Find the exact value of sin(x + y), given sin(x) = -1/2 , cos(y) = -1/3, x is an angle in quadrant III, and y is an angle in quadrant II.
StartFraction 2 minus StartRoot 5 EndRoot Over 6 EndFraction
StartFraction 1 minus 2 StartRoot 6 EndRoot Over 6 EndFraction
StartFraction 6 minus StartRoot 5 EndRoot Over 6 EndFraction
StartFraction StartRoot 3 EndRoot minus StartRoot 5 EndRoot Over 6 EndFraction
Given:
[tex]\sin (x)=-\dfrac{1}{2}[/tex]
[tex]\cos (y)=-\dfrac{1}{3}[/tex]
x is an angle in quadrant III, and y is an angle in quadrant II.
To find:
The value of sin(x+y).
Solution:
We know that, only sin and cosec are positive in II quadrant. Only tan and cot are positive in III quadrant.
x is an angle in quadrant III,
[tex]\cos x=-\sqrt{1-\sin^2 x}[/tex]
[tex]\cos x=-\sqrt{1-(-\dfrac{1}{2})^2}[/tex]
[tex]\cos x=-\sqrt{1-\dfrac{1}{4}}[/tex]
[tex]\cos x=-\sqrt{\dfrac{4-1}{4}}[/tex]
[tex]\cos x=-\dfrac{\sqrt{3}}{2}[/tex]
y is an angle in quadrant II.
[tex]\sin y=\sqrt{1-\cos^2x}[/tex]
[tex]\sin y=\sqrt{1-(-\dfrac{1}{3})^2}[/tex]
[tex]\sin y=\sqrt{1-\dfrac{1}{9}}[/tex]
[tex]\sin y=\sqrt{\dfrac{9-1}{9}}[/tex]
[tex]\sin y=\sqrt{\dfrac{8}{9}}[/tex]
[tex]\sin y=\dfrac{2\sqrt{2}}{3}[/tex]
Now,
[tex]\sin(x+y)=\sin x\cos y+\cos x\sin y[/tex]
[tex]\sin(x+y)=(-\dfrac{1}{2})\times (-\dfrac{1}{3})+(-\dfrac{\sqrt{3}}{2})\times (\dfrac{2\sqrt{2}}{3})[/tex]
[tex]\sin(x+y)=\dfrac{1}{6}-\dfrac{2\sqrt{6}}{6}[/tex]
[tex]\sin(x+y)=\dfrac{1-2\sqrt{6}}{6}[/tex]
Therefore, the correct option is B.
Answer:
Choice B
Step-by-step explanation:
what is the rate of change of y with respect to x for this function
Answer:
8
one fourth
2
4
Step-by-step explanation:
hope with helped ^^
x⁴+1 by x+1 ( Long division of polynomials).Please if anyone knows the answer of this question please let mr know.....if you want points and waste my time your answer will be reported...
[tex] {x}^{3} - {x}^{2} + x - 1 + \frac{2}{x + 1} [/tex]
lmk if u want an explanation for this I can try type it out
Answer:
[tex]x^3-x^2+x-1+\frac{2}{x+1}[/tex]
Step-by-step explanation:
See the picture attached.
Notice how I set up [tex]x^4+1[/tex] as [tex]x^4+0x^3+0x^2+0x+1[/tex], as it makes it easier to solve.
Also, notice that the 2 as the remainder doesn't have anything else to divide to, so that means there will be an extra term [tex]\frac{2}{x+1}[/tex] in the end of the answer.
f(x) = 2x + 3
g(x) = x
(a) Find fg(6).
(b) Solve the equation gf(x) = 100.
Answer:
a) 15
b) 97/2
Step-by-step explanation:
a) f(g(6))
g(6) = 6
2(6)+3
12 + 3
15
b) gf(x) = 10
2x+3
2x+3 = 100
2x = 97
x = 97/2
The graph of the function y=tan(x) was horizontally stretched so that its period became 10pi Which is the equation of the transformed function?
Answer:
A is the answer
Step-by-step explanation: Edge 2020
What is m / 5 - 2 = 8
Answer:
m=24
Step-by-step explanation:
First, we can combine like terms:
m/(5-2)=8
m/3=8
Now, we need to get m by itself. To do this, multiply by 3:
m/3*3=8*3
m=24
50
50 ÷ 5 = 10, 10-2 =8
kdjrjrjdjjfhrhy to truth thhrjrhejd
I NEED HELP PLEASEEEE HABSJQBSKQSBQISBWKEJKQDJIQSB :(
Answer:
5
Step-by-step explanation:
within the brackets do the parentheses (14-12)=2
according to PEMDAS, multiply first 2x3 to get 6
then add 3
you end up with 9 in the brackets so now all that’s left is 45/9 which is 5
I need to know the answer to part b please
Answer:
Part B is Both batches have 2 more quarts of pineapple juice than sparkling water. The ratio of quarts of pineapple juice to quarts of fruity drink for the first batch is 3 to 5 or 3:5 or 3/5. The ratio for the second batch is 5 to 8 or 5:8 or 5/8. The second batch has a greater ratio of quarts of pineapple juice to quarts of fruity drink.
Solve the quadratic equation by completing the square. X^2+14x+38=0
Can you explain the steps too so I can understand it better. Also if there are more than one solution can you add all of the solutions. Thank you!
Answer:
[tex] \rm x = - 7 \pm \sqrt{11} [/tex]
Step-by-step explanation:
Solve for x over the real numbers:
[tex] \longrightarrow [/tex] x² + 14x + 38 = 0
Subtract 38 from both sides:
[tex] \longrightarrow [/tex] x² + 14x + 38 - 38 = 0 - 38
[tex] \longrightarrow [/tex] x² + 14x = -38
Add 49 to both sides:
[tex] \longrightarrow [/tex] x² + 14x + 49 = 49 - 38
[tex] \longrightarrow [/tex] x² + 14x + 49 = 11
Write the left hand side as a square:
[tex] \longrightarrow [/tex] x² + 7x + 7x + 49 = 11
[tex] \longrightarrow [/tex] x(x + 7) + 7(x + 7) = 11
[tex] \longrightarrow [/tex] (x + 7)(x + 7) = 11
[tex] \longrightarrow [/tex] (x + 7)² = 11
Take the square root of both sides:
[tex] \longrightarrow [/tex] [tex] \sf \sqrt{{(x + 7)}^{2}} = \pm \sqrt{11} [/tex]
[tex] \longrightarrow [/tex] [tex] \sf x + 7 = \pm \sqrt{11} [/tex]
Subtract 7 from both sides:
[tex] \longrightarrow [/tex] [tex] \sf x = - 7 \pm \sqrt{11} [/tex]
Identify the slope and the y-intercept of the following: g(x)=-3/2x + 4
Answer:
x = 6
Step-by-step explanation:
In a survey of 3000 people who owned a certain type of car, 2100 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
70%Step-by-step explanation:
Step one:
given data
we are told that the number of people under the survey is 3000
and also that 2100 people would like to buy again, these 2100 people represent the number of people who are satisfied with the type of car.
Step two:
Therefore the percentage of this number related to the total people under the survey is given below
=2100/3000*100
=21//30*100
=7/10*100
=7*10
=70%
Hence 70% of the people surveyed are satisfied with the type of car
Anyone need help on math:(?
Answer:no hbu cutie?
Step-by-step explanation:
I do lol- can u help me
3.4–2.8d+2.8d-1.3=?
Someone please help me
Mary has sold 90 boxes of cookies. If her goal was to sell 120 boxes, what percentage of her goal has she sold?
the percentage is 75%
because 90 divided by 120 is 0.75.
If a pair of standard dice are rolled,
what is the probability that the sum
will be greater than 7?
[ ?
Answer:
P(Pair of dice greater than 7) = 5/12
Step-by-step explanation:
When rolling a pair of dice, there are 36 combinations for the rolls.
(1,1), (1,2), (1,3), .... (2,1), (2,2), .... (6,1), ... (6,6)
Of those, there are 15 where the total is greater than 7.
15/36 = 5/12
#1 #2 Sum > 7
1 1 2 FALSE
1 2 3 FALSE
1 3 4 FALSE
1 4 5 FALSE
1 5 6 FALSE
1 6 7 FALSE
2 1 3 FALSE
2 2 4 FALSE
2 3 5 FALSE
2 4 6 FALSE
2 5 7 FALSE
2 6 8 TRUE
3 1 4 FALSE
3 2 5 FALSE
3 3 6 FALSE
3 4 7 FALSE
3 5 8 TRUE
3 6 9 TRUE
4 1 5 FALSE
4 2 6 FALSE
4 3 7 FALSE
4 4 8 TRUE
4 5 9 TRUE
4 6 10 TRUE
5 1 6 FALSE
5 2 7 FALSE
5 3 8 TRUE
5 4 9 TRUE
5 5 10 TRUE
5 6 11 TRUE
6 1 7 FALSE
6 2 8 TRUE
6 3 9 TRUE
6 4 10 TRUE
6 5 11 TRUE
6 6 12 TRUE
Answer:
5/12
Step-by-step explanation:
I can’t really explain it. I did the same problew though.
find the area k of triangle ABC WHEN A =19.2 b= 2.05 and c=9.12
Step-by-step explanation:
Area of a triangle= 1/2breadth × height
Algebra Find the values of x and y.
5.
olgaus 1986.
115°
х”
081 91129 rast
Answer:
hey look up it up it's better
Step-by-step explanation:
Solve for x.
4x - 8 = -3(2x + 6)
Answer:
x= -1
Step-by-step explanation:
First, distribute the -3 through the parentheses
4x-8= -3(2x+6)
= 4x-8= -6x-18
Second, move the variable to the left-hand side and change its sign
4x+6x= -18+8
10x= -10
Divide both sides by 10
x=-1
Answer:
x=-7
Step-by-step explanation:
first u wanna multiply (2x+6) which equals 12 the what u wanna do is move the constant to the right which is 4x-8=-36. Then calculate 4x=-36+8. then after that then u should end up with 4x=-28 then u divide it then u end up with ×=-7
What is the equation of the line shown in this graph?
Answer:
y=0x+1
Step-by-step explanation:
Hope this helps!(^-^)
Answer: either -4,1 (+) 6 or 2,1 (-) 6
Step-by-step explanation:
The dress store is having a sale where all merchandise is 1/4 off. A woman buys $50 of merchandise at the sale price. What would she have to pay at the regular price?
ANSWER PLZZ!!
Answer:
200
Step-by-step explanation:
1/4 would be 25 percent and 50 times 4 would be 200
A jacket regularly costs $65.How much would the jacket cost if it was on sale with a 20% discount
Answer:
Suppose you earned extra money by having a part-time job. You open up a bank account in order to save your money. Your body acts similar to a bank account—you can “deposit” and “store” energy.
\
Step-by-step explanation:
In FGH, K is the midpoint of GH. What type of segment is FK?
median?
altitude?
angle bisector?
perpendicular bisector?
Answer:
Median
Step-by-step explanation:
In FGH, K is the midpoint of GH.
Therefore, FK is the median segment.
2x (3x + 5)
=6x^2+20x
Answer:
Are you 1 grade or what......
Answer:
6x^2 + 10x
Step-by-step explanation:
2x(3x + 5) = 2x * 3x + 2x * 5
= 6x^2 + 10x
Point T, the midpoint of segment RS, can be found using the formulas x = (6 – 2) + 2 and y = (4 – 6) + 6. What are the coordinates of point T? T(3, 2) T(3, 4) T(4, 5) T(4, 7)
Question:
Point T, the midpoint of segment RS, can be found using the formulas x = (1/2) (6 – 2) + 2 and y = (1/2) (4 – 6) + 6. What are the coordinates of point T?
Answer:
[tex]T(4,5)[/tex]
Step-by-step explanation:
Given
[tex]x = \frac{1}{2}(6 - 2) + 2[/tex]
[tex]y = \frac{1}{2}(4 - 6) + 6[/tex]
Required
Determine the coordinates of T
The coordinates of T can be represented as [tex]T(x,y)[/tex]
To do this, we simply solve for x and y
[tex]x = \frac{1}{2}(6 - 2) + 2[/tex]
Solve 6 - 2
[tex]x = \frac{1}{2}*4 + 2[/tex]
Solve 1/2 * 4
[tex]x = 2 + 2[/tex]
[tex]x = 4[/tex]
[tex]y = \frac{1}{2}(4 - 6) + 6[/tex]
Solve 4 - 6
[tex]y = \frac{1}{2}*-2 + 6[/tex]
Solve 1/2 * -2
[tex]y = -1 + 6[/tex]
[tex]y = 5[/tex]
Hence, the coordinates of T(x,y) is:
[tex]T(x,y) = T(4,5)[/tex]
Answer:
C
Step-by-step explanation:
(help) During a snowstorm the temperature drops from 0 F to - 7 in 7 hours on average by how many degrees is the temperature changing per hour
Answer:-1
Step-by-step explanation:
I got it wrong and it said that that is the right answer
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Answer: The Answer is 64
Step-by-step explanation: there isnt much really to it
Answer:
The answer is 64
Step-by-step explanation:
If you need me to explain my answer let me know.
A coin is flipped and a normal dice is rolled. How many possible outcomes are there? What is the probability of getting no heads? What is the probability of getting at least two tails?
Answer:
Below.
Step-by-step explanation:
(a) There 8 possible outcomes.
HHH TTT HHT HTH THH TTH THT HTT
(b) Prob(No Heads)
= Prob(TTT)
= 1/8.
(c) Possible outcomes of at least 2 tails are:
TTT, TTH THT HTT = 4
So Probability of this is 4/8 = 1/2.
12. Find the value of x.
(10x - 11)
(7x + 4)
Answer:
Step-by-step explanation:
7x+4=10x-11
4=3x-11
15=3x
x=5
(GIVING BRAINLIEST) Which expression uses the associative property to make it easier to evaluate
Answer:
Its D.
Step-by-step explanation:
Give him brainliest he deserves it
hi can someone answer these 3 questions for me?? thank you :)
Answer:
1) 1[tex]\frac{1}{8}[/tex]
2) 2[tex]\frac{5}{7}[/tex]
3) 1[tex]\frac{8}{9}[/tex]
Step-by-step explanation:
Step-by-step explanation:
4 7/8 + __ = 6
__ = 6 - 4 7/8
__ = 1 1/8
3 2/7 + __ = 6
__ = 6 - 3 2/7
__ = 2 5/7
3 1/9 + __ = 5
__ = 5 - 3 1/9
__ = 1 8/9
Topic: Fractions
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