \: that \: line \: starts \: from \: \\ \\ A \: \: and \: ends \: with \: C \\ \\ so \: \: its \: name \: is \: \: \: \: AC \\ \\ hope \: it \: is \: helpful \: to \: you....[/tex]
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The table shows the lengths of picket fence pieces Jude has to make a flower garden
He wants the garden to have 4 sides and a perimeter of 30 feet.
He cannot cut the pieces into smaller lengths.
Fence Length
Number of Pieces
6 feet
feet
2
12 feet
1
Choose all of the possible sizes of gardens that Jude could make.
А.
B.
LIVE
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a square with a side length of 6 feet
a rectangle with a length of 9 feet and a width
of 6 feet
D.
• LIVE
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a trapezoid with side lengths of 6 feet, 6 feet,
6 feet, and 12 feet
a quadrilateral with side lengths of 6 feet, 9
feet, 9 feet, and 9 feet
E.
LIVE
a triangle with side lengths of 9 feet, 9 feet,
and 12 feet
Answer:
all except for D. he can build A, B, C and E out of the available pieces of fence.
but A violates the overall goal of a circumference of 30ft.
and E violates the overall goal of the garden having 4 sides.
D cannot be built, because it would require 3 pieces of 9 ft (and we have only 2).
Answer: All except for D.
Step-by-step explanation: I would make one, but someone has already made a decent explanation.
Please Find the value of x and y
Answer: x=40° and y=140°
Step-by-step explanation:
From the figure, we know that x and 40 are vertical angles. Therefore, they are equal to each other.
x=40°
With the value of x, we know that x and y are supplementary angles. That means they are equal to 180°.
40+y=180 [subtract both sides by 40]
y=140°
Now we know x=40° and y=140°.
Simplify:{x(6x - 1
A)
B)
2x-1
9
2x
x-
2x7.5
D
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {D. \:= 2 {x}^{2} - \frac{1}{3} x}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] \frac{1}{3} x \: ( \: 6x - 1 \: )\\[/tex]
[tex] = \frac{x \: ( \: 6x - 1 \: )}{3}\\[/tex]
[tex] = \frac{6 {x}^{2} - x}{3} \\[/tex]
[tex] = \frac{6 {x}^{2} }{3} - \frac{x}{3}\\ [/tex]
[tex] = 2 {x}^{2} - \frac{1}{3} x\\[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
I was wondering if someone could answer this :)
Answer:
17
Step-by-step explanation:
2a+30 = 4a-4
+4 +4
2a+34 = 4a
-2a -2a
34 = 2a
÷2 ÷2
a=17
Hope this helps! :)
Answer:
A = 17
Step-by-step explanation:
Opposite angles are congruent in a parallelogram
Hence 2a + 30 = 4a - 4
( Note that we've just created an equation that we can use to solve for a)
We now solve for a
2a + 30 = 4a - 4
Add 4 to both sides
2a + 34 = 4a
Subtract 2a from both sides
34 = 2a
Divide both sides by 2
a = 17
A hotel spent $504 on new hair dryers. The hair dryers cost $8 each. The hotel has 6 floors with the same number of rooms on each floor. If every room gets a new hair dryer, how many hair dryers will be left over?
Answer:
3
Step-by-step explanation: 6 11 10 48
spent $504
hair dryers cost $8 each
6 floors with the same number of rooms on each floor.
Money spent / hair dry cost = number of hair dryers bought
number of hair dryers = number of floors = hair dryers per floor Plus any remainder
504 / 8 = 63 hair dryers
63 / 6 = 10.5 so 10 rooms per floor = 60 hairs dryers with 3 left over
Answer:
well IMA just copy the other guy and say 3
Step-by-step explanation:
just cause it is.
In △CDE, DE=14, CE=9, and m∠E=71∘. What is the length of CD⎯⎯⎯⎯⎯⎯? Enter your answer, rounded to the nearest hundredth, in the box.
Answer:
13.96units
Step-by-step explanation:
To get the length of CD, we will use the cosine rule as shown:
CD² = DE²+CE²-2(DE)(CE)cos m<E
Substitute the given values
CD² = 14²+9²-2(14)(9)cos71
CD² = 196 + 81 - 252cos71
CD² =277 - 252cos71
CD² = 277 - 82.0431
CD² = 194.95682
CD = √194.95682
CD = 13.96 units
Hence the length of CD of 13.96units
given a group of six students consisting of four female and two male how many different three member committee can be chosen from this group probability question
Given:
Total number of students = 6
Number of female students = 4
Number of male students = 2
To find:
Total number of outcomes if 3 students are chosen at random (Should i find the probability of something?)
Steps:
To find the total number of outcomes, we need to list the outcomes
Outcomes = {M,M,F} , {M,F,F} , {F,F,F}
Therefore, the total number of outcomes if 3 students are chosen at random is 3, if we don't consider order.
Could you elaborate the question a bit more if i made a mistake of what to find.
3x^2 - 4x + 2 = 0
how many solutions does the equation above have?
What is the volume of the solid figure?
152 cubic ft
Answer:
Volume of solid figure=Volume of
upper cuboid+volume of lower cuboid
=l*b*h+l*b*h=10*4*3+4*4*2=152 cubic ft
152 cubic ft
Answer:
Volume of solid figure=Volume of
upper cuboid+volume of lower cuboid
=l*b*h+l*b*h=10*4*3+4*4*2=152 cubic ft
Can you see them ⟟ need help
A random sample of items is selected from a population of size . What is the probability that the sample mean will exceed if the population mean is and the population standard deviation eq
Answer:
The probability is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which X is the value we want to find the probability of the sample mean exceeding, [tex]\mu[/tex] is the population mean, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Central Limit Theorem for the sample mean:
Sample of size n, and thus:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]Z = \frac{X - \mu}{s} = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Probability of the sample mean exceeding a value:
The probability is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which X is the value we want to find the probability of the sample mean exceeding, [tex]\mu[/tex] is the population mean, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Which statements describe the sequence –3, 5, –7, 9, –11, …? Check all that apply. The sequence has 5 terms. The 4th term of the sequence is 9. f(5) = 2 The domain of the sequence is all natural numbers. (4, 9) lies on the graph of the sequence.
forth term in a sequence =9
domain=set of all natural number
(4,9) lies in a graph
Answer:
Solution given:
–3, 5, –7, 9, –11, …are in a sequence
domain=set of all natural number.
forth term in a sequence =9
(4,9) lies in a graph.
and
f(5)=2
f(4)=9
Hence
(4,9) lies of graphThe domain is set of inetegers Z .as -3 is not N set member .
4th term of the sequence is 9The sequence has infinite terms
B and D are correct
Plz help me solve this thanks
Answer:
[tex]-2\sqrt{3}+8\sqrt{5}[/tex]
Step-by-step explanation:
[tex]-2\sqrt{3} -\sqrt{5} +3\sqrt{9\times5} = -2\sqrt{3} -\sqrt{5} +3\sqrt{9}\times\sqrt{5} = -2\sqrt{3} -\sqrt{5} +9\sqrt{5} = -2\sqrt{3}+8\sqrt{5} \\[/tex]
A vacant city lot is being turned into a neighborhood garden. The neighbors want to fence in a triangular section of the lot and plant flowers there. The longest side of the triangle section is 8 feet shorter than twice the shortest side. The third side is 2 feet longer than the shortest side. The perimeter is 58 feet. How long is each side?
Step-by-step explanation:
=>>. Hello mate. (◕ᴗ◕✿)
= Given :-
perimeter of traingle = 58 feet
let the third side be. "X" feet longest side = (2x - 8) feet shorter side = (x + 2) feetPerimeter of traingle = sum of all three sides
=> A/q. ,
( x ) + ( 2x - 8 ) + ( x + 2) = 58. ✓✓✓
x + 2x - 8 + x + 2 = 58
=>. 4x - 6 = 58
=> 4x = 58 + 6
=> 4x = 64
=>. x = 64/4
=|. x = 16 feet
length of third side = 16 feet length of shorter side = 18 feet length of longest side = 24 feet
Hope it helps you.......
The graphs below show measurements from cubes
with different side lengths.
Which pairs of variables have a linear relationship?
Select two options.
24
side length and perimeter of 1 face
20
perimeter of 1 face and area of 1 face
16
Perimeter of 1 Face
surface area and volume
A
area of 1 face and surface area
side length and volume
1
2
3
4
5
6
Side Length
40
36
32
Answer:
the first one and the third one
Step-by-step explanation:
Answer:
Side length and perimeter of 1 face
Area of 1 face and surface area
Step-by-step explanation:
Margot surveyed a random sample of 180 people from the United States about their favorite sports to watch. Then she sent separate, similar, survey to a random sample of 180 people from the United Kingdom. Here are the results:
Favorite sport to watch United States United kingdom Total
Basketball 60 51 111
Football 67 14 81
Soccer 28 86 114
Tennis 25 29 54
Total 180 180 360
Margot wants to perform a x^2 test of homogeneity on these results. What is the expected count for the cell corresponding to people from the United Kingdom whose favorite sports to watch is tennis?
Answer:
27
Step-by-step explanation:
The expected count in a χ² test can be obtained thus :
Expected count for each each point in a two way table ::
(row total * column total) / total
Therefore, expected count for cell corresponding to people from United Kingdom whose favorite sport is tennis :
Row total = (51+14+86+29) = 180
Column total = (25 + 29) = 54
Total = 360
Hence,
Expected count = (180 * 54) / 360
Expected count = 27
Help with this Geometry question please
Answer:
Angle A = [tex]77^{o}[/tex]
Step-by-step explanation:
cos A = adjacent / hypotenuse
cos A = 18/82
cos A = 0.22
A = [tex]cos ^{-1}[/tex]0.22
A = [tex]77^{o}[/tex]
Please help me with this question
9514 1404 393
Answer:
D(1, 2)
Step-by-step explanation:
The ordered pair is always (x-coordinate, y-coordinate).
The x-coordinate is the distance to the right of the y-axis. (It is negative for points left of the y-axis.) Here, point D lies 1 unit right of the y-axis, so its x-coordinate is 1.
The y-coordinate is the distance above the x-axis. (It is negative for points below the x-axis). Here, point D lies 2 units above the x-axis, so its y-coordinate is 2.
The ordered pair describing the location of D is ...
(x-coordinate, y-coordinate) = (1, 2)
Please I need help in finding the diameter
Answer:
20
Step-by-step explanation:
diameter=√(12²+16²)=√[4²(3²+4²)]=4√(9+16)=4√25=4×5=20
I need big help on this one
Find the value of X
Answer:
100°
Step-by-step explanation:
the lower right angle is 180-149 = 31°
the sum of all three angles in a triangle is 180°.
so the solution is 180-31-49
Aarti posted a comment on her blog. Each day the number of responses to her comment was 125% of the number she received on the previous day. If there were 64 responses the first day, how many were there on the fourth day?
Answer:
156 were there on the fourth day.
Step-by-step explanation:
125% of the number she received on the previous day
This means that the previous day number is multiplied the 125%/100% = 1.25.
64 responses the first day
This means that the number of responses after x days is given by:
[tex]R(x) = 64(1.25)^x[/tex]
How many were there on the fourth day?
This is R(4). So
[tex]R(4) = 64(1.25)^4 = 156[/tex]
156 were there on the fourth day.
Answer:
125
Step-by-step explanation:
Find the solution set of the inequality
\qquad8x - 8 \leq -72.8x−8≤−72.
Step-by-step explanation:
- 8 is the ans .hope this help you. mark me as brainliest
SOMEONE HELP ME PLEASE
Answer:
The missing value is 5/2
Step-by-step explanation:
Which expression is equivalent to 4-(-7)
Answer:
4-(-7)=11
-4-7=-11
-4+7=3
-7-4=-11
so neither 3 choices work
hope this helps
have a good day :)
Step-by-step explanation:
Complete the problems in measurements. Show answers in simplest terms.
e. Joseph has a bag of dog food that weighs 5 lb. He wants to feed his dog 7 oz. of dog food per day, How many days will the bag of dog food last?
Someone please help I have 40 mins for this test !
Answer:
It would be Linear
Step-by-step explanation:
Answer:
i think its quadratic because the graph isnt straight and has different slopes between the x,y.
Step-by-step explanation:
Logan bought stocks and later sold them for $3,437,500, making a profit of 25%. How much did he pay for the stocks?
Answer:
Logan bought the stocks at $2,750,000
Step-by-step explanation:
So according to the question $3,437,500 is the amount at which 25% interest was made
This means that the original value(100% value) has been increased to 125%(thus 100+25%)
By using ratio and proportion,
If 125%-$3437500
then 100% ={100%/125%}×$3,437,50
=$2,750,000
3. Find the measure of the exterior angle in the diagram below.
Answer:
the value of x is 29° which is b
