Answers
Answer: see proof below
Step-by-step explanation:
Use the following Power Reducing Identities:
[tex]\sin^3\theta= \dfrac{1+\cos 2\theta}{2}\\\\\\\cos^2\theta=\dfrac{3\sin \theta-\sin 3\theta}{4}[/tex]
Use the following Product to Sum Identity:
[tex]\sin A \cdot \cos B = \dfrac{1}{2}\bigg[\sin (A + B) + \sin (A - B)\bigg][/tex]
Proof LHS → RHS
LHS: cos² Ф · sin³ Ф
[tex]\text{Power Reducing:}\qquad \bigg(\dfrac{1+\cos 2\theta}{2}\bigg)\bigg(\dfrac{3\sin \theta-\sin 3\theta}{4}\bigg)[/tex]
[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}(3\sin \theta -\sin 3\theta +3\sin \theta\cdot cos 2\theta-\sin 3\theta \cdot \cos 2\theta)[/tex]
[tex]\text{Product to Sum:}\\ \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin (\theta +2\theta) +\sin(\theta -2\theta)\bigg)-\dfrac{1}{2}\bigg(\sin (3\theta+2\theta) +\sin (3\theta-2\theta)\bigg)\bigg][/tex]
[tex]\text{Simplify:}\quad \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin 3\theta +\sin(-\theta)\bigg)-\dfrac{1}{2}\bigg(\sin 5\theta +\sin \theta\bigg)\bigg][/tex]
[tex]\text{Cofunction:}\quad \dfrac{1}{8}\bigg[3\sin \theta -\sin 3\theta +\dfrac{3}{2}\bigg(\sin 3\theta -\sin(\theta)\bigg)-\dfrac{1}{2}\bigg(\sin 5\theta +\sin \theta\bigg)\bigg][/tex]
[tex]\text{Simplify:}\qquad \dfrac{1}{16}\bigg(6\sin \theta -2\sin 3\theta +3\sin 3\theta -3\sin(\theta)-2\sin 5\theta -2\sin \theta\bigg)\\\\\\.\qquad \qquad =\dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)[/tex]
[tex]\text{LHS=RHS:}\quad \dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)=\dfrac{1}{16}\bigg(2\sin \theta + \sin 3\theta -\sin 5\theta\bigg)\quad \checkmark[/tex]
Related Questions
Factor u⁴+7u²-8
honestly I'm just confused how to solve ;-; I see the answer is (u-1)(u-1)(u²+8) but I'm not sure how to show the work.
Answers
Answer:
(u + 1)(u - 1)(u² + 8)
Step-by-step explanation:
Here is the steps:
u⁴ + 7u² - 8 = u⁴- u² + 8u²-8 =u²(u² - 1) + 8(u² -1) =(u² - 1) (u² +8) = (u + 1)(u - 1)(u² + 8)Answer:
[tex] (u - 1)(u + 1)( {u}^{2} + 8)[/tex]
Step-by-step explanation:
[tex] {u}^{4} + 7 {u}^{2} - 8 \\ = {u}^{4} + 8 {u}^{2} - {u}^{2} - 8 \\ = {u}^{2} ( {u}^{2} + 8) - 1( {u}^{2} + 8) \\ = ( {u}^{2} - 1)( {u}^{2} + 8) \\ = (u - 1)(u + 1)( {u}^{2} + 8) \\ [/tex]
In a test (+5)marks are give for every correct answer and (-2)marks for every incorrect answer. Jay answered all questions and scored (-12)m though he got four correct answer)how many incorrect answer he attempted
Answers
Answer:
32 incorrect answers was attempted by JayStep-by-step explanation:
Let the amount of correct answer gotten be x and that of wrong answer be y. The sum of Jay score = 5x+ (-2)y [since(+5)marks are give for every correct answer and (-2)marks for every incorrect answer]
If Jay answered all questions and scored (-12)m, then 5x - 2y = -12
If Jay got four answers correctly, the number of correct answers x = 4
Substituting x = 4 into the equation 5x - 2y = -12 to get the value of y, we will have;
5(4) - 2y = -12
20 - 2y = -12
-2y = -12-20
-2y = -32
y = 16
This means that Jay attempted 16 incorrect answers.
It is estimated that 26% of all california adults are college graduates and that 31% of california adults are regular internet users. It is also estimated that 19% of california adults are both college graduates and regular internet users.
Required:
a. What is the probability that a california adult is an internet user, given that he or she is a college graduate?
b. Among California adults, what is the probability that a randomly chosen internet user is a college graduate?
Answers
Answer:
Step-by-step explanation:
a) The probability that a california adult is an internet user, given that he or she is a college graduate can be represented with the following
P(internet user|college graduate) = P(internet user ∩ college graduate) P(college graduate) = 0.19/26= 0.7307
= 0.73
b) The probability that a randomly chosen internet user is a college graduate?
P(college graduate|internet user) = P(internet user ∩ college graduate) P(internet user) = 0.19/0.31= 0.6129
= 0.61
person sold a house
for Rs 20,00,000 then he gets 5% commission. Find
commission amount .
Answers
Answer:
₹1, 00,000
Step-by-step explanation:
Amount of commission
[tex] = 5 \% \: of \: 20, 00, 000 \\ \\ = \frac{5}{100} \times 20, 00, 000 \\ = 5 \times 20000 \\ = Rs. \: 1, 00, 000[/tex]
A school painted 1/2 of a school wall its gym with 3 colors each color take the same amount of space on the wall what fractions of the wall does each colors occupy
Answers
Each color occupies 1/6 of the school wall
The fraction of each color that occupies the wall will be 1/6.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A school painted 1/2 of a school wall has its exercise center with 3 tones each variety takes a similar measure of room on the wall.
The fraction of the color that occupies the wall will be given as,
⇒ (1/2) x (1/3)
⇒ 1/6
The small part of each variety that possesses the wall will be 1/6.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
If i have 150 cookies for 4 people how many does each person get?
Answers
Answer: 37.5
Step-by-step explanation: just multiply! hope this helps!
10 points and brainliest!
Answers
Answer:
x > 0 and y > 0
Step-by-step explanation:
If the point (x,y) is in Quadrant I, then that means both x and y must be positive. For this to be true, x must be greater than 0 and y must be greater than 0.
Cheers.
jake works at Whataburger and earns $12.50 per hour. How many hours will it take for him to earn $125.
Answers
1 The metal used to make a coin is a mixture of steel and copper. The ratio mass of steel
: mass of copper is 108 :7. The coin has a total mass of 230 milligrams.
Calculate the mass of copper in this coin.
uene
Answers
[tex] \huge{ \underline{ \underline{ \gray{ \bf{Solution:}}}}}[/tex]
Let,
Mass of the steel be 108xMass of the copper be 7xThen, Total mass = 108x + 7x = 115xGiven,
Total mass of the coin = 230 mgThat means,
⇛ Total mass of the coin = 230 mg
⇛ 115x = 230 mg
⇛ x = 230 mg/115
⇛ x = 2 mg
Then,
Mass of the steel = 108(2) = 216 mgMass of the copper = 7(2) = 14 mg☁️ ANSWER - 14 mg (Mass of copper)
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hey does anyone know the answer to this? Alexa agreed to pay back her friend $10 per week and originally borrowed $170.
Answers
Answer:
L(t) = 170 - 10t
Step-by-step explanation:
Alexa borrowed some money from her friend in order to help buy a new video game system. Alexa agreed to pay back her friend $10 per week and originally borrowed $170. Write an equation for L, in terms of t, representing the amount Alexa owes her friend after t weeks.
Let
Initial amount Alexa borrowed= L(o)
Amount Alexa pays per week= k
Number of weeks= t
Amount Alexa owes her friend after t weeks= L(t)
The amount that Alexa owes after t weeks is given by the equation:
L(t) = L(o) - kt
Where,
L(o) = $170
k= $10
Substituting the values into the equation, we have,
L(t) = L(o) - kt
L(t) = 170 - 10t
Therefore,
The amount Alexa owes her friend after t weeks is given by
L(t) = 170 - 10t
Choose all true statements All real numbers are rational numbers. Some rational numbers are natural numbers. No real numbers are irrational numbers. All whole numbers are integers. Some integers are natural numbers. No rational numbers are integers.
Answers
Answer:
The answer is: All whole numbers are integers, No rational numbers are integers, and No real numbers are irrational numbers.
Step-by-step explanation:
Determine whether each ordered pair is a solution of the inequality. 2x + y >4
Answers
Answer:
2x + y > 4
(1,3) → 2(1) + 3 = 5 > 4 -- solution
(2, 0) → 2(2) + 0 = 4 = 4 -- not a solution
(4, -5) → 2(4) - 5 = 3 < 4 -- not a solution
(-1, 8) → 2(-1) - 8 = -10 < 4 -- not a solution
8-7x-6-8x=5
solve for x
Answers
Answer:
x =-1/5Step-by-step explanation:
[tex]8-7x-6-8x=5\\\\\mathrm{Group\:like\:terms}\\-7x-8x+8-6=5\\\\\mathrm{Add\:similar\:elements:}\:-7x-8x=-15x\\-15x+8-6=5\\\\\mathrm{Add/Subtract\:the\:numbers:}\:8-6=2\\-15x+2=5\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\-15x+2-2=5-2\\\\Simplify\\-15x=3\\\\\mathrm{Divide\:both\:sides\:by\:}-15\\\frac{-15x}{-15}=\frac{3}{-15}\\\\Simplify\\x=-\frac{1}{5}[/tex]
on tuesday bill bought five hats. on wednesday half of all the hats he had were destroyed. on thursday there were only 17 left. how many did she have on monday?
Answers
Answer:29
Step-by-step explanation:I think he had 29 hats on Monday because if he had 17 left because half were destroyed then that means he had 34 after he bought the hats on tuesday. So 34-5=29. Im not sure but here.
Select all of the expressions that are
equal to 6.
161
1-61
-161
-1-61
10 - 61
O 1-21 · 131
Answers
|6| is equal to 6
|-6| is equal to 6
-|6| is NOT equal to 6
-|-6| is NOT equal to 6
|0 - 6| is equal to 6
|-2| · |3| is equal to 6
Hope this helps! (❁´◡`❁)
Answer: |6|, |-6|, |0-6|, |-2| x |3|
Step-by-step explanation:
if the negative sign is in front of the line instead on inside it makes the whole thing negative. Anything inside the lines is automatically positive.
In the xy-plane, the graph of which of the following linear has a negative x-intercept?
Answers
Answer:
[tex]\Large \boxed{\mathrm{E}}[/tex]
Step-by-step explanation:
The x-intercept is when y = 0.
[tex]y = 3x + 1[/tex]
Let y = 0.
[tex]0=3x+1[/tex]
Subtracting 1 from both sides.
[tex]-1=3x[/tex]
Dividing both sides by 3.
[tex]\frac{-1}{3} =x[/tex]
The x-intercept is negative.
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Identify the mapping diagram that represents the relationship and determine whether the relation is a function. {(–5, –4), (–1, 5), (–5, 3), (7, 8)}
Answers
Answer:
The circled in in the image.
Step-by-step explanation:
The input and outputs matched the ones that were asked for.
Find the Square of 9x – 7xy
Answers
Answer:
[tex]\huge \boxed{49x^2 y^2 -126x^2 y +81x^2}[/tex]
Step-by-step explanation:
[tex]\sf (9x - 7xy)^2[/tex]
Expanding brackets.
[tex]\sf (9x - 7xy)(9x-7xy)[/tex]
Applying the FOIL method.
[tex]\sf 9x(9x-7xy)-7xy(9x-7xy)[/tex]
[tex]\sf 81x^2 -63x^2 y -63x^2 y+49x^2 y^2[/tex]
Combining like terms.
[tex]\sf 81x^2 -126x^2 y+49x^2 y^2[/tex]
f(x) = -3x + 2 for x =3
Evaluate each function for the given value of x, and write input x and the output f(x) as an ordered pair.
Answers
Answer:
x = -7
Step-by-step explanation:
f(x) = -3x + 2
= -3(3) + 2
= -9 + 2
= -7
What is "seven less than a number cubed"?
Answers
Answer:
n³ - 7
Step-by-step explanation:
number = n
because 7 is less then the number cubed it's being subtracted by n³
A group of objects or numbers is called a A part of a set is called a
Answers
Answer:
Set; subset.
Step-by-step explanation:
A group of objects or numbers is called a set while a part of a set is called a subset. The objects or numbers that make up a set are generally referred to as elements or members and are written inside a pair of curly braces {}.
A set can be made up of elements such as numbers, alphabets, people, cars etc.
For instance, Set A = {2, 4, 6, 8, 10, 12} represents all the even number between 1 - 12.
On the other hand, a subset is a part of a larger set.
For instance, comedy movies, horror movies, romance movies, action movies are a subset of movies.
Kindly help with this Surd question
Answers
Explanation:
(1 + sqrt(2))/sqrt(2)
= 1/sqrt(2) + sqrt(2)/sqrt(2)
= 1/sqrt(2) + 1
Answer:
Step-by-step explanation:
Rationalize the denominator, to do that multiply denominator and numerator by √2
[tex]\frac{1+\sqrt{2}}{\sqrt{2}}=\frac{(1+\sqrt{2})*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\ =\frac{1*\sqrt{2}+\sqrt{2}*\sqrt{2}}{\sqrt{2*2}}\\\\\\=\frac{\sqrt{2}+2}{2}\\\\\\[/tex]
Mary wants to put a fence around her garden. The garden measures 10 feet by 6 feet. If fencing costs $5 per foot, how much will the fence cost Mary?
Answers
First, find the cost of how much fence Mary needs per side.
10 * 5 = 50
10 * 5 = 50
6 * 5 = 30
6 * 5 = 30
Second, add all together.
50 + 50 + 30 + 30 = 160
Therefore, the total cost of the fence will be $160.
Best of Luck!
The 2020 population of Charlotte,NC is nine hundred five thousands, three hundred eighteen. How is the population of charlotte written in standard form?
Answers
Answer:
9.05318 × 10^5
Step-by-step explanation:
The population of Charlotte NC in words is given in words as:
nine hundred five thousands, three hundred eighteen.
Writing this in figures = 905,318
Converting this to standard form = 9.05318 × 10^5
Therefore, the population of charlotte written in standard form is 9.05318 × 10^5
Pump it up gym's daily revenue each can be modeled by R(x)=5x where x represents the number of customers that visit the gym each day. The gym's daily costs can be modeled by the function C(x)=2x+150. Find the profit function P(x)=R(x)-C(x) A) P(x)=3x-150 B) P(x)=7x-150 C) P(x)=7x+150 D) P(x)=3x+150
Answers
Answer:
P(x) = 3x - 150
hey guys please help with this questoin Find (x+y) ÷ (x-y) if x=5/4 y=-1/3
Answers
Answer:
11/19Step-by-step explanation:
[tex](\frac{5}{4} + (-\frac{1}{3})) \div (\frac{5}{4} - (-\frac{1}{3}))\\\\\frac{\frac{5}{4}+\left(-\frac{1}{3}\right)}{\frac{5}{4}-\left(-\frac{1}{3}\right)}\\\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a,\:-\left(-a\right)=a\\=\frac{\frac{5}{4}-\frac{1}{3}}{\frac{5}{4}+\frac{1}{3}}\\\\\mathrm{Join}\:\frac{5}{4}+\frac{1}{3}:\quad \frac{19}{12}\\\mathrm{Join}\:\frac{5}{4}-\frac{1}{3}:\quad \frac{11}{12}\\\\=\frac{\frac{11}{12}}{\frac{19}{12}}\\\\=\frac{11\times\:12}{12\times \:19}[/tex]
= 11/19
Answer:
199/144
Step-by-step explanation:
(5/4-1/3)(5/4+1/3)
25/16-1/9
(135-16) /144
119/144
Help pleaseeeeee I need help ASAP
Answers
Answer:
2nd option is true
Step-by-step explanation:
Jane owns 60% of the private catering corporation there are 1200 shares in the entire corporation how many shares does Jane own
Answers
1. Rick renovated his home. He made his bedroom 40% larger (length and width) than its original size. If the original dimensions were 144 inches by 168 inches, how big is his room now if measured in feet?
Answers
Answer:
New dimension: 16.8 feet by 19.6 feet.
Step-by-step explanation:
Given that,
The original dimensions of the room were 144 inches by 168 inches. Rick renovated his home. He made his bedroom 40% larger than its original size.
40% of 144 = 57.6
New length is 144 + 57.6 = 201.6 inches
40 % of 168 = 67.2
New breadth is 168 + 67.2 = 235.2 inches
Since, 1 foot = 12 inch
201.6 inches = 16.8 feet
235.2 inches = 19.6 feet
The new dimension of the room is 16.8 feet by 19.6 feet.
Given: FJ bisects _HFG, where ZHEJ = (5x+3)° and GFV = (7x-11)°.
H
Solve for the value of x. *
Answers
Answer:
Step-by-step explanation:
7x - 11 = 5x + 3
2x - 11 = 3
2x = 14
x = 7