Answers
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A + B = π - C
A + C = π - B
B + C = π - A
Cofunction Identities: sin [(π/2) - A] = cos A
cos [(π/2) - A] = sin A
Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]
Pythagorean Identity: cos²A + sin²A = 1 → cos²A = 1 - sin²A
Even/Odd Identity: cos (-A) = -cos(A)
Double Angle Identity: cos (2A) = 2 cos²A - 1
Proof LHS → RHS:
LHS: cos [(B + C) - A] - cos [(A + C) - B] + cos [(A + B) + C]
Given: cos [(π - A) - A] - cos [(π - B) - B] + cos [(π - C) - C]
= cos (π -2A) - cos (π -2B) + cos (π -2C)
Cofunction: cos (-2A) - cos (-2B) + cos (-2C)
Even/Odd: -cos (2A) + cos (2B) - cos (2C)
Double Angle: -(2cos²A - 1) + cos (2B) - cos (2C)
= 1 - 2cos²A + cos (2B) - cos (2C)
Sum to Product: 1 - 2cos²A - 2sin(B+C) · sin (B-C)
Given: 1 - 2cos²A - 2sin (π - A) · sin (B - C)
Cofunction: 1 - 2cos²A - 2sin A · sin (B - C)
Pythagorean: 1 - 2(1 - sin²A) - 2sin A · sin (B - C)
= 1 - 2 + 2sin²A - 2sin A · sin (B - C)
= -1 + 2sin²A - 2sin A · sin (B - C)
Factor: -1 + 2sin A (sin A - sin (B - C))
Given: -1 + 2sin A [sin (π - (B + C)) - sin (B - C)]
Cofunction: -1 + 2sin A [sin (B + C) - sin (B - C)]
Sum to Product: -1 + 2sin A [2 cos B · sin C]
= -1 + 4sin A · cos B · sin C
LHS = RHS [tex]\checkmark[/tex]
Related Questions
PLS HELP GIVING BRAINLIEST TO FIRST PERSON
Answers
Answer:
Solve for x
by simplifying both sides of the equation, then isolating the variable. x=ordw
Step-by-step explanation:
or it could be word
Answer:
x=57
Step-by-step explanation:
I think i already answered this question, but i will rewrite it again! since the angles 'x' and '2x+9' add up to become a supplement angle or a straight line.
We can establish the relation which says that the sum of these two angles is equal to 180.
[tex]x + 2x + 9 = 180[/tex]
[tex]3x + 9 = 180[/tex]
[tex]3x = 180 - 9[/tex]
[tex]3x = 171[/tex]
[tex]x = \frac{171}{3} = 57[/tex]
I need help ASAP, with numbers 3-6 above. Please help.
Answers
Answer:
3. 2 6 30 6. 8:5
3 9 45
Step-by-step explanation:
A man can make 12 birdhouses in 8 hours. How many hours will it take him to make 30 birdhouses?
Answers
Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch's 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo's margin of error, rounded to the nearest whole number? (The formula is 1.96 straight x left parenthesis StdDev right parenthesis divided by square root of straight N)
Answers
Answer:
The answer is "20".
Step-by-step explanation:
Given value:
[tex]\to Z_{critical}= 1.96\\\\\to {StdDev} = standard\ deviation = 50 \\\\\to n= 25\\\\[/tex]
formula:
[tex]\bold{Margin error}= Z_{critical} \times \frac{\text{StdDev}}{\sqrt{n}}\\[/tex]
[tex]= 1.96 \times \frac{ 50 }{\sqrt{25}}\\\\= 1.96 \times \frac{ 50 }{\sqrt{5 \times 5}}\\\\= 1.96 \times \frac{ 50 }{{5}}\\\\= 1.96 \times 10 \\\\= 19.6 \\\\= 20[/tex]
PLEASE HELP 30 POINTS
Line A is represented by the equation, y=1/4x +5
(a) Write in slope-intercept form the equation of a line that is parallel to Line A and passes through the point, (8, -2). Show your work
(b) Write in slope-intercept form the equation of a line that is perpendicular to Line A and passes through the point, (4,1). Show your work.
Answers
Answer:
(a) y = 1/4x - 4
(b) y = -4x + 17
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
(a)
Parallel lines have the same slope but different y-intercepts.
m = 1/4x
y = 1/4x + b
-2 = 1/4(8) + b
-2 = 2 + b
b = -4
y = 1/4x - 4
(b)
Perpendicular lines have the negative reciprocal slope.
m = -4
y = -4x + b
1 = -4(4) + b
1 = -16 + b
b = 17
y = -4x + 17
Answer:
(a) y = 1/4x - 4
(b) y = -4x + 17
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope but different y-intercepts
Perpendicular lines have the negative reciprocal slope.
HELP
and hurry please
(picture)
Answers
The Pyramid of Khufu in Giza, Egypt was the world's tallest free-standing structure for more than 3,500 years. Its original height was about 144
meters. Its base is approximately a square with a side length of 231 meters.
The diagram shows a cross section created by dilating the base using the top of the pyramid as the center of dilation. The cross section is at a
height of 96 meters
144 m
=> A
96 m
231 m
231 m
Complete the following about the cross section
The scale factor used to create the cross section is 13
Part B
Complete the following about the cross section
The dimensions of the cross section is a Select Choice y meter by Select Choice y meter Select Choice
Answers
The scale factor used to create the cross section is 1/3. The cross section has a base side length of 77 meters.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The height of the dilated pyramid = 144 m - 96 m = 48 m
Scale factor of dilation = 48 m / 144 m = 1/3
The side length of dilated pyramid = (1/3) * 231 m = 77 m
The scale factor used to create the cross section is 1/3. The cross section has a base side length of 77 meters.
Find out more on equation at: https://brainly.com/question/2972832
The area of a triangle 36 ×39×15
Answers
Answer:
a=21060[tex]in^{3}[/tex]
Step-by-step explanation:
A= B*W*H
A=36*39*15
A=1404*15
A=21060
Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the coefficient 'k' in the factored form?
6x3 + 4x2 − 6x − 4 = 2(x + k)(x − k)(3x + 2)
k=
Answers
1
2*(x+1)*(x-1)*(3x+2)
hope this helps
The distance between city A and city B is 760km. A car starts to travel from A to B at 80 km/h at 8 o'clock. The other car starts to travel from B to A at 120 km/h at 10 o'clock. At what time will the cars meet?
Answers
Speed of 2nd car = 120km/h
So, 120+80= 200km/hr
Distance between city A and B is 760km
T= D/S
760/200
= 3.8
The cars will meet after 3.8 hours.
Hope this helps
What is the slope of the equation y=5/4x - 7/4
Answers
Answer:
The equation of a line is given by y = mx + c; where m is the slope.
The given equation is y = 5/4 x - 7/4.
Therefore, the slope is 5/4.
There are 36 carpenters in a crew. On a certain day, 29 were present. What percent were at work? (Round your answer to the nearest hundreth - 2 decimal places.)
Answers
Answer:
80.56%
Step-by-step explanation:
divide 36 by 29 and you get 0.8055555555. Change that into a percent to get 80.56%
What is the area of this figure?
Answers
Answer:
70 m^2
Step-by-step explanation:
I did this quickly, so please check the numbers.
Divide the figure into 3 recdtangles and one triangle. Calculate the area of each and take the sum.
I realize after looking at the image that one could have made only two rectangles and gotten the same result.
(n − m)to the power of 2 for m = −3 and n = 7.
Answers
Answer:
100
Step-by-step explanation:
(n-m) = (7+3)
7+3 = 10
10 x 10 = 100
Part 2:
2.4.3: Denver to Chicago
A plane flew at a constant speed between Denver and Chicago. It took the plane 1.5 hours to fly 915 miles.
Answers
Answer:
Whats the question?
Step-by-step explanation:
NEED HELP WITH MATH!!! 10pts
Answers
Answer:
D
Step-by-step explanation:
Divide the two equations using polynomial division and you will get your answer.
Hope this helps
Which of these is a unit of density?
Answers
[tex]\longrightarrow \textsf{The unit of density is\;} [/tex][tex]\sf kg/m^3[/tex]
Solution :-[tex]\green{ \underline { \boxed{ \sf{Density = \frac{Mass}{Volume}}}}}[/tex]
[tex]\longrightarrow[/tex]The unit of mass is kg and unit of Volume is m³ . Since density is division of mass by volume , the corresponding units will also get divided and unit of density would come out to be kg/m³
Some basic derived Units :-
area => m²volume cubic meter => m3speed meter per second => m/sacceleration => m/s²mass density meter => kg/m3specific volume cubic meter per kilogram m³/kgWhich function has an inverse that is also a function?
G(x)=2x-3
Answers
Answer:
x/2+3/2
Step-by-step explanation:
How did Athaliah impose wickedness upon Judah?
Answers
Answer:
By killing all but one of his family members
Jim made $143 for 11 hours of work at the same rate how many hours would he have to work to make $91
Answers
Answer:
Step-by-step explanation:
The equation is
Salary = 11 * x Where x is the number of hours.
salary = 143
hours = 11
x = ?
143 = 11x Divide both sides by 11
143/11 = 11x/11
13 = x
So to get 143 he works for 13 dollars / hour
salary = 13 * x
salary = 91
13 x = 91
13x/13 = 91/13
x = 7
He must work 7 hours to get 91 dollars.
Jim made 143 dollar for 11 hours of work at the same rate how many hours would he have to work to make 91 dollar
✺ Explanation -:Given:
Jim made $143 for 11 hours of work.To Find:
Hours he have to work to make $91.Solution:
We can solve this question using two methods Unitary Method and Method of proportion.
Unitary Method -
For $143 he work 11 hours
For $1 he work [tex]\dfrac{11}{143}[/tex] hrs
For $91 he works [tex]\dfrac{\cancel{11}} {\cancel{143}\: \: \cancel{13}}[/tex] × [tex]\cancel{91}\: \: 7 [/tex]hrs
= 7 hours
He must work 7 hours to get $91.
[tex] \ {\rule{50mm}{3pt}}[/tex]
Method of proportion -
He work 'x' hours for $91. (x as no. of hrs)
[tex] \left[\begin{array}{c | c}\ \bf{Salary} & \bf{Number \: of \: hrs} \\ \sf{143 \: dollar} & \sf{11hrs} \\ \sf{91 \: dollar}& \sf{x}\end{array} \right][/tex]
143 : 91 :: 11 : x
Product of mean = Product of extreme
143 × x = 91 × 11
→ x = [tex]\dfrac{91 × 11}{143}[/tex] = 7hrs
He must work 7 hours to get $91.
[tex] \ {\rule{90mm}{3pt}}[/tex]
Joe's fitness club charges $40 a month for a membership. Mike's fitness club charges $20 for a membership per month and a $100 starting fee. After how many months will the total amount paid to the two clubs be the same?
Answers
Answer:
5 months
Step-by-step explanation:
Create an Equation:
m=months
Joe- 40m
Mike- 20m +100
Make each equation equivalent:
40m=20m+100
Solve:
40m-20m=100
20m=100
m=5
If you plug it back in, the equation is satisfied:
40(5)=20(5)+100
200=100+100
200=200
There are 40 monkeys and 60% of the monkeys are in the trees. How many monkeys are in the trees?
Show your work: Write an equation, solve and explain your thinking
Answers
Answer:
24 monkeys are in the tree
Step-by-step explanation:
We solve it by writing [tex]\frac{60}{100}[/tex] times [tex]\frac{40}{1}[/tex]
Why is it over 100? Because every percent is out of 100!
[tex]\frac{60}{100}[/tex] X [tex]\frac{40}{1}[/tex] (your equation)
60 times 40 = 2400 and 100 times 1 = 100, We get, [tex]\frac{2400}{100}[/tex],
Lastly, we simplify the fraction by 100 on each side:
[tex]\frac{2400}{100}[/tex] / [tex]\frac{100}{100}[/tex]
you get 24
Am i right please help asap
Answers
Answer:
yea i think
Step-by-step explanation:
area of a triangle = (hb)/2
19x14 = 266
266/2 = 133
The answer has to be a fraction, number 10!!! Urgent!!!
Answers
Answer:
x = 0
Step-by-step explanation:
Calculate the product
Any expression multiplied by 0 equales 0
Solution
X = 0
Hope this helps!
helpppp plsssssssssss
Answers
Answer:
65 degrees
Step-by-step explanation:
corresponding angles
2i-3n=8
i+2n=-3
solve for i and n
Answers
Answer:
n= -2/7 i= 3 4/7
Step-by-step explanation:
i=3-2n
2(3-2n)-3n=8
6-4n-3n=8
6-7n=8
6-8=7n
-2=7n
-2/7=n
=3-2(-2/7)
3+4/7
i=3 4/7
If a club has 20 members and 4 officers how many choices are there for secretary
A. 20
B. 18
C.19
note: The secretary is the third officer to be elected.
Answers
Is the figure shown in the xy-coordinate plane a parallelogram? Why or why not? Use the given coordinates to justify your answer.
Answers
The figure shown would represent a parallelogram if opposite sides are parallel and congruent
It is true that the figure is a parallelogram
How to determine if the figure is a parallelogram
The coordinates of the figure are given as:
O = (0,0)
P = (a,b)
S = (a + c,b)
T = (c,0)
Vertices O and T are on the same horizontal level, because they have the same y-coordinate
The above is also applicable to vertices P and S
By observation, we have the following distances:
PS = c
OT = c
This means that the opposite sides are parallel and congruent
Hence, the figure is a parallelogram
Read more about parallelograms at:
https://brainly.com/question/24056495
1. The first three terms and the last term of a finite arithmetic sequence are - 92,- 88. -
84, ...,12.Find the number of terms in the sequence.
A. 20
B. 25
C. 27
D. 30
Answers
= 4
First term = -92
Formula -> Tn = First term + (n-1)d
12 = -92 + (n-1)(4)
104 = 4n-4
108= 4n
n= 27
Hope this helps, and please award brainliest if you could!
The number of terms in the given arithmetic sequence is 27 so option (C) will be correct.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Now it has the same difference between any two consecutive terms d =2-1 = 3-2
Given the AP;
- 92,- 88, -84, ...,12.
First term (a) = -92
Common difference(d) = -88 + 92 = 4
The nth term or last term = 12
Nth term is given as ;
⇒ a + (n - 1)d
12 = -92 + (n - 1)4
n - 1 = 26
n = 27
Hence "The number of terms in the given arithmetic sequence is 27".
For more about Arithmetic progression
https://brainly.com/question/20385181
#SPJ2
Claire has a hot tub with a diameter of 7 feet. She wants to purchase a cover to protect the hot tub. What is the area of the cover? Use Pi = 3. 14 and round the answer to the nearest square foot.
Answers
Answer:
38 square feet
Step-by-step explanation:
How do we find the area of a circle?
❖ The area of a circle is πr², where r = radius. For this case, we're going
to approximate pi as 3.14.
How do we find the radius given diameter?
❖ We are given the diameter of Claire's hot tub as 7 feet. The diameter
is 2x the radius, so we divide 7 by 2 to get the radius, which is 3.5
feet.
Solving
[tex]3.14*3.5^2[/tex] [tex]3.14 *12.25[/tex] [tex]38.465[/tex] 38.465 ≈ 38Therefore, the answer is 38 square feet. Have a lovely rest of your day/night, and good luck with your assignments! ♡