Answers
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
[tex]2=\dfrac{\sin B\cdot \sin C}{\cos B \cdot \cos C}[/tex] Division
2 = tan B · tan C
[tex]\text{Use the Sum Identity:}\quad \tan(B+C)=\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}[/tex]
Proof LHS → RHS
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
[tex]\text{Sum Identity:}\qquad \qquad \qquad =-\bigg(\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}\bigg)[/tex]
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C [tex]\checkmark[/tex]
Related Questions
Lyons evaluated the expression analyze Leon’s work check all that apply
Answers
Answer: The answer is C, and D.
Answer: The answer is actually C D and E
Step-by-step explanation:
I tried what the person said was “correct” and got it wrong
The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought? x = 8, y = 45 x = 10, y = 22 x = 16, y = 22 x = 18, y = 18
Answers
He'll buy 16 new releases and 22 classic movies.
Let x = number of new releases
Let y = number of classics.
The equation to solve the question will be:
20x + 8y = 500
When x= 16 and y = 22, thus will be:
= 20x + 8y
= 20(16) + 8(22)
= 320 + 176
= 496
Therefore, since this is the number closest to $500, therefore this will be the appropriate number of movies that he can buy.
In conclusion, he'll buy 16 new releases and 22 classic movies.
Read related link on:
https://brainly.com/question/17742381
Answer:
x = 16, y = 22
Step-by-step explanation:
749,381 in standard form
Answers
Answer:
Standard form of 749381
=> 7.49381 x 10^5
Can someone help me
Answers
Hello! I can help you! I did not know what numbers you needed so I worked on problems 43- 46. For problems 43 and 44 you are going to be doing the same thing, but I can show you have to do both. So for number 43, y=-4x-2; (0,-1), you want to keep it parallel, so you are going to keep the slope ( -4) the same. You use point slope form which is y-y1=m(x-x1) and you plug it in. So I used the points that they gave at the top (0,-1) which means 0 is x and -1 is y so my new equation in point slope is y+1=-4(x-0). I did y+1 instead of y-1 because two negatives make a positive so the negative 1 makes the equation positive. After I wrote the equation, I solved it by distributing the -4 to the numbers in the parentheses (x-0). I got y+1=-4x and from there I just subtracted 1 on both sides so all that’s left is y=-4x-1 and that’s the answer for 43. You would do the same thing for number 44 but instead of getting the question in slope form you need to get there. You would just subtract 2x on both sides and get -y=-2x-4 and from there you divide a negative 1 on both sides so that y is positive ( y is always positive) and your equation will be y=2x+4 and then you do the same thing you did for question 43 with the point slope information. For the next to problems, 45 and 46, it going to be a little different but it’s not too difficult. Instead of just taking the slope and plugging it into the point slope equation you need to flip the reciprocal and make it negative. So for 45, 2/3 would turn into -3/2 and that is what you would plug into the equation. It would be y+2=-3/2(x+6) and you would solve and get y+2=-3/2x-9 from there you would subtract 2 on both sides and you would get y=-3/2-11. You would do the same for number 46, except in the beginning you need to subtract 4x from both sides to get y=4x-6 and the just flip the reciprocal and make it negative ( -1/4x). I hope that helped you understand! Good luck! :)
Answer:
all work is shown and pictured
increase £100 by 30%
Answers
Step-by-step explanation:
100+(100*30/100)
=100+30
=130
Answer:
=£130
Step-by-step explanation:
£100=100%
= 130% I add 30 to 100
130×100÷100=130
=£130
Please help me! -3a+6(1+6a)=4(8a+1)
Answers
Answer:
-3a + 6 + 36a = 32a + 4
a = - 2
Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents Gemma’s position with respect to sea level?
Answers
Answer:
-24 or B
Step-by-step explanation:
Because is she rises up 4, it is +4. Then subtract 28 from 4. That makes it -24.
The integer represents Gemma’s position with respect to sea level 24.
We have given that,
Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet.
What is the integer?An integer is colloquially defined as a number that can be written without a fractional component.
We have to determine which integer represents Gemma’s position with respect to sea level
Because if she rises up 4, it is +4.
Then subtract 28 from 4. That makes it -24.
To learn more about the integer visit:
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If an 8MB-mp3 music file player can store 3,780 songs. How many albums can a 16MB store if there are 12 songs on each album?
Answers
Answer:
Hey there!
8MB=3780 songs
16MB=3780(2), or 7560 songs.
If there are 12 songs per album, the 16MB music file can store 7560/12, or 630 albums.
Let me know if this helps :)
Find the least common multiple (LCM) of 7 and 12.
Answers
Answer:
84Step-by-step explanation:
Method 1 ; Prime factorization
[tex]7 ,12\\\mathrm{Prime\:factorization\:of\:}7:\quad 7\\\mathrm{Prime\:factorization\:of\:}12:\quad 2\cdot \:2\cdot \:3\\= 847\times\:2\times\:2\times\:3\\= 84[/tex]
Method 2 ;Multipliers
[tex]\mathrm{The\:multipliers\:of\:}7\\=7,\:14,\:21,\:28,\:35,\:42,\:49,\:56,\:63,\:70,\:77,\:84,\:91,\:98,\:105...\\\\\mathrm{The\:multipliers\:of\:}12\\=12,\:24,\:36,\:48,\:60,\:72,\:84,\:96,\:108,\:120,\:132,\:144,\:156,\:168,\:180...\\\\\mathrm{The\:smallest\:common\:number\:is} \\=84[/tex]
Method 3 ; Using GCD
[tex]lcm\left(a,\:b\right)=\frac{|a\cdot b|}{gcd\left(a,\:b\right)}\\\\\mathrm{Greatest\:Common\:Divisor\:of\:}7,\:12:\quad 1\\=\frac{\left|7\times\:12\right|}{1}\\\\= 84[/tex]
Solve the inequality $-4(x + 4) > x + 7.$ Give your answer as an interval.
Answers
Answer:
[tex](-\infty,-4.6)[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]-4(x+4)>x+7[/tex]
First, let's distribute the left:
[tex]-4x-16>x+7[/tex]
Now, let's add 16 to both sides:
[tex]-4x>x+23[/tex]
Subtract x from both sides:
[tex]-5x>23[/tex]
Divide both sides by -5. Since we're dividing by a negative, flip the sign:
[tex]x<-4.6[/tex]
This is saying all values less than -4.6.
In other words, in an interval, this would be from negative infinity all the way up to -4.6. Thus:
[tex](-\infty,-4.6)[/tex]
We do not use brackets because we do not include -4.6 into our set.
And we're done!
Can someone please help
Answers
Answer:
D can be used
Step-by-step explanation:
During summer, Bryan earns $8.75 an hour working as a lifeguard. He works 43 hours. What is the total amount of money Bryan will have on his paycheck?
Answers
Answer:
$8.75 X 43 equals $376.25
Step-by-step explanation:
find the real numbers x and y that make the equation true (x+6i)=(3-i)+(4-2yi)
Answers
Answer:
x = 7
y = -7/2
Step-by-step explanation:
(x+6i)=(3-i)+(4-2yi)
First look at the real parts
x = 3 +4
x = 7
Then look at the imaginary part
6i= -i -2yi
6 = -1-2y
Add 1 to each side
6+1 = -2y
7 = -2y
Divide by -2
7/-2 = y
Dylan is 15, which is 3 years older than twice his sister Savannah’s age. How old is savannah
Answers
Answer:
Savannah's age = 6 years
Step-by-step explanation:
Let
Savannah's age = x
Dylan's age = 15
Dylan is 15, which is 3 years older than twice his sister Savannah’s age
Dylan = 2x + 3
Find Savannah's age
2x + 3 = 15
Subtract 3 from both sides
2x + 3 - 3 = 15 - 3
2x = 12
Divide both sides by 2
2x / 2 = 12 / 2
x = 6
Therefore,
Savannah's age = x
= 6 years
Dylan's age = 2x +3
= 2*6 + 3
= 12 + 3
= 15 years
Two hikers are 22 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other
Answers
Answer:
The hikers A and B travel at rates of 1.1 miles per hour and 3.3 miles per hour, respectively.
Step-by-step explanation:
Let suppose that each hiker travels at constant speed, such that kinematic formulas are, respectively:
Hiker A
[tex]x_{A} = x_{A,o}+v_{A}\cdot t[/tex]
Hiker B
[tex]x_{B} = x_{B,o} +v_{B}\cdot t[/tex]
Relationship
[tex]v_{A} =- v_{B}-2.2\,mph[/tex] (They walk toward each other)
Where:
[tex]x_{A,o}[/tex], [tex]x_{A}[/tex] - Initial and final position of the hiker A, measured in miles.
[tex]x_{B,o}[/tex], [tex]x_{B}[/tex] - Initial and final position of the hiker B, measured in miles.
[tex]t[/tex] - Time, measured in hours.
[tex]v_{A}[/tex], [tex]v_{B}[/tex] - Velocities of hikers A and B, measured in miles per hour.
Given that [tex]x_{A,o} = 0\,mi[/tex], [tex]x_{B,o} = 22\,mi[/tex], [tex]x_{A} = x_{B}[/tex] and [tex]t = 5\,h[/tex], the system of equation is reduced to the following:
[tex]0\,mi -(v_{B}+2.2\,mph)\cdot (5\,h) = 22\,mi+v_{B}\cdot (5\,h)[/tex]
[tex]-5\cdot v_{B}-11 = 22+5\cdot v_{B}[/tex]
[tex]10\cdot v_{B} = -33[/tex]
[tex]v_{B} = -3.3\,mph[/tex]
Now, the velocity of the hiker A is:
[tex]v_{A} = - (-3.3\,mph)-2.2\,mph[/tex]
[tex]v_{A} = 1.1\,mph[/tex]
The hikers A and B travel at rates of 1.1 miles per hour and 3.3 miles per hour, respectively.
Help please !!!!!!!!!!!!
Answers
Answer:
You would need to Quadruple the length.
Step-by-step explanation:
In this picture, the scaled drawing's perimeter is equal to 12. So if you quadruple the length, the actual perimeter would be 48.
You have a bag with 30 fireballs and another bag with 42 jolly ranchers. For a party, you want to repackage the candy into smaller bags, and you want each bag to have the same number of fireballs and jolly ranchers and. How many bags will you be able to make?
Answers
Answer: 6 bags 5 fire balls and 7 jolly ranchers in one bad
Step-by-step explanation:Ok so you got 30 fire balls 42 ranchers what you can do is see like wow more ranchers in a bag we know that hmm 42/6 is ya know 7 and that 6 does it go into 30 yeah it does 30/6=5 so you got 5 fire balls and 7 jolly ranchers is each bag with 6 bags
Answer:
6 bags
Step-by-step explanation:
The GCF of 30 and 42 is 6.
30/6 = 5
42/6 = 7
To use all candy, put 5 fireballs and 7 jolly ranchers in each bag. You will make 6 bags.
Simplify 4a – 7b + 2ab – a + b.
Answers
Answer:
3a-6b+2ab
Step-by-step explanation:
I need help solving this!!
Answers
Answer:
addition
Step-by-step explanation:
32(d/2 - 5) = 224
divide both side by 32
d/2 - 5 = 224/32
d/4 - 5 = 7
multiply both sides by 4
d - 20 = 28
lastly, add 20 to both sides
d = 28 + 20
d = 48
therefore, the last step is addition
how can you reflect a point over the y axis without graphing it?
Answers
Answer: You switch the point in the x-axis to the negative/positive of the number.
Step-by-step explanation:
So for example if you have the point (3,7), you would switch the 3 to -3 and you would keep the y the same.
Hope this helps!
PLEASE HELP :((
Which inequality is represented by the graph?
Answers
Answer:
y < 5/3x -3
Step-by-step explanation:
Used Desmos graphing calculator :)
6x + y = 4x + 11y
Write a formula for h(x) in terms of x.
h(x)=
Answers
Answer:
h(x) = 10y/2
Step-by-step explanation:
6x + y = 4x + 11y
6x - 4x = 11y - y
2x = 10y
divide both side by 2
x = 10y/2
h(x) = 10y/2
If AB = 4x +10, BC = 2x +3 and AC= 9x - 15 find AC. and show work plzz !!!!
Answers
Answer:
Step-by-step explanation:
AB + BC = AC
4x + 10 + 2x + 3 = 9x - 15
6x + 13 = 9x - 15
6x + 13 + 15 = 9x
6x + 28 = 9x
3x = 28
x = 9 1/3 = 28/3
AC = 9 * 28/3 - 15
AC = 3 * 28 - 15
AC = 84 - 15
AC = 69
A lunch bill is 12 before tax. If the tax on the bill is 7.5 what is the total cost of the lunch including tax
Answers
Answer:
$12.90
Step-by-step explanation:
Before Tax Price: $12.00
Sale Tax: 7.50% or $0.90
After Tax Price: $12.90
A fencing compony charges $22 per foot to install
a wood fence. How much will it cost to install a
wood fence around a rectangular pool area that is
20 feet wide and 38 feet long?
Answers
I need help ASAP please !!!
Answers
Answer:
Step-by-step explanation:
6x + 19 + x = 180
7x + 19 = 180
7x = 161
x = 23°
6(23) + 19= 138 + 19 = 157°
I hope this helps
Which set of equivalent fractions can be used when adding 7/8 and 5/12 ?
Answers
Answer: 84/96 and 40/96
Step-by-step explanation: You find a denominator that they both have in common. The LCM is 96 and you get the answer! You multiply 1 side by 8 and the other by 12 and you get the answer!
tell the absolute value of:
Answers
The absolute value of any number is that number as a positive one.
Absolute value of -1/2 is 1/2
( 100 POINTS FOR EVERYTHING )
[ Integers ]
You know what to do, there are 2 images and make sure to answer every single one. I know 1 person who knows this topic very well.
Answers
Answer:
3. x+8
4. 6y
5. 1/2m
6. 50/h
7. 7-n
8. 15+x
9. 2t/12
10. p² -3
11. 2k-7
12. 3(w+5)
13. C
14. The error was it was written that you would subtract the pages read by pages in the article which is incorrect. You would subtract pages total (5) by pages read (p). So it is 5-p.
15. 4v
16. 16/p
17. 2.97/p
18. 20+j
19. 7-d
20. m/60
21. y/12
22. unit rate-8
23. unit rate-1.5
24. unit rate-2.4
25. unit rate-6.8
26. C
The first drop down: (x-12),(x-80), (80-x), (12-x)
Second drop down: 12(80-x)=816,12(x-80)=816,80(12-x)=816,80(x-12)=816
Answers
Answer:x=12 and 68$
Step-by-step explanation: