Answers
Answer: see proof below
Step-by-step explanation:
Use the following Sum to Product Identities:
[tex]\sin x-\sin y=2\cos\bigg(\dfrac{x+y}{2}\bigg)\sin\bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x-\cos y=2\cos\bigg(\dfrac{x+y}{2}\bigg)\cos\bigg(\dfrac{x-y}{2}\bigg)[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \qquad \dfrac{\sin 2A+\sin 5A-\sin A}{\cos A+\cos 2A+\cos 5A}[/tex]
[tex]\text{Regroup:}\qquad \qquad \qquad \dfrac{\sin 2A+(\sin 5A-\sin A)}{\cos 2A+(\cos 5A+\cos A)}[/tex]
[tex]\text{Sum to Product:}\qquad \dfrac{\sin 2A+2\cos\bigg(\dfrac{5A+A}{2}\bigg)\sin\bigg(\dfrac{5A-A}{2}\bigg)}{\cos2A+\cos\bigg(\dfrac{5A+A}{2}\bigg)\cos\bigg(\dfrac{5A-A}{2}\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{\sin 2A+2\cos 3A\sin 2A}{\cos 2A+2\cos 3A\cos 2A}[/tex]
[tex]\text{Factor:}\qquad \qquad \qquad \dfrac{\sin 2A(1+2\cos 3A)}{\cos 2A(1+2\cos 3A)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{\sin 2A}{\cos 2A}\\\\.\qquad \qquad \qquad \qquad =\tan 2A[/tex]
LHS = RHS: tan 2A = tan 2A [tex]\checkmark[/tex]
Related Questions
26. Given the point A(-2,4) translate (x,y) → (x – 4, y - 3) and then reflect over the line y = -x.
What are the coordinates of the final image? (4 points)
Math
Answers
Greetings from Brasil...
Here is the graphical explanation in the annex.
A = (-2; 4)
A' = (-2 - 4; 4 - 2) = (-6; 1)
After reflection on F(X)
A'' = (-1; 6)hey please help!! Thank you <33
Answers
Answer:
4+6j
Step-by-step explanation:
[tex]4+(6\times j)\\4+6j[/tex]
Look at image for question
Answers
Answer:
P = 19.76 unitsStep-by-step explanation:
1. Finding [tex]\overrightarrow{AB}[/tex] (or [tex]\overrightarrow{BA}[/tex]):
[tex]\overrightarrow{AB}=\overrightarrow{OA}-\overrightarrow{OB}= \left[\big5\atop\big3\right]-\left[\big2\atop-\big5\right]= \left[\big5-\big2\atop\big3-(-\big5)\right]=\left[\big3\atop\big8\right][/tex]
2. Calculating length of [tex]\overrightarrow{OA}\,,\ \overrightarrow{OB}\ \text{and}\ \overrightarrow{AB}[/tex]:
[tex]|\overrightarrow{OA}|=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}\approx5.831\\\\ |\overrightarrow{OB}|=\sqrt{2^2+(-5)^2}=\sqrt{4+25}=\sqrt{29}\approx5.385\\\\ |\overrightarrow{AB}|=\sqrt{3^2+8^2}=\sqrt{9+64}=\sqrt{73}\approx8.544[/tex]
3. Calculating perimeter:
[tex]P=|\overrightarrow{OA}|+|\overrightarrow{OB}|+|\overrightarrow{AB}|=\sqrt{34}+\sqrt{29}+\sqrt{73}\approx5.831+5.385+8.544=19.76[/tex]
A 3/4 pound box contained 36 fruit
tarts. How many tarts would be in a
one-pound box?
Answers
If I am in Vermont, then I am in the North.
Write the converse of the conditional. Choose the correct answer below.
O A. If I am not in Vermont, then I am not in the North.
O B. If I am in the North, then I am not in Vermont.
C. If I am not in the North, then I am not in Vermont.
D. If I am in the North, then I am in Vermont.
Answers
This is because a converse statement switches the places of the hypothesis and conclusion.
please help lots of points
Answers
Answer:
see below
Step-by-step explanation:
The area is given by
A = l*w
A = (4x-1) ( 3x+6)
FOIL
first 4x*3x =12x^2
outer 6*4x = 24x
inner -1*3x = -3x
last -1 *6 = -6
Add together
12x^2 +24x-3x-6
12x^2 +21x-6
Answer:
The area is given by
A = l*w
A = (4x-1) ( 3x+6)
first 4x*3x =12x^2
outer 6*4x = 24x
inner -1*3x = -3x
last -1 *6 = -6
Add together
12x^2 +24x-3x-6
12x^2 +21x-6
Which statement is supported by the histograms? The two data sets have the same distribution and same range. The two data sets have the same distribution but different ranges. The two data sets have different distributions but the same range. The two data sets have different distributions and different ranges.
Answers
Answer:
The two data sets have different distributions and different ranges.
Step-by-step explanation:
When you subtract for both of the ranges they are different numbers. So that's the second part. The numbers along the bottom are different too so that is the different distributions.
Answer:
The two data sets have different distributions and different ranges.
Step-by-step explanation:
The shape of the data for German male adult heights is skewed left, but the shape of the data for female adult heights is close to symmetric. So, the two data sets have different distributions.
Each data set has the same minimum height of 145 centimeters. However, the maximum male adult height is 220 centimeters, and the maximum female height is 185 centimeters. So, the two data sets have different ranges.
Solve for x: 4 over 5 x + 4 over 3 = 2x x =
Answer Write your answer as a fraction in simplest form.
(write x = 'answer')
Answers
Answer:
over 5 x + 4 over 3 = 2x
can't find x
Hi McDa:
Here's a couple hints. (I have no idea what you already understand. Please check out our posting guidelines.)
Express the Natural number 3 in Rational form 3/1.
4
5
x
+
4
3
1
=
2
x
Regarding the left-hand side above, have you learned the property that says we may multiply by the reciprocal of 3/1, instead of dividing by 3/1?
Step-by-step explanation: Incorrect? Let me know!
Plz, help ASAP!!! WILL MARK U BRAINLIST IF UR ANSWER IS CORRECT Question #2
Answers
Answer:
Graph 2 contains a function, but graphs 1 and 3 do not (1st Option).
Step-by-step explanation:
In order for a graph to be a function, it must pass the Vertical Line Test. Every x-value must have it's own y-value.
This means that 2 different y-values cannot have the same x-value.
If B is the midpoint of AC, solve for x, and find the lengths of AB, BC, and AC.
Please show all work and not just the answers.
Answers
Answer:
x = 2
AB = 15
BC = 15
AC = 30
Step-by-step explanation:
Given that B is the midpoint of AC, then AB = ½ of AC.
AB is given as 3(3x - 1),
AC = 5(2x + 2),
Therefore:
[tex] 3(3x - 1) = \frac{1}{2}*5(2x + 2) [/tex]
Solve for x
[tex] 9x - 3 = \frac{5}{2}(2x + 2) [/tex]
Multiply both sides by 2
[tex] 2(9x - 3) = \frac{5}{2}(2x + 2)*2 [/tex]
[tex] 18x - 6 = 5(2x + 2) [/tex]
[tex] 18x - 6 = 10x + 10 [/tex]
[tex] 18x - 10x = 6 + 10 [/tex]
[tex] 8x = 16 [/tex]
Divide both sides by 8
[tex] x = 2 [/tex]
[tex] AB = BC = 3(3x - 1) [/tex]
Plug in the value of x
[tex] AB = BC = 3(3(2) - 1) [/tex]
[tex] = 3(6 - 1) = 3(5) = 15 [/tex]
[tex] AC = 5(2x + 2) [/tex]
[tex] AC = 5(2(2) + 2) [/tex]
[tex] AC = 5(4 + 2) = 5(6) = 30 [/tex]
Powers of 10 with positive exponents are:
less than 1
greater than 1
Answers
Answer:
greater than 1
Step-by-step explanation:
A grocery store has small bags of apples for 5$ and large bags of apples for 8$. If you buy 6 bags of apples and spend 45$, how many of each bags did you buy?
Answers
Answer:
He bought 1 small bag and 6 large bags.
Step-by-step explanation:
We can set up 2 equations with the given information.
5x+8y=45
x+y=6
We can rearrange the second equation to solve for x.
x=6-y
Now we substitute x for 6-y in the first equation
5(6-y)+8y=45
30-5y+8y=45
30+3y=45
y+10=15
y=5
x=1
He bought 1 small bag and 6 large bags.
There were 7 songs on one side of a record. It took 20 minutes and 18 seconds to play the side. What is the average number of seconds per song?
i will mark brainliest
Answers
Answer:
174 seconds.
Step-by-step explanation:
So there was a total of 7 songs.
And it took a total of 20 minutes and 18 seconds to play them all.
20 minutes and 18 seconds is the same as 20(60)+18=1218 seconds.
Thus, the average number of seconds per song was:
[tex]1218/7=174[/tex]
174 seconds,
or about 2 minutes and 54 seconds.
A health club charges an initiation fee of $50. Members then pay $45 per month. You have $400 to spend on a health club membership. For how many months can you afford to be a member? Let n represent the number of months you can pay for a membership.
Answers
Answer:
8 monthsStep-by-step explanation:
In this problem we must first of all write the inequality that describes the problem.
Given that
1. you have a limit of $400
2. there is an initial fee of $50
3. monthly payment is $45
let the number of months be n
therefore
[tex]50+45n\leq 400\\\\45n\leq 400-50\\\\45n\leq350[/tex]
Divide both sides by 45 we have
[tex]n\leq \frac{350}{45} \\\\n=\frac{70}{9} \\\\n= 7.77\\\\[/tex]
approximately you are going to be member for 8 months
On Friday, the temperature was 82°F. The temperature changed by –2°F on Saturday, and then it changed by 5°F on Sunday. What was the temperature on Sunday? How did the temperature change?
Answers
Answer:
the temp on Sunday was 85, it changed by going down 2 degrees, and up 5 degrees
Step-by-step explanation:
when it says -2 degrees F its basically saying subtract 2, and then go on and add 5
Answer:
it was 85 goes up by 3
Step-by-step explanation:
what is the square root of 655.36
Answers
Answer: 25.6
Step-by-step explanation: Have an Amazing Day :)
Answer:
25.6 this will be the answer
Step-by-step explanation:
Hope it helps
There are three numbers. The first number is twice the second number. The third number is twice the first number. The sum of the three numbers is 112.
Answers
Answer:
x = 32 y = 16 z = 64
Step-by-step explanation:
x is the 1st number
y is the 2nd number
z is the 3rd number
The first number is twice the second number so
x = 2 y
The third number is twice the first number.
z = 2 x
Their sum is 112
x + y + z = 112
Plus in what we know:
x + y + z = 112
2 y + y + 2x = 112
3y + 2x = 112 Let's solve for y and subtract 2x from each side
3y = 112 - 2x Divide both sides by 3
y = [tex]\frac{112 - 2x}{3}[/tex]
Now plug our answer back in to solve for x.
x = 2y
x = 2 ( [tex]\frac{112 - 2x}{3}[/tex] )
x = (224 - 4x) / 3 Multiply each side by 3.
3x = 224 - 4x Add 4x to each side
3x + 4x = 224
7x = 224 Divide each side by 7
7x / 7 = 224 / 7
x = 32
Now we can solve for z.
z = 2x
z = 2 ( 32 )
z = 64
Now we can solve for the numerical value of y.
x + y + z = 112
32 + y + 64 = 112
96 + y = 112 Subtract 96 from each side.
y = 112 - 96
y = 16
Answer:
1st number = 36
Second = 16
Third = 64
Step-by-step explanation:
We have 3 numbers
Let's call the second number g
Then the first would be , 2x g = 2g
Then the third would be twice the first = 2 x 2g = 4g
We add up all numbers and equate it to 112
2g + g +4g = 112
7g = 112
g = 112/7
g = 16
First number = 2g = 2x16 = 32
Second number = g = 16
Third number = 4g = 4x16 = 64
Therefore the numbers are 32, 16, 64.
I hope this helps!
One number is 9 more than twice another number. If the sum of the numbers is 129, find both numbers.
Answers
Answer:
40 and 89
Step-by-step explanation:
let x be the number then the other number is 2x + 9, then
x + 2x + 9 = 129, that is
3x + 9 = 129 ( subtract 9 from both sides )
3x = 120 ( divide both sides by 3 )
x = 40
Thus the numbers are
x = 40 and 2x + 9 = 2(40) + 9 = 80 + 9 = 89
Represent the following sentence as an algebraic expression, where "a number" is the
letter x.
The difference of 3 and a number.
Answers
Answer: 3 - x
Step-by-step explanation: With
Subtraction be careful. 3 - x is not the same as x - 3. You have to keep the values given in order.
In 201620162016, the city of Rio de Janeiro had a population density of 5377\,\dfrac{\text{people}}{\text{km}^2}5377 km 2 people 5377, start fraction, start text, p, e, o, p, l, e, end text, divided by, start text, k, m, end text, squared, end fraction . What was the population density of Rio de Janeiro in people per square meter?
Answers
Complete question:
In 2016, the city of Rio de Janeiro had a population density of 5377 people/km2.
What was the population density of Rio in people per square meter?
Answer:
0.005377 peope/m²
Step-by-step explanation:
Given that :
Population density of Rio in 2016 = 5377 people/km²
To obtain population density in people per square meter, we convert 5377people/km² to people per m²
Recall:
1000 m = 1km
Hence,
5377 people/km² = 5377 people / (1000²)m
= (5377/1000000)people/m²
= 0.005377 peope/m²
Answer:
0.005377
Step-by-step explanation:
KHAn
a line of best fit for the data is y=0.9x-4.5, where x represents age in year, and in years, and y represents hourly pay, in dollars.Based on the data, what is the best prediction for the hourly pay of a 25 year old?
Answers
Answer:
$18
Step-by-step explanation:
Given:
y = 0.9x - 4.5
Where,
x = age in years
y = hourly pay in dollars
what is the best prediction for the hourly pay of a 25 year old?
That is, find y when x=25
y = 0.9x - 4.5
= 0.9(25) - 4.5
= 22.5 - 4.5
= 18
y = $18
The prediction for the hourly pay of a 25 year old is $18
Answer:
$18:00
Step-by-step explanation:
Thank You To The Guy Above Me
Write the sentence as an equation. A number added to -6 is -33
Answers
Answer:
x+(-6)= -33
hope that helps : )
Answer: x+-6=-33
Step-by-step explanation: The x is a variable which is added to -6 which equals -33.
1. A standard dice has 6 sides with the numbers 1-6 on it. What is the probability of rolling a 4 on a
standard dice?
Answers
Answer:
1/6
Step-by-step explanation:
There are six sides on a die and only one of them has a 4
P( 4) = number of sides with a 4/ total number of sides
= 1/6
Answer:
P (4) = 1/6
Step-by-step explanation:
The probability can be found by creating a fraction. The numerator is the number of favorable outcomes and the denominator is the total number of outcomes.
P (4) = sides with a 4 / total sides
The standard dice has 6 sides numbered 1 through 6.
P (4) = sides with a 4/ 6
Only one side on the cube has a 4.
P (4) = 1/6
This fraction cannot be simplified further, so it is our final answer.
The probability of rolling a 4 on a standard dice is 1/6
Robert and his friends are going into a grocery store. How much would it cost to buy 4 bananas and 5 peaches if each banana costs $0.40 and each peach costs $0.75? How much would it cost to buy 4 4 bananas and 5 5 peaches if each banana cost $ x $x and each peach cost $ y ? $y
Answers
Answer:
4*0.40+5*0.75=5.35
Step-by-step explanation:
Answer:
like so i could get points pls, answer is in screenhot lol
Step-by-step explanation:
Identify the incorrect Algebra forms that multiplication is represented in the expressions 5 times 3x.
A 5(3x)
B (5) x (3x)
C (5)3x
D 5(3)(x)
Answers
Answer:
5 x 3x = A 5(3x)
Step-by-step explanation: () = multiply
EX: 6(8) = 48
solve equation by taking square roots n^2+4=40
Answers
Answer:
n = ±6
Step-by-step explanation:
n² + 4 = 40
n can be solved by finding the square root
n² = 40 - 4
n² = 36
n = √36
n = ±6
which two values of X are roots of the polynomial below?
Answers
Answer:
C and D
Step-by-step explanation:
As determinant of this quadratic equation is given by-
(-b±√(b²-4ac))/2a
Y=2x +7
Find the x interception
Answers
Answer:
Step-by-step explanation:
hello :
the x interception for Y=2x +7 when Y=0 means : 2x +7=0
so x = -7/2
Of the students at Milton Middle School, 110 are girls. If 50% of the students are girls, how many total students are there at Milton middle school
Answers
Answer:
220
Step-by-step explanation
Write the equation of a line that is perpendicular to y= 2/3x + 3 and passes through the point (4, -8).
Answers
Answer:
Step-by-step explanation:
Perp. : -3/2
y + 8 = -3/2(x - 4)
y + 8 = -3/2x + 6
y = -3/2x - 2