Answers
Answer: see proof below
Step-by-step explanation:
Use the following Product to Sum Identities:
2 sin A sin B = cos (A - B) - cos (A + B)
2 sin A cos B = sin (A + B) + sin (A - B)
Use the Unit Circle to evaluate: cos 120 = -1/2 & sin 60 = √3/2
Proof LHS → RHS
LHS: sin 20 · sin 40 · sin 80
Regroup: (1/2) sin 20 · 2 sin 40 · sin 80
Product to Sum Identity: (1/2) sin 20 [cos(80-40) - cos (80+40)]
Simplify: (1/2) sin 20 [cos 40 - cos 120]
Unit Circle: (1/2) sin 20 [cos 40 + (1/2)]
Distribute: (1/2) sin 20 cos 40 + (1/4) sin 20
Product to Sum Identity: (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20
Simplify: (1/4)[sin 60 + sin (-20)] + (1/4) sin 20
= (1/4)[sin 60 - sin 20] + (1/4) sin 20
Unit Circle: (1/4)[(√3/2) - sin 20] + (1/4) sin 20
Distribute: (√3/8) - (1/4) sin 20 + (1/4) sin 20
Simplify: √3/8
LHS = RHS: √3/8 = √3/8 [tex]\checkmark[/tex]
We are given the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = √3 / 8. Let's once again start by applying the identity 'sin(s)sin(t) = - cos(s + t) + cos(s - t) / 2. In this case if we focus on the expression 'cos(20°)(cos(40°),' s would be = 20°, and t = 40°.
[tex]\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}[/tex]
[tex]\sin \left(20^{\circ \:}\right)\sin \left(40^{\circ \:}\right)=\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}[/tex]
[tex]\mathrm{Substitute}:\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\sin \left(80^{\circ \:}\right)[/tex]
[tex]\mathrm{Multiply\:fractions}:\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]
Remember that cos(- x) = cos(x). Respectively cos(- 20°) = cos(20°). Let's substitute and afterwards apply the identity 'cos(60°) = 1 / 2.'
[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\sin \left(80^{\circ \:}\right)\left(-\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
And if we further simplify the expression, we should receive the following...
[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-1+2\cos \left(20^{\circ \:}\right)\right)}{4}[/tex]
Now we want to prove that this expression = √3 / 8. The denominator here is 4 so we can multiply the whole thing by 2 to have a denominator of 8. 2((sin(80°)(- 1 + 2cos(20°)) when simplified = √3. Therefore the expression is true.
Related Questions
What is the length of the diagonal of a square of side 8cm, after getting your answer, put it in one decimal place. 13.1cm 12cm 11.4cm 11.3cm
Answers
Answer:
11.3 cm
Step-by-step explanation:
The diagonal d divides the square into 2 right triangles with legs 8 and hypotenuse the diagonal d.
Using Pythagoras' identity in one of the right triangles, then
d² = 8² + 8² = 64 + 64 = 128 ( take square root of both sides )
d = [tex]\sqrt{128}[/tex] ≈ 11.3 cm
Answer:
[tex]\huge\boxed{c = 11.3 cm}[/tex]
Step-by-step explanation:
Using Pythagorean Theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of diagonal and a and b are the sides of the square
[Remember that all sides of the square are equal]
=> [tex]c^2 = 8^2 + 8^2[/tex]
=> [tex]c^2 = 64+64\\[/tex]
=> [tex]c^2 = 128[/tex]
Taking sqrt on both sides
=> c = 11.3 cm
Simplify this expression 7/3+3(2/3-1/3)^2
Answers
Answer:
8/3
Step-by-step explanation:
Hope its correct:)
The difference of a number and 10 is equal to eleven times the number
Answers
Answer:
let the number be x
x-10=11*x
x-10=11x
-10=11x-x
-10=10x
x= -10/10
x= -1
Simplify the expression: 3(x-5)+ 2x-3
Answers
Answer:
5x - 18
Step-by-step explanation:
3(x-5)+ 2x-3
Distribute
3x -15 +2x -3
Combine like terms
5x -18
Answer:
5x - 18
Step-by-step explanation:
3(x-5) + 2x - 3
=(3*x + 3*-5) + 2x - 3
= 3x - 15 + 2x - 3
= 5x - 18
Please help me understand this
Answers
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
So we have the equation:
[tex]\frac{-2-2x}{3} =-8[/tex]
First, multiply both sides by 3. This cancels out the denominator:
[tex]3(\frac{-2-2x}{3} )=3(-8)[/tex]
The left side cancels. Multiply the right:
[tex](-2-2x)=-24[/tex]
Add 2 to both sides. The 2s on the left cancel:
[tex](-2-2x)+2=(-24)+2\\-2x=-22[/tex]
Divide both sides by -2. The -2 on the left cancel.
[tex](-2x)/-2=(-22)/-2\\x=11[/tex]
Therefore, the answer is 11.
Answer:
x = 11
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:
*(-2-2*x)/(3)-(-8)=0
Simplify:
*-2 - 2x / 3
Pull out like factors:
*-2 - 2x = -2 • (x + 1)
Now It should look like this:
-2 • (x + 1) / 3 - (-8) = 0
Rewrite the whole as a equivalent fraction using 3 as the denominator:
*-8 = -8 / 1 = -8 • 3 / 3
Add the two equivalent fractions which now have a common denominator
-Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
*-2 • (x+1) - (-8 • 3) / 3 = 22 - 2x / 3
Pull out like factors:
*22 - 2x = -2 • (x - 11)
Now you should have this:
*-2 • (x - 11) / 3 = 0
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
-Now, to get rid of the denominator, multiply both sides of the equation by the denominator.
*-2•(x-11) / 3 • 3 = 0 • 3
-Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
Now you should have this:
*-2 • (x-11) = 0
Now Solve:
x-11 = 0
-Add 11 to both sides of the equation:
x = 11
please answer fast i dont get it
Answers
Answer:
7
Step-by-step explanation:
7
A fisherman can tow upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point
How far did the fisherman row if the entire trip took 5 hours?
The distance the fisherman rowed is mi. (Type an integer or a decimal.)
Answers
He went upstream 3 hours and downstream two. 4x3=12 6x2=12
He went 24 miles.
Answer:
Its 9.6
Step-by-step explanation: i did savas
In a basketball arena, all four sides are filled with people. If each side of the arena is 20 ft. X 30 ft., and each person takes up 2.5 square feet, approximately how many people are in the arena?
Answers
Answer:
960 peopleStep-by-step explanation:
If each side of the basketball arena is 20 ft. X 30 ft, the area of each side of the basketball arena = 20ft * 30ft = 600ft².
Since all the four sides are filled with people, the total area of the 4 sides will be expressed as 4*600 = 2400ft²
If each person takes up 2.5ft², total number of people in the arena will be gotten by simply dividing the area of all the four sides by the area took up by each person.
Total number of people in the arena = area of all the four sides by the area/ area took up by each person.
Total number of people in the arena = 2400/2.5
Total number of people in the arena = 960 people.
Hence there are approximately 960 people in the arena.
What was the political impact of the Justinian Code?
It reformed old, existing Greek laws.
It made women and enslaved people citizens.
It made Justinian I the emperor of Rome.
It influenced the laws of other countries.
Answers
Answer:
The correct option is;
It influenced the laws of other countries
Step-by-step explanation:
The Justinian Code was the rationalization of previous existing Roman laws so as to remove contradiction and eliminate conflicting statutes including the repeal of laws not included in the code.
For close to a millennia, the Justinian Code served as the bedrock of the Byzantine Judiciary and of civil law, fostering law and order for the people of Byzantines and civil law spread to Europe and Latin America.
The Justinian Code influenced the laws of other countries.
The Justinian Code consisted of a collection of older imperial regulations and especially rescripts, which mainly applied during the early 2nd century.It was directly and continuously valid until 1946 in various states and countries that previously belonged to the Eastern Roman Empire. Not only in the East, but also in the West, the creation of Justinian has been attributed authority for centuries by legal scholars, even in areas that had previously fallen outside the Roman sphere of influence. During the Middle Ages, and in many areas afterwards, this law was regarded by legal scholars as an important source of law.Learn more in https://brainly.com/question/1892861
(2.3 x 10^-4)(4.5 x 10^6)=
does anyone know the answer to this
Answers
Answer:
1035
Step-by-step explanation:
(2.3 × 10^4)(4.5 × 10^6)
First we do the exponents:
10^-4 = 0.0001
10^6 = 1,000,000(1 mil)
Now we plug them into the equation:
(2.3 × 0.0001)(4.5 × 1,000,000)
Now we multiply the numbers in the paranthesis:
(0.00023)(4,500,000) = 0.00023 × 4,500,000
Now we multiply both of them:
0.00023 × 4,500,000 = 1035
Owen knows he only has three pencils in his backpack , and they are all yellow. He reaches into his backpack without looking and takes out a pencil . What is the probability that the pencil was yellow
Answers
100% cause owen only has 3 yellow pencils
Answer:
Step-by-step explanation:
The
O over 3 or 1 over 3 or 3 over 3 or 3 over 1
PLEASE HELP!!! Find the measure of AB¯¯¯¯¯¯¯¯. A. 11 B. 13 C. 12 D. 14
Answers
Answer:
A. 11
Step-by-step explanation:
BC×AC = DC × LC
7(2x +3 +7 ) = 9 ( x+ 1 +9)
7 ( 2x +10) = 9( x + 10 )
14x - 9x = 90 - 70
5x = 20
x = 4
then,
AB = 2x + 3
= 2× 4 + 3
= 11
I am thinking of a number. When you add the
number to itself then multiply by 3 you get 36.
What is the number?
Answers
Hi there! :)
Answer:
[tex]\huge\boxed{6}[/tex]
Let "x" represent a number.
Adding the number to itself gives us x + x, or 2x.
Multiplying by 3 gets 36, therefore:
36 = 3 · 2x
Simplify:
36 = 6x
Divide both sides by 6:
36/6 = 6x/6
x = 6.
Which of the following is an equivalent expression of 76543−4? Question 1 options: 176543−4 765434 1765434 765436
Answers
Answer:
1/76543⁴
Step-by-step explanation:
76543¯⁴
The above expression can be simplified as follow:
76543¯⁴
Recall:
a¯ⁿ = 1/aⁿ
Therefore,
76543¯⁴ = 1/ 76543⁴
Thus, 76543¯⁴ is equivalent to 1/76543⁴.
Answer:
Answer:
1/76543⁴
Step-by-step explanation:
76543¯⁴
The above expression can be simplified as follow:
76543¯⁴
Recall:
a¯ⁿ = 1/aⁿ
Therefore,
76543¯⁴ = 1/ 76543⁴
Thus, 76543¯⁴ is equivalent to 1/76543⁴.
Step-by-step explanation:
Can you help me with that?
Answers
Answer:
x<3. Hope this helps!
Step-by-step explanation:
Find the area of this parallelogram.
8.7 cm
10.1 cm
16.9 cm
Answers
Answer:
[tex]A=147.03\text{ cm}^2[/tex]
Step-by-step explanation:
Recall that area for a parallelogram is given by the formula:
[tex]A=bh[/tex]
Where b is the base length and h is the vertical height.
The base length is 16.9 while the vertical height is 8.7. Thus:
[tex]A=(16.9)(8.7)[/tex]
Multiply using a calculator:
[tex]A=147.03\text{ cm}^2[/tex]
In conclusion, the area of the parallelogram is 147.03 square centimeters.
Answer:
147.03 sq.cm.
Step-by-step explanation:
Equation for finding the area of a parallelogram:
b·h=area
Equation for this parallelogram(you don't need the 10.1):
16.9·8.7=147.03
Vishal wants to burn at least 2,400 calories during his weekly workouts. He burns 400 calories per hour swimming and 600 calories per hour rollerblading. He decides to swim for 3 hours this week. How many hours must he rollerblade to reach his goal?
Answers
Answer:
2 hours
Step-by-step explanation:
given that the calorie burn rates are:
swimming: 400 cal / hour
rollerblading: 600 cal / hour
If he swims for 3 hours, he will burn:
400 cal / hour x 3 hours
= 1200 cal
Since his goal is 2400 calories, the number of calories that he has left to burn after swimming is:
2400 - 1200
= 1200 calories.
Number of hours of rollerblading to burn 1200 calories
= 1200 calories ÷ 600 calories per hour
= 2 hours
Answer:
B. y > = 2
The second part is
A. At least 2
Step-by-step explanation:
Just took it. Edg 2020. Hope this helps :)
Please help me graph and find the slope. I need an answer ASAP will mark brainliest!
Answers
Answer:
y = 0.6x
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (1.2 - 0)/(2 - 0)
m = 1.2/2
m = 0.6
y = 0.6x
Step 2: Find y-intercept b
(0, 0) is y-int
Equation is y = 0.6x
Step 3: Graph
Use point (-5, -3) and (0, 0) to graph
f(x)=3x+10
g(x)=x-2
find f(g(5)
Answers
Answer:
Step-by-step explanation:
g(5) = 5 - 2 = 3
f(3) = 3(3) + 10 = 9 + 10 = 19
simplify (5+1)^2-(11+3^2) divides by 4
Answers
Answer:
4
Step-by-step explanation:
(5+1)^2−(11+3^2) / 4 = 4
Answer: 31
Step-by-step explanation:
Simplify the expression.
(the quantity x to the one-sixth power end quantity to the power of 3.)
Answers
Answer:
[tex]\sqrt{x}[/tex]
Step-by-step explanation:
If we have that worded expression, we can convert it into actual mathematical terms.
x to the one sixth power: [tex]x^{\frac{1}{6}}[/tex]
That to the power of 3:
[tex](x^{\frac{1}{6}})^3[/tex]
Using exponent rules, since we have a power to a power, the powers multiply, so:
[tex]x^{\frac{1}{6}\cdot 3}\\\\x^{\frac{3}{6}}\\\\ x^{\frac{1}{2}}[/tex]
If we have a number to a fraction power, the denominator becomes the “find the (denominator) root of x.
So:
[tex]x^{\frac{1}{2}} = \sqrt{x}[/tex]
Hope this helped!
Answer:
x 1/2 took the quiz
David’s family is driving from New York to Florida. They know the distance they will travel is about 1100 miles. If a map has a scale of 1 in. = 80 mi, about how far will the trip be on the map?
Answers
Answer:
Step-by-step explanation:
do the proportion ...
1 inch/ 80 miles =x inch/ 1100 miles
1100= 80x
x=1100/80=13.75
The trip would be about 13.75 inches on the map
hope this will help u
Answer:
Basically to sum it up the answer is C. 13 3/4 in.
Step-by-step explanation:
This is just for the people that don't understand- or have this answer.
Have a great day.
please help :) love you guys so much thank you for being here :) Choose the number that is greater than: 4.526 x 10 to the 6 power A. 5.79 x 10 to the 5 power B. 9.99 x 10 to the 5 power C. 4.123 x 10 to the 6 power D. 55,264,900
Answers
Answer:
D.
Step-by-step explanation:
4.526 x 10^6 = 4,526,000.
55,246,900 is greater than this.
Answer: Hi!
First, we will find value of the equation given, 4.526 * 10^6.
We will solve the exponent first.
10^6 = 10*10*10*10*10*10 = 1,000,000
Now, we will multiply 1,000,000 by 4.526.
4.526 * 1,000,000 = 4,526,000
4,526,000 is the value of 4.526 * 10^6.
We can automatically tell that d), 55,264,900 is greater than 4,526,000. Therefore, d) is your answer.
Hope this helps!
if the distance between the points (2, -2) and (1, x) is 5 one of the values of x is
Answers
Answer:
2.899
Step-by-step explanation:
The formula for calculating the distance between two points P(x1, y1) and (x2, y2) is expressed as:
D = √(x2-x1)²+(y2-y1)²
Given the points (2,-2) and (1,x) and the distance between the point as 5, we are to get x. To get x we will substitute the points and the distance given into the formula.
Given x1 = 2, y1 = -2, x2 = 1, y2 = x and D = 5
On substitution:
5 = √(1-2)²+(x-(-2))²
5 = √1²+(x+2)²
5 = √1+(x+2)²
Square both sides of the equation
5² = (√1+(x+2)²)²
25 = 1+(x+2)²
(x+2)² = 25-1
(x+2)² = 24
Square both sides
√(x+2)² = √24
x+2 = √24
x = √24- 2
x = 4.899-2
x = 2.899
Hence the other value is 2.899
look at picture and solve
Answers
Ok
Answer:
Option C: x = 300
Step-by-step explanation:
Step 1. Expand the brackets.
When factorising (putting into brackets) and expanding (taking out of brackets), it is always important to remember that the number on the outside multiplies everything on the inside. It is also important to remember the signs of the outside and inside numbers (i.e. if the numbers are positive or negative).
[tex]\frac{1}{3}[/tex](x - 15)
= ([tex]\frac{1}{3}[/tex] × x) - ([tex]\frac{1}{3}[/tex] × 15)
= (x ÷ 3) - (15 ÷ 3)
= [tex]\frac{x}{3}[/tex] - 5
Step 2. Solve the equation.
[tex]\frac{x}{3}[/tex] - 5 = 95
What we want to do is to get x on its own on one side, so that we can figure out the value of x.
[tex]\frac{x}{3}[/tex] - 5 = 95
+ 5 to both sides (do the opposite of what is there, [tex]\frac{x}{3}[/tex] is subtracting 5 right now, but we want to cancel that subtraction out, so we do the opposite of subtraction, i.e. addition)
[tex]\frac{x}{3}[/tex] = 95 + 5
[tex]\frac{x}{3}[/tex] = 100
× 3 to both sides (do the opposite of what is there: x is divided by 3 right now, but we want to cancel that division out, so we do the opposite of division, i.e. multiplication)
[tex]\frac{x}{3}[/tex] x 3 = 100 x 3
x = 100 x 3
x = 300
Step 3. We look for out answer within the options given.
As we can see, the option of [x = 300] is option C, so the answer we would give would be "C".
Simplify (x + 4)(x2 − 6x + 3). (5 points) a x3 − 14x2 + 3x + 12 b x3 − 6x2 − 17x + 12 c x3 − 10x2 − 27x + 12 d x3 − 2x2 − 21x + 12
Answers
Answer:
the answer is x −[tex]5x+6(x5)24+|−2|[/tex] ohhh i didnt see the abcd
Step-by-step explanation:
Answer:
The answer is option DStep-by-step explanation:
( x + 4)( x² - 6x + 3)
Using the distributive property expand the expression
That's
x³ - 6x² + 3x + 4x² - 24x + 12
Group like terms
That's
x³ - 6x² + 4x² + 3x - 24x + 12
Simplify
We have the final answer as
x³ - 2x² - 21x + 12Hope this helps you
The following list details the numbers of tickets sold for a talent show grade 9:22; grade 10:32; grade 11: 41; and grade 12:30. What are the domain and range of this relation? A domain: (22, 32, 41, 30); range: {9, 10, 11, 12} B. domain: {9, 22, 10, 32); range: {11, 41, 12, 30} C. domain: {9, 10, 11, 12); range: (22, 32, 41, 30) D domain: {11, 41, 12, 30}; range: {9, 22, 10, 32)
Answers
Answer:
The correct option is;
C. Domain: {9, 10, 11, 12}; range {22, 32, 41, 30}
Step-by-step explanation:
The given parameters are;
The ticket sold at the talent show for different grades;
For grade 9, 22 tickets were sold
Grade 10, had 32 tickets sale
The number of tickets sold for grade 11 = 41 tickets
The number of tickets sold for grade 12 = 30 tickets
We note that the domain are the inputs and independent variables, x, of a function,f(x), while the range is the set of outputs, dependent, variables, of the function or the values of f(x)
Therefore, given that the domain are the independent variable, that is their values are not influenced by other variables, then the domain are the grades, which are 9, 10, 11, 12, while the range are the range are the number of tickets sold (22, 32, 41, 30) which are dependent on the grades
Which measurement is greater:640 ft or 0.5 mi
Answers
Answer:
0.5 mi (2640 feet)
Step-by-step explanation:
Answer:
0.5 mi
Step-by-step explanation:
1 mile = 5280 feet
1 foot = 0.000189394 miles
0.5 miles = 2640 feet
640 feet = 0.121212
therefore, 0.5 mi is greater
I need help on this right quick please someone help
Answers
Answer:
the answer seems to be A
Which of the following functions is graphed below
Answers
Answer:
b
Step-by-step explanation:
bet