Both a and b lie in the second quadrant, which means
π/2 < a < π
π/2 < b < π
for which we have both cos(a) and cos(b) negative, while both sin(a) and sin(b) are positive. We're also given that
cos(a) = -2/3
csc(b) = 2 => sin(b) = 1/2
Now, recall the following identities:
• sin^2(x) + cos^2(x) = 1
• sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
• cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
• tan(x) = sin(x)/cos(x)
Now,
sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
… = √(1 - cos^2(a)) (-√(1 - sin^2(b))) + cos(a) sin(b)
* * where we take the negative square root because we expect cos(b) < 0 * *
… = - √(1 - (-2/3)^2) √(1 - (1/2)^2) + (-2/3) (1/2)
… = - √(1 - 4/9) √(1 - 1/4) - (2/3) (1/2)
… = - √(5/9) √(3/4) - 1/3
… = - (√5/3) (√3/2) - 1/3
… = -√15/6 - 1/3
… = -(√15 + 2) / 6
From the above, we know sin(a) = √5/3 and cos(b) = -√3/2. Then
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
… = (-2/3) (-√3/2) - (√5/3) (1/2)
… = √3/3 - √5/6
… = (2√3 - √5) / 6
and so it follows that
tan(a + b) = sin(a + b) / cos(a + b)
… = (-(√15 + 2) / 6) / ((2√3 - √5) / 6)
… = - (√15 + 2) / (2√3 - √5)
… = - (√15 + 2) (2√3 + √5) / ((2√3 - √5) (2√3 + √5))
… = - (2√45 + 4√3 + √75 + 2√5) / (12 - 5)
… = - (6√5 + 4√3 + 5√3 + 2√5) / 7
… = - (8√5 + 9√3) / 7
please help, no links
Answer:
150
Step-by-step explanation:
Remark
The exterior angle = the sum of the two given interior angles. The first job is to solve for x and then use that to find the exterior angle.
Equation
83 + 6x + 7 = 15x
Solution
Combine like terms
90 + 6x = 15x Subtract 6x from both sides.
6x 6x
90 = 9x Divide both sides by 9
90/9 = 9x/9
x = 10
Now the exterior angle = 15x
Exterior angle = 15*10
Exterior angle = 150
I think it’s 393.75 But not Sure can anyone confirm ? Or share the right answer
Answer:
$415.63
Step-by-step explanation:
it would have been 393.75, but he worked 5 hours overtime and got paid time and a half for it, meaning his normal pay plus half of it. (only for overtime tho).
so first calculate his normal pay:
40 × 8.75 = 350
then add overtime to it
8.75 × 5 = 43.75
43.75 × 1.5 = 65.625
65.625 + 350 = 415.625
round that and its 415.63!
This is worth my grade plz help 20pt
Answer:
C
Step-by-step explanation:
According to Math.way C would be the correct answer :)
question number nine answer
Answer:9
Step-by-step explanation:
Answer:
I think it's either A or D
Hey luvs!
The endpoints of AB are A(1,4) and B(5,-1). What are the coordinates of the point that divides AB in the ratio
2:3?
Answer:
I don't know I'm sorry.............
Solve for x.
x + 2 over 4 = 8
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x +2}{4}=8}[/tex]
[tex]\large\textsf{MULTIPLY 4 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{x +2}{4}\times4=8\times4}[/tex]
[tex]\large\textsf{CANCEL out: 4}\times\large\textsf{4.}[/tex]
[tex]\large\textsf{KEEP: 8}\times\large\textsf{4 because it helps you solve for x}[/tex]
[tex]\mathsf{8\times4=\bf 32}[/tex]
[tex]\large\text{New equation: \textsf{x + 32 = \bf 32}}[/tex]
[tex]\large\textsf{x + 2 = 32}[/tex]
[tex]\large\textsf{SUBTRACT 2 to BOTH SIDES}[/tex]
[tex]\mathsf{x +2-2=32-2}[/tex]
[tex]\large\textsf{CANCEL out: 2}-\large\textsf{2 because that gives you 0}[/tex]
[tex]\large\textsf{KEEP: 32}-\large\textsf{2 because that helps you solve for x}[/tex]
[tex]\large\textsf{New EQUATION: \mathsf{x = 32 - 2}}[/tex]
[tex]\mathsf{x = 32 - 2}[/tex]
[tex]\large\textsf{Simplify above and you have your result to this equation}[/tex]
[tex]\mathsf{32-2=\bf 30}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x =30}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What positive integer is closest to the value of the square root of 230 ?
9514 1404 393
Answer:
15
Step-by-step explanation:
Your calculator can tell you √230 ≈ 15.17. The closest integer is 15.
__
If you have memorized the squares of small integers, you know that 15² = 225 and 16² = 256. 230 is closer to 225 than to 256, so √230 will be closer to 15.
Matthew has a bag that contains orange chews, cherry chews, and lime chews. He
performs an experiment. Matthew randomly removes a chew from the bag, records
the result, and returns the chew to the bag. Matthew performs the experiment 24
times. The results are shown below:
A orange chew was selected 10 times.
A cherry chew was selected 11 times,
A lime chew was selected 3 times.
Answer: 13/24
Step-by-step explanation:
The experiment occurred 24 times orange or lime was selected 10+3=13
Probability the next chew will be orange or lime: 13/24
HELP ME PLEASEEEEEEEEEEEEEEEEEEE
Answer:
The second answer choice
Step-by-step explanation:
The pyramid shown is a triangular pyramid. A triangular pyramid consist of 4 faces; 1 triangular base and 3 triangular lateral faces.
Hence, the correct answer would be the second choice.
A bag contains eight white marbles, six red marbles and four blue marbles.
How many blue marbles must be added to the bag so that the probability
of choosing a blue marble is 1/2?
a. 6
b. 5
c. 10
d. 0
Answer:
c) 10
Step-by-step explanation:
you need to add the white and red marbles which would be 14.
then you subtract 14 by the amount of blue marbles.
Find the distance of the two given points (1,5) and (4,10)
Answer:
5.831
Step-by-step explanation:
Distance between both given points=Lenght=5.831
Which angle has a positive measure?
Answer:
what angles
Step-by-step explanation:
i do not see anything to solve
Solve for X (round to the nearest hundred)
Step-by-step explanation:
We use tangent because it uses opposite over adjacent.
So,
tan 33 = x/46
or
46 * tan 33 = x
Type this into the calculator and you get around 29.87
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
What is Tarah's new total balance?
Answer:
$258.48
Step-by-step explanation:
Consider the triangle below
What is the answer for the four at the bottom?
2 4/5*1 1/12=
Help plz it’s for grade recovery
Answer:
3.03 (if you're rounding to nearest hundredth, 3 if nearest whole/tenth.
which equation is not a linear function:
y=2x
y=x+2
y=x-2
y=x²
Answer:
Step-by-step explanation:
A linear equation can be written in the form
y = mx+b.
y = x² is not linear.
the final answer math
Answer:
$10.50
Step-by-step explanation:
$39.90 ÷ 3.8 pounds
= 10.50263157894735
after rounding, your answer must be 10.50
hope this helps.
If s =unit and A = 1652, what is the value of A, in square units?
___ square unit(s). (Input whole number only.)
Plz help this is due today NO LINKS OR GROSS PICTURES OR I Will REPORT And please show work
It is not 480 480 is the incorrect answer
Answer:
2280 the volume
Step-by-step explanation:
So one box = 480
So then what about 6 boxes?
you do 480 x 6 = 2880
480+ 480+ 480+ 480+480+480= 2880
Help me guys find the solution please and thank you
4x+17=23
Find indicated side of right triangle 45 percent 7
Answer:
a = 7
b = 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
in a 45-45-90° triangle, the length of legs to hypotenuse is 1 : [tex]\sqrt{2}[/tex]
Find the surface area and volume of the figure. Round to the nearest tenth.
5th grade math. correct answer will be marked brainliest
The answer is b
saddsadsadas
Answer:
B
Step-by-step explanation:
Cause he added 24.76 more pounds to the 3.6 pounds. So you can take 24+3=27 and you might think C, but 0.76+0.6 that equals more than 1, so 27+1=28, and B has 28 as its answer, so its B
B
what is AC? pls help 30 points if u awnser
Answer:
C. 6
Step-by-step explanation:
ΔADC and ΔACB are similar because two of their angles are congruent (∠ACD and ∠ABC, and ∠DAC and ∠CAB)
Because the sides are similar, you can create a proportion
[tex]\frac{AC}{AD}=\frac{AB}{AC}[/tex]
substitute the given values for the sides. AD=4 and AB=4+5=9
[tex]\frac{AC}{4}=\frac{9}{AC}[/tex]
cross multiply
[tex]AC^{2} =36[/tex]
take the square root of both sides
AC=6
write the percent of each figure
that is shaded.
Answer:
1. 21% 2. 70%
Step-by-step explanation:
1. 21 out of 100 are filled in
2. 7/10 are filled in
In the diagram below, xy and z are tangent to 0. What is the measure of XZ?
Answer:
A. 130°
Step-by-step explanation:
Answer:130
Step-by-step explanation:
I just finished the quiz :)
Evaluate each series.
Help pls 50 points
Answer:
1. 2,555
2. 23.25
Step-by-step explanation:
1. 5+10+20+...
S9 = 5(2^9-1)/(2-1)
= 5(511) = 2,555
2. 12+6+3+1.5+0.75 = 23.25
Giving brainliest ; What is the mean of the data set? {20,1,14,14,9,8} Enter your answer in the box.
Answer:
11
Step-by-step explanation:
(20 + 1 + 14 + 14 + 9 + 8) / 6
= 66 / 6
= 11