Answers
Step-by-step explanation:
[tex]\sin(\theta + \phi) = 2\cos(\theta - \phi)[/tex]
Using the addition identity formulas, we can write
[tex]\sin{\theta}\cos{\phi} + \cos{\theta}\sin{\phi} = 2\cos{\theta}\cos{\phi} + 2\sin{\theta}\sin{\phi}[/tex]
Dividing both sides by [tex]\cos{\phi}[/tex], we get
[tex]\sin{\theta} + \cos{\theta}\tan{\phi} = 2\cos{\theta} + 2\sin{\theta}\tan{\phi}[/tex]
Dividing both sides by [tex]\sin{\theta}[/tex], we get
[tex]\tan{\theta} + \tan{\phi} = 2 + 2\tan{\theta}\tan{\phi}[/tex]
or
[tex]\tan{\theta}(1 - 2\tan{\phi}) = 2 - \tan{\phi}[/tex]
Rearranging the terms,
[tex]\tan{\theta} = \dfrac{2 - \tan{\phi}}{1 - 2\tan{\phi}}[/tex]
Related Questions
Two trains leave towns 1285 kilometers apart at the same time and traveled towards each other. One train travels 17 km/h faster than the other. If they meet in 5 hours what is the rate of each train
Answers
Distance = (Rate)(Time)
Let x = speed of slower train
x + 17 = speed of faster train
The trains meet when the sum of the distances = 1285
5x + 5(x+17) = 1285
(5 came from 5 hours)
10x + 85 = 1285
10x = 1200
x = 120 mph
The speeds are 120 mph and 137 mph
wyzant
A teacher wants to find out the average number of weekly reading hours of her students. She noted the number of reading hours of 5 of her students as shown below:
6, 2, 5, 3, 4
Which measure of central tendency is most appropriate for this situation, and what is its value?
Only the median; 5
Only the mean; 4
Either the mean or median; both are 5
Either the mean or median; both are 4
Answers
helpppppppppppppopnanannsnsnnsnakaknfnsn
Answers
Step-by-step explanation:
y=107(vertically opposite angles)
x=180-107=73(angles on a straight line)
z=73(vertically opposite angles)
Answer:
[tex]{ \sf{y = 107 \degree}} \: \{ \sf{alternate \: angles} \}[/tex]
[tex]{ \sf{z + 107 \degree = 180 \degree}} \: \{ \sf{straight \: line \: angles \}} \\ z = 180\degree - 107\degree \\ z = 73\degree[/tex]
[tex]{ \sf{x = z}} \: \{ \sf{alternate \: angle \}} \\ x = 73\degree[/tex]
x=-9 y=-8 evaluate the expression 8 x^2 - 6 y^2
Answers
Answer:
264Step-by-step explanation:
Let x= -9 y= -88x² - 6y² = ?8(-9)² - 6(-8)² = ?8(81) - 6(64) = ?648 - 384 = ?264[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
What is the equation of the line in Ax + By = C form that passes through the points (1, -3) and (-5, 9)
Answers
Answer:
-2x-y=1
Step-by-step explanation:
steps are in the picture above.
Note:if you need to ask any question please let me know.
two numbers are at ratio of 5:9 find the larger number if the smaller number 35
Answers
9514 1404 393
Answer:
63
Step-by-step explanation:
We observe that multiply the smaller number in the ratio by 7 we get 35. Then the ratio is ...
5 : 9 = 35 : 63 . . . . . . multiply both numbers by 7
The larger number is 63.
A submarine is 1000 feet below sea level and then rises 450 feet. Where is the submarine now?
Answers
Sea level is 0
1000 feet below sea level would be -1000. It rises 450 feet. Add 450 to -1000:
-1000 + 450 = -550
The submarine is at -550 feet ( 550 feet below sea level).
khloe’s parents allow her to watch 8 1/2 hours of tv a week. so far this week she has watched 4 1/2 hours. how many hours does she have left?
Answers
Answer:
4
Step-by-step explanation:
8 1/2- 4 1/2 is 4
simplify the equation 5+4(8-6)^2
Answers
Answer:
21
Step-by-step explanation:
5+4(8-6)^2
5 + 4 (2)^2
5 + 4 (4)
5 + 16
21
Answer:
21
5+4(8-6)^2
5 + 4 (2)^2
5 + 4 (4)
5 + 16
=21
Hope this helps <3
Hi guys plz plz plz thank my answer to this question and i am really trying to win this brainliy competition. i have to get at the min 15 to catch up! plz help and thank and 5 star it but anyway have a great day and stay safe!
https://brainly.com/question/24385647
solve 4(x-3) -2(x+1) =2
Answers
Answer:
8
Step-by-step explanation:
4(x-3) -2(x+1) =2
=> 4x - 12 - 2x - 2 = 2 [opening brackets]
=> 4x - 2x - 12 - 2 = 2
=> 2x - 14 = 2
=> 2x = 14 + 2
=> 2x = 16
=> x = 16/2
=> x = 8
4 ( x - 3 ) - 2 ( x + 1 ) = 2
2 ( x - 3 ) - ( x + 1 ) = 1
2x - 6 - x -1 = 1
2x - x = 1 + 6 + 1
x = 1 + 6 + 1
x = 7 + 1
x = 8
if M ABD =75 and M abc =40 then m CBD =
Answers
m∠CBD = 35
Step-by-step explanation:
m∠ABD = 75 which is the total * among all angle measures
m∠ABC = 40 (given angle)
m∠CBD = ?
To find m∠CBD, subtract the total - the given angle
m∠CBD = m∠ABD - m∠ABC
m∠CBD = 75 - 40
m∠CBD = 35
What is the difference between opposites and integer
Answers
Answer:
An integer is any positive whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa
Step-by-step explanation:
-5 and 5 are an example.
Solve the inequality for t. 12 >t+3 Simplify your answer as much as possible
Answers
Answer:
t < 9
Step-by-step explanation:
12 > t + 3
We can subtract 3 from both sides getting us 9 > t.
2. The product of 7 and a number
Answers
I think the answer you are looking for is 7n, which also means 7 times n.
Answer:
7x
Step-by-step explanation:
Product refers to multiplication. "A number" refers to an unknown number otherwise known as a variable. In this case, I use x.
P- 24000 R-10% T-2 years find the sum
Answers
Answer:
here
I =p×t×r/100
= 24000×2×10/100
= 4800
again,
sum = p+I
= 24000+4800
= 28800
Solve the equation 12v+10v+14=80
Answers
Answer:V=3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
12v+10v+14=80
(12v+10v)+(14)=80
(Combine Like Terms)
22v+14=80
22v+14=80
Step 2: Subtract 14 from both sides.
22v+14−14=80−14
22v=66
Step 3: Divide both sides by 22.
22v/22=66/22
V=3
:)
round 6.7 to the nearest whole number.
Answers
5,6,7,8,9 rounds up
6.7 >>.7 rounds up
6.7 >> 7
Write an equation in slope-intercept form of the line passing through (0, 3) and (2, -1).
y=2x+3y=2x+3
y=-2x+3y=−2x+3
y=-2xy=−2x
y=-x+3y=−x+3
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]y = -2x + 3[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Slope-Intercept Form Is:}}\\\\y=mx + b\\---------------\\\boxed{\text{Key:}}\\\\m - slope\\b - y-intercept\\---------------\\\boxed{\text{\underline{Known Information:}}}\\\\\rightarrow \text{We are given the points: } (0,3) \text{ and } (2, -1)\\---------------\\\boxed[/tex]
[tex]\boxed{\text{\underline{Y-Intercept:}}}\\\\\rightarrow \text{Since the line passes at point (0, 3), the y-intercept would be 3.}\\---------------\\\boxed{\text{\underline{Slope:}}}\\\\\rightarrow m =\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1} \\\\\rightarrow m = \frac{-1-3}{2-0}=\frac{-4}{2}=\boxed{-2}\\\\\text{The slope is: } \boxed{-2}\\---------------[/tex]
[tex]\boxed{\text{\underline{Equation:}}}\\\\\text{Our equation should be:}\\\\y = -2x + 3[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Enter the degree of the polynomial below:
9x2 + 3x8 + 6x + 586 -7x5
Answers
[tex] \large \mathfrak{Answer : }[/tex]
The degree of a polynomial is the highest power among its terms .
i.e 8 for the above expression :
9x² + 3x⁸ + 6x + 586 - 7x⁵
(-8\9×1\-5)+(-8\9×-7\11)= -8\9×(1\-5×-7\11)
Answers
[tex]( \frac{ - 8}{9} \times \frac{1}{ - 5} ) + (\frac{ - 8}{9} \times \frac{ - 7}{11} ) = \frac{ - 8}{9} \times ( \frac{1}{ - 5 } \times \frac{ - 7}{11} )[/tex]
[tex] \frac{ - 8}{9} = 0[/tex]
all like terms to be cancel = -0.888888please mark this answer as brainlist
Sum is -4
We should make a question to get this integer answer
please
Answers
Answer:
{4,8,3,7,2,6,1,5,9}
Step-by-step explanation:
this is the multiple of 4
and the sum of -4 is -4 + -4 = 8
8x – 3 = 11 + 6x
What is x
Answers
Answer:
x = 7
Step-by-step explanation:
[tex]8x-3=11+6x\\\\2x-3=11\\\\2x=14\\\\x=7[/tex]
Answer:
x = 7
Step-by-step explanation:
8x - 3 = 11 + 6x
8x - 3 + 3 = 11 + 6x +3
8x = 6x + 14
8x - 6x = 6x + 14 - 6x
2x = 14
2x/2 = 14/2
x = 7
Round to the nearest thousandth.
-49.5176
Answers
Answer:
-49.518
This should suffice.
1. Write the following numbers in words:
(a) 74 325 (b) 43 711 (c) 19 560
(e) 67 459
(1) 25 302
(g) 36 721
(1) 62 897 () 37 264 (k) 45 129
(d) 75 434
(h) 78 065
(1) 43 275
numerals
Answers
(B) 43,711 forty-three thousand seven hundred eleven
(C) 19,560 nineteen thousand five hundred sixty
(E) 67,459 sixty-seven thousand four hundred fifty-nine
(1) 25302 = twenty-five thousand three hundred two
(G) 36,721 thirty-six thousand seven hundred twenty-one
(1) 62,897 = sixty-two thousand eight hundred ninety-seven
() 37, 264 = thirty-seven thousand two hundred sixty-four
(K) 45,129 forty-five thousand one hundred twenty-nine
(D) 75,434 seventy-five thousand four hundred thirty-four
(H) seventy-eight thousand sixty-five
(1) 43, 275 = forty-three thousand two hundred seventy-five
The quotient c and -19 is 38
Answers
Answer:
c = 722
Step-by-step explanation:
-19/c = 38
c = 38 x 19 (positive)
c = 722
hope it helped !
99. Savings Bronwyn wants to buy a house, so she has decided
to save one quarter of her salary. Bronwyn earns $47.00 per hour
and receives an extra $28.00 a week because she declined
company benefits. She wants to save at least $550.00 each week.
How many hours must she work each week to achieve her goal?
Answers
Answer:
46.5 hours per week
Step-by-step explanation:
At least 550 a week.
Which is 1\4 of Bronwyn salary.
550 x 4 = 2200
To find minimum work hours
2200-28 = 2172
2172 \ 47 = 46.212 hours per week
So, bronwyn needs to work at least 46.5 hours per week
Answer:
Bronwyn must work nearly 47 hours each week to achieve her goal.
Step-by-step explanation:
Let x be the number of hours Bronwyn works per week.
If Bronwyn earns $47 per hour, if x is the number of hours she works per week and if Bronwyn earns $28 per week because she declined company benefits, lets assume that the left hand side of the equation is:
[tex]47x + 28[/tex]
Now onto the salary. Since Bronwyn wants to save $550 each week and since she also wants to save one quarter of her salary, her salary becomes $2200 for each week she works
Making the equation...
[tex]47x + 28 = 2200[/tex]
Time to solve for x
[tex]47x = -28 + 2200\\47x = 2172\\x = 46.2[/tex]
Since its at least, you can round it up to 47 making 47 the number of hours she must work each week to achieve her goal.
Ruben needs to read 4 novels each month let N be the number of novels Ruben needs to read in M months write an equation relating in to M
Answers
Answer:
Step-by-step explanation:
N = 4(12) = 48 novels
Write the number in standard form.
ninety-two billion, seventy thousand,
one hundred eight
Answers
92.000.070.108
Step-by-step explanation:
Thousand has 3 zeros, a million has 6 and a billion has 9.
So for ninety-two billion, you take 92 and add 9 zeros behind it because a billion has 9 zeros
(92.000.000.000)
Mercury has a freezing point of -38°F.
Water has a freezing point of 32°F. What is
the difference?
Answers
The difference between the freezing point of water and mercury is 70°F.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that mercury has a freezing point of -38°F and water has a freezing point of 32°F.
The difference between the freezing point of water and mercury is calculated below
Difference = freezing point of water - freezing point of mercury
Difference = 32 - ( -38)
Difference = 70°F
Therefore, the difference between the freezing point of water and mercury is 70°F.
To know more about an expression follow
https://brainly.com/question/1563087
#SPJ5
What is 10 by the power of 8
Answers
Answer:
100000000
Step-by-step explanation:
10^1=10
10^2=100
10^3=1000
10^4=10000
10^5=100000
10^6=1000000
10^7=10000000
10^8=100000000