Answers
Answer: see proof below
Step-by-step explanation:
Use the Triple Angle Identity: sin 3A = 3sinA - 4sin³A
[tex]\text{Given:}\quad \sin\bigg(\dfrac{\theta}{3}\bigg)=\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)[/tex]
Proof LHS → RHS
LHS: sin Ф
Let A = Ф/3 sin 3A
Triple Angle Identity: 3sinA - 4sin³A
Substitute Ф/3 = A: 3sin(Ф/3) - 4sin³(Ф/3)
Substitute sin(Ф/3): [tex]3\bigg(\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)\bigg)-4\bigg(\dfrac{1}{2}\bigg(m+\dfrac{1}{m}\bigg)\bigg)^3[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{3m}{2}+\dfrac{3}{2m}-4\bigg(\dfrac{1}{8}\bigg(m^3+3m+\dfrac{3}{m}+\dfrac{1}{m^3}\bigg)\bigg)\\\\.\qquad \qquad \qquad =\dfrac{3m}{2}+\dfrac{3}{2m}-\dfrac{m^3}{2}-\dfrac{3m}{2}-\dfrac{3}{2m}-\dfrac{1}{2m^3}\\\\.\qquad \qquad \qquad =-\dfrac{m^3}{2}-\dfrac{1}{2m^3}\\\\\text{Factor:}\qquad \qquad -\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)[/tex]
[tex]\text{LHS = RHS:}\quad -\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)=-\dfrac{1}{2}\bigg(m^3+\dfrac{1}{m^3}\bigg)\quad \checkmark\\[/tex]
Related Questions
Find the measure of AB¯¯¯¯¯¯¯¯. A. 14 B. 22 C. 21 D. 20
Answers
Answer:
C. 21
Step-by-step explanation:
We use the Power of Point theorem, which states that for points A, B, C, D, and E oriented in the way shown in the attachment:
BC * AC = DC * EC
Here:
AC = AB + BC = (2x + 5) + 9 = 2x + 14
BC = 9
DC = 10
EC = KC = (1 + 2x) + 10 = 2x + 11
So plug all these in:
BC * AC = DC * EC
9 * (2x + 14) = 10 * (2x + 11)
18x + 126 = 20x + 110
2x = 126 - 110 = 16
x = 8
Put this back into the expression for AB:
AB = 2x + 5 = 2 * 8 + 5 = 16 + 5 = 21
The answer is thus C.
~ an aesthetics lover
Does The Point(6, 10)satisfy the inequality
8x + 2y ≤ 2 ? yes no
Answers
Answer:
No
Step-by-step explanation:
Substitute (6, 10 ) into the left side of the inequality and compare value with right side.
8(6) + 2(10) = 48 + 20 = 68 > 2
Thus (6, 10 ) is not a solution of the inequality
A rectangle has an area of 90 units. what is the rectangles length and width?
Answers
Step-by-step explanation:
You must specify the length or the breadth either in values, variables or ratio. ..
There are infinite answers for this question., so I guess you have missed printing some information in it.. so rewrite the question please
Given that (0,-5) is on the graph of f(x), find the
corresponding point for the function
f(-4x).
Answers
Answer:
the corresponding point for the function f(x) − 4 is (0,-9)
Step by Step Explanation --
Given that (0, -5) is on the graph of f(x),
WE need to find the corresponding point for the function f(-4x}
f(x) means the output y
f(x)-4 means subtract 4 from the output y
In the given point (0, 5) , x is 0 and y is -5
To get the corresponding point we subtact 4 from y
that is [-5]- 4 = -9
the corresponding point for the function f(x) − 4 is (-3,1)
Step-by-step explanation:
Answer:
(0,-5)
Step-by-step explanation:
Paj is filling a -cubic-inch flower pot with soil from small bags. Each bag of soil contains cubic inches of soil. Exactly how many bags of soil are needed for Paj to fill the flower pot?
Answers
Complete Question
Paj is filling a 9-cubic-inch flower pot with soil from small bags. Each bag of soil contains 2 2/3 cubic inches of soil. Exactly how many bags of soil are needed for Paj to fill the flower pot?
Answer:
[tex]Number\ of\ Bags = 3\frac{3}{8}[/tex]
Step-by-step explanation:
Given
[tex]Flower\ Pot = 9 in^3[/tex]
[tex]Small\ Bag = 2\frac{2}{3} in^3[/tex]
Required
How many bag of soil can fill the flower pot
To solve this,we simply divide the volume of flower pots by the small bags. This is done as follows;
[tex]Number\ of\ Bags = \frac{Flower\ Pot}{Small\ Bag}[/tex]
[tex]Number\ of\ Bags = \frac{9 in^3}{2\frac{2}{3} in^3}[/tex]
Convert fraction
[tex]Number\ of\ Bags= \frac{9 in^3}{\frac{8}{3} in^3}[/tex]
[tex]Number\ of\ Bags = 9 in^3/\frac{8}{3} in^3[/tex]
[tex]Number\ of\ Bags = 9 * \frac{3}{8}[/tex]
[tex]Number\ of\ Bags = \frac{9 * 3}{8}[/tex]
[tex]Number\ of\ Bags = \frac{27}{8}[/tex]
[tex]Number\ of\ Bags = 3\frac{3}{8}[/tex]
Hence, the number of bags needed is [tex]3\frac{3}{8}[/tex]
Use the Order of Operations to evaluate: 19 •4 - 3+3
Answers
Answer:
76
Step-by-step explanation:
multiply 19^4 first to get 76, then minus 3 from that to get 73, and add 3 back to that to get 76.
A diver swims 5.875 feet up to the surface of the water which number represents the divers position in relation to the surface before swimming to the top -5.9 ft -5 3/4 -58 or -5 7/8
Answers
Answer:
-5 7/8 = -5.875
Step-by-step explanation:
Before swimming to the top, the swimmer was 5.875 ft down
Answer:
-5 7/8 feet
Step-by-step explanation:
The opposite of 5.675 is 5 7/8 feet (I don't know if the explanation is right but the answer is)
Suppose a population
consists of 85,000 people. Which of the following
numbers of members of the population being surveyed could result in a
parameter but not a sample statistic?
O A. 850
O B. Both 850 and 85,000
O C. 85,000
D. Neither 850 nor 85,000
Answers
Answer:
c
Step-by-step explanation: A P E X
An experiment's or random trial's sample space is the set of all conceivable outcomes or results. The correct option is C.
What is a sample?A sample is a statistically significant subset of a larger population. The utilisation of samples enables researchers to conduct investigations with more manageable data and more quickly. Randomly chosen samples exhibit little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
Given that a population consist of 85,000 people. Now, the number of members of the population that being surveyed could result in a parameter but not a sample static is 8500. This is because a parameter is a value that describes a specific attribute of the population as a whole. A sample survey cannot provide this information. To determine the real value of a parameter, the entire population must be examined.
Hence, the correct option is 85,000.
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im bad with shapes just look at the picture and tell me best of luck
Answers
Answer: They are both right triangles so you can use the Pythagorean Theorem to get the length of the missing side
12^2 = 144. 5^2 = 25. 144 + 25 = 169. 13^2 = 169. Or you could say the sure root of 169 is 13.
Step-by-step explanation:
The triangles are congruent because the three sides of triangle A are equal to the three sides of triangle B.
In geometry they call that proof "sss" meaning 3 same sides. Or you could prove by "sas" 2 equal sides and an equal angle.
Answer:
Answer: They are both right triangles so you can use the Pythagorean Theorem to get the length of the missing side
12^2 = 144. 5^2 = 25. 144 + 25 = 169. 13^2 = 169. Or you could say the sure root of 169 is 13.
Step-by-step explanation:
The triangles are congruent because the three sides of triangle A are equal to the three sides of triangle B.
In geometry they call that proof "sss" meaning 3 same sides. Or you could prove by "sas" 2 equal sides and an equal angle.
Classify the following triangle. Check all that apply.
A. Obtuse
B. Acute
C. Equilateral
D. Isosceles
E Scalene
F Right
Answers
I know Iscoscles and acute only
The value of 5s in 25,578
Answers
Answer:
500 and 5,000
Step-by-step explanation:
The value of the first 5 is five hundred (500)
The value of the second is five thousand (5,000)
The place value of 5 in the number 25,578 is 500 and 5,000.
What is a place value?The value of each digit in a number is known as the place value. The 5 in 5,006 signifies 5 thousand, or 5,000, while the 5 in 350 represents 5 tens, or 50. Children must learn that while a digit can have the same value, its value changes depending on where it appears in the number.
A number is a numerical unit of measurement and labeling in mathematics. The first examples are the numbers 1, 2, 3, and 4.
The place value of 5 in the number 25,578 will be calculated as below:-
The value of the first 5 is five hundred 500.
The value of the second is five thousand 5,000.
Therefore, the place value of 5 in the number 25,578 is 500 and 5,000.
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HELP ME PLEASE
Evaluate each one. Then tell if starting number (100) grew or decreased.
Warm Up
Evaluate.
1. 100(1.08)^20
2. 100(0.95)^25
3. 100(1 - 0.02)^10
4. 100(1 + 0.08)^-10
IS IT DECREASING OR INCREASING??!???
Answers
Answer:
Decreased
Step-by-step explanation:
Answer this question
Answers
Answer:
Option C
Step-by-step explanation:
angle B = angle C
angle B + angle C = angle DAC
angle DAC = 2 x angle DAX
angle DAX = 70 deg
=> angle DAC = 2 x 70 = 140 deg
=> angle B = angle C = 70 deg
Please help me similar triangles make no sense to me
I have to determine if they are similar or not and make a similarity statement
Answers
Answer:
Step-by-step explanation:
Compare the ratios of the triangles like so:
Bigger to smaller
[tex]\frac{15}{10}=\frac{12}{8}[/tex]
This statement is true. Both fractions simplified are equal to 1.5. Since they have the same ratios, they should be similar.
Find the distance between (-4,-1) and (-3,-1).
Answers
Answer:
The answer is 1 unitStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-4,-1) and (-3,-1)
The distance between them is
[tex]d = \sqrt{ ({ - 4 + 3})^{2} + ({ - 1 + 1})^{2} } \\ = \sqrt{ ({ - 1})^{2} } \\ = \sqrt{1} [/tex]
We have the final answer as
1 unit
Hope this helps you
find the greatest common factor of 72 90 and 126
Pls show working
Answers
72 90 126............ (2)
36 45 63..............(3)
12 15 21...............(3)
4 5 7................can't be divided more.
So, 2 x 3 x 3 = 18 is the biggest common factor of 72, 90, and 126.
Answer:
6
Step-by-step explanation:
72={1,2,3,4,6,8,9,12,18,24,36,72}
90={1,2,3,5,6,9,10,15,18,30,45,90}
126={1,2,3,4,6,7,9,1418,21,42,63,126}
Common factors of 72,90 and 126
1,2,3,4,6
6 is greater than 1, 2, 3 and 4.
Hope this helps ;) ❤❤❤
Find the midpoint of the segment with the given endpoints.
(-5,3) and (-4,-8)
The midpoint is _
Answers
Answer: (-4.5, -2.5)
Step-by-step explanation:
Help plzzzzzzz......
Answers
Answer:
A. England = 56000000
B. 1.046 * 10^7
C. 9.7 to 2sf
Step-by-step explanation:
A. England = 5.60*10000000
=56000000
B. Wale = 3.14*1000000 = 3140000
Scotland = 5.44*1000000 = 5440000
Northern Ireland = 1.88*1000000 =1880000
Total = 10460000
In standard form =1.046*10^7
C. Total population as at 2018 = 66460000
expected population by 2041 = 72900000
increase or change = (72900000 - 66460000) = 6440000
% change = (6440000/66460000)*100
= 0.0969003912 * 100
= 9.69003912
= 9.7 to 2sf
Hadley buys 7 boxes of markers with 8
in each box. Delaney buys 6 boxes of
markers with 12 markers in each box.
How many markers did Hadley and
Delaney buy in all?
Answers
Answer:
128 markers.
Step-by-step explanation:
7 x 8 = 56
12 x 6 = 72
72+ 15 = 87
Hadley and Delaney therefore bought 128 markers all in total.
Hope I helped ! :))))))
The amount of markers Hadley and Delaney bought in all is equal to 128 markers.
Given the following data:
Hadley = 7 boxes of markers with 8 in each box.Delaney = 6 boxes of markers with 12 markers in each box.To determine the amount of markers Hadley and Delaney bought in all:
First of all, we would determine the total number of marker in each box.
For Hadley:
[tex]Hadley = 7 \times 8[/tex]
Hadley = 56 markers
For Delaney:
[tex]Delaney = 6\times 12[/tex]
Delaney = 72 markers
Now, we can find the total markers:
[tex]Total \;markers = Hadley + Delaney\\\\Total \;markers = 56+72[/tex]
Total markers = 128 markers
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Find the Absolute Value of: |-16+9|
Answers
Answer:
7
Step-by-step explanation:
|-16+9|
Calculate the number inside the absolute value
|-7|
Now take the absolute value
7
Answer:
its 7
Step-by-step explanation:
Susan plans to rent a bike in New Orleans to tour the city. The cost of the rental is $20 per day. The cost of a helmet is $7 for as long as Susan needs the bike. Barbara has $250 to rent a bike for 15 days. Does Barbara have enough money? Explain. First answer gets Brainiest and 48 points hurry please tho
Answers
Answer:
No, she does not.
Step-by-step explanation:
Using the words here, we can create the expression [tex]20d + 7[/tex] where d is the number of days.
We can now substitute 15 in as d, to see how much this will cost.
[tex]20\cdot15 + 7\\\\300+7\\\\307[/tex]
So the total cost will be $307.
Since $307 is more than $250, she does not have enough money.
Hope this helped!
Kyle challenges you to a game. Each player rolls a standard number cube twice. If the sum of the results is divisible by 3, you win. If it is not, Kyle wins. What is your probability of winning? Is this a fair game?
Answers
Answer:
The probability of you winning is 1/3
No, it is not a fair game
Step-by-step explanation:
The first thing we need to have here is the sample space. This refers to the set of all possible results that can occur from the rolling.
Please check attachment for this
Kindly note that the total number of possible outcomes is 36.
And in the attachment, sums which are divisible by 3 are circled.
The number of circles we can count is 12
Thus, the probability of you winning would be number of circles/total number of outcomes = 12/36 = 1/3
Is it a fair game?
No, it is not
It can only be a fair game if the probability of winning equals probability of losing ( which is 18/36 = 1/2 or 0.5)
Please answer quickly I will give BRAINLIEST to the person who is fastest and correct please hurry thank you
Answers
Answer:
0.5 m³
Step-by-step explanation:
You have a rectangular prism and a cube. Find the volume of each separately. After solving, add the two volumes together to find the total volume.
Cube
The side length is 0.5 m.
V = a³
V = (0.5 m)³
V = 0.125 m³
Rectangular Prism
The height is 0.75 m, the width is 0.5 m, the length is 1 m.
V = lwh
V = (0.75 m)(0.5 m)(1 m)
V = 0.375 m³
0.125 m³ + 0.375 m³ = 0.5 m³
Factor the expression and use the factor to find the x-intercepts of the quadratic relationship it represents.
The x intercepts occur where x= ___ and x= ___
Answers
Answer:
-3 and 8
Step-by-step explanation:
take a look at the picture. Hope it helps! Mark Brainliest pleaseee :)
The x intercepts occur where x = 8 and x= -3
What is Quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2}+bx+c=0[/tex].
What is x intercept?The x-intercept is where a line crosses the x-axis
Given,
[tex]-x^{2} +5x+24=0[/tex]
Factor the expression,
[tex]-x^{2} +5x+24=0\\-(x^{2} -5x-24)=0\\x^{2} -5x-24=0\\(x-8)(x+3)=0\\[/tex]
Therefore,
x= 8 and x = -3
Hence, the x intercepts occurs where x= 8 and x= -3
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2x – 5 + 3x + 12
5x + 7
Answers
Answer:
x=-5
Step-by-step explanation:
I used my ti-84 plus ce calculator to calculate this
>math
>numerical solver
>type equation
>enter
>you answer appears
what is quadratic and it's formula
Answers
Answer:
A quadratic (equation or expression) involves the second and no higher power of an unknown quantity or variable.
Step-by-step explanation:
The quadratic formula is derived from the General form of a quadratic equation :
ax+bx+c=0
using completing the square method.
Quadratic formula=
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
Bob sets the price of the plants according to their height in inches. A plant that is 9.5 inches high costs $2.28 in his store. What is the price per inch of a plant? Show your calculation.
Answers
Answer:
1 inches = $0.24
Step-by-step explanation:
9.5 inches =$2.28
$2.28 ÷ 9.5= .24
so the answer is 1 inch = $0.24
The price per inch of plant is $0.24.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Bob sets the price of the plants according to their height in inches.
A plant that is 9.5 inches high costs $2.28 in his store.
To find the price of the plant per inch:
Use division operation;
2.28 / 9.5
= $0.24 per inch.
Therefore, price is $0.24 per inch.
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Describe a real-world situation in which opposite quantities add together to equal zero.
Answers
Answer: Answer is in the steps.
Step-by-step explanation:
One situation is this.
Jason borrowed $5 from his best friend during a field trip and agreed to pay him back the next school day.The next day, he came back to school with $10 and used $5 to pay his friend back.Now answer the this question. How much does Jason owe his best friend now?
The answer to the question will be zero because Jason has already paid his friend all the money he borrowed.
f(x)=[tex]\sqrt{x+4}[/tex] and g(x)=[tex]x^{2}[/tex]
find f(g(-6)
Answers
Answer:
[tex]f(g(-6))=2\sqrt{10}[/tex]
Step-by-step explanation:
first we need to find g(-6)
[tex]g(x)= x^2\\\\g(-6)=(-6)^2\\\\g(-6)=36[/tex]
so g(-6)=36
so we need to find f(36)
[tex]f(x)=\sqrt{x+4} \\\\f(36)=\sqrt{36+4} \\\\f(36)=\sqrt{40}\\\\f(36)=\sqrt{4}* \sqrt{10} \\\\f(36)=2\sqrt{10}[/tex]
so that's answer
[tex]f(g(-6))=2\sqrt{10}[/tex]
What is the image of the point (6,0)(6,0) after a rotation of 180^{\circ}180 ∘ counterclockwise about the origin?
Answers
Answer:
(-6,0)
Step-by-step explanation:
Whether we rotate a point 180° clockwise or counterclockwise, we'll always end up at the same point.
When we rotate a point by 180°, assuming the original point is [tex](x,y)[/tex], the new coordinate becomes [tex](-x,-y)[/tex].
So:
[tex](-6,-0)\\\\(-6,0)[/tex]
Hope this helped!