for positive acute angles A and B, it is known that cos A=9/41 and tan B=21/20. Find the value of sin(A+B) in simplest form.
Answers
Answer:
Step-by-step explanation:
I attached a pic so you can see what the angles look like when you draw them out and construct right triangles out of them. We need to find the missing side lengths, ?, in each triangle. For A:
and
x = 40 For B:
and
x = 29. Now that we know all the sides of each triangle, we will use the sum identity for sin:
sin(A + B) = sinAcosB + cosAsinB. Filling in what we found in our triangles for each ratio: sin A = 40/41, sin B = 21/29, and cos B = 20/29
sin(A + B) = which simplifies to
And that's it. It doesn't simplify any further.
Related Questions
An SRS of 100 flights by Nite-flite Airlines showed that 64 were on time. An SRS of 100 flights by Waxwing Airlines showed that 80 were on time. Let pN be the proportion of on-time flights for all Niteflite Airline flights, and let pW be the proportion of all on-time flights for all Waxwing Airlines flights. Is there evidence of a difference in the on-time rate for the two airlines
Answers
Answer:
Step-by-step explanation:
pN = 64/100 = 0,64 = 64%
pW = 80/100 = 0,8 = 80%
The planes of Waxwing airlines are more punctual
i need someone to help me with my math assignments
Answers
Answer:
okay depending on the question
Answer:
I can try
Step-by-step explanation:
PLS HELP ASAP ITS DUE IN 2HR PLS
Answers
Answer:
From 10 a.m. to 2 p.m., the temperature at Sam's house increased by 8 degrees Fahrenheit.
Step-by-step explanation:
Write as a number equation ----> 2 - (-6) = 8
Evaluate (2.4 x 10^4) (4.5 x 10^3)
Plss help!
Answers
Answer:
Step-by-step explanation:
2.4*10^4*10^3*4.5
=10.8*10^4+3
=10.8*10^8
=10.8*100000000
=1080000000
what is 1/2 cups into pints
Answers
Answer:
0.25 pints
Step-by-step explanation:
Hehe, i used goo. gle
The volume of the triangular prism is 54 cubic units.
What is the value of x?
O 3
O 5
O 7
O 9
Answers
Explanation:
Volume = Base Area x Height
54 = (1/2 * b * h) * 3x
54 = (1/2 * 4 * x) * 3x
54 = 2x * 3x
54 = 6x^2
9 = x^2
x = 3
can someone help me please?? i really appreciate it
Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.
Answers
Answer:
In summary, the translation and scale factor are:
Translation: (x,y)↦(x+5,y+4)
Scale factor: 2
Step-by-step explanation:
Evaluate the algebraic expression h + h when b = 3, d = 12, h = 2 and r = 7.
A. 12
B. 8
C. 4
D. 0
Answers
Answer:
4
Step-by-step explanation:
h + h
h=2
2+2
4
For what value of is the expression 4+2+36 a perfect square?
Answers
Answer:
[tex]2^2+2+6^2[/tex]
Step-by-step explanation:
Use the given area A of the rectangle to find the value of x . A rectangle with its length labeled left-parenthesis 4 x plus 3 right-parenthesis feet and width labeled left-parenthesis 4 x minus 5 right-parenthesis feet. The area of the rectangle is 209 square feet.
Answers
Answer:
x = 4
Step-by-step explanation:
Length = (4x + 3) feet
Width = (4x - 5 )feet
Area = Length x Breadth
209 = (4x + 3)(4x - 5)
209 = 4x( 4x -5) + 3 (4x -5)
[tex]209 = 16x^2 -20x +12x -15\\\\0 = 16x^2 -8x -15 -209\\\\16x^2 -8x -224 = 0[/tex]
[tex]Quadratic \ Equation \ with a = 16, b = -8, c = -224 \\\\x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}\\\\Substitute \ a, b, c \ in \ the \ equation.\\\\x = \frac{-b + \sqrt{b^2 -4ac}}{2a}, x =\frac{-b \ - \sqrt{b^2 -4ac}}{2a}\\\\x = \frac{8+ \sqrt{64 +14336}}{32}, x = \frac{8- \sqrt{64 +14336}}{32}\\\\x = \frac{8+ \sqrt{14400}}{32}, x = \frac{8-\sqrt{14400}}{32}\\\\x = \frac{8+120 }{32}, x= \frac{8-120}{32}\\\\x = \frac{128}{32} , x = \frac{-112}{32}\\\\x = 4 , x = \frac{-7}{2}[/tex]
Since measure of length or width cannot be negative, we take x = 4
Write the equation of a line that passes
through point (-5,3) and is perpendicular to
y=3/5x +2.
Answers
Answer:
[tex]y=-\frac{5}{3}x-\frac{16}{3}[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 4/3 and -3/4, etc.)1) Determine the slope (m)
[tex]y=\frac{3}{5} x +2[/tex]
From the given equation, we can see that [tex]\frac{3}{5}[/tex] is the slope of the line since it's in the place of m. Because perpendicular lines always have slopes that are negative reciprocals, the line we're currently solving for would have a slope of [tex]-\frac{5}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-\frac{5}{3}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{5}{3}x+b[/tex]
Plug in the given point (-5,3)
[tex]3=-\frac{5}{3}(-5)+b\\3=\frac{25}{3}+b[/tex]
Subtract [tex]\frac{25}{3}[/tex] from both sides to isolate b
[tex]3-\frac{25}{3}=\frac{25}{3}+b-\frac{25}{3}\\-\frac{16}{3} = b[/tex]
Therefore, the y-intercept is [tex]-\frac{16}{3}[/tex]. Plug this back into [tex]y=-\frac{5}{3}x+b[/tex]
[tex]y=-\frac{5}{3}x+(-\frac{16}{3})\\y=-\frac{5}{3}x-\frac{16}{3}[/tex]
I hope this helps!
hey! i’ll give brainliest please help
Answers
Answer:
c
Step-by-step explanation:
Answer:
D, a sentence that includes only one independent clause
Step-by-step explanation:
A compound-complex sentence has two independent clauses, and 1 or more dependent clauses. A compound sentence has two independent clauses, and is connected by a conjunction.
This isn't a math question but idrc
-3•2•a+5(-7b)+(12•c•4)
Answers
-6a + -35b + 48c
What is 5/9 +1/3 = I appreciate all answers!!
Answers
1.) Multiply Denominator:
9x3= 27
27 will be your new denominator for your answer.
then take 5 and multiply by 3.
5x3=15
then take 1 and multiply by 9.
1x9=9
Afterwards, you plus 15 and 9 to get 24.
so your fraction for the end will be 24/27.
find angle a given that a=18.2, angle b=62° and angle c=48°
Answers
Answer:
They only add up to 128.2, so if they are asking for the final angle to equal 180, then it would equal 51.8.
Hope that this helps!
Find the error & explain why it is wrong: Megan wanted to solve this problem: given that sin 0=-divided2/2, and cos =divided3/2, find tan 0
What did she do wrong
Answers
Answer:
As seen on the picture, all the steps A to D are correct.
Step A. Identity is correctStep B. The fraction is correctStep C. Simplification is correctStep D. Solution is correctNote:
It could be more simplified by adding a step and multiplying both the numerator and denominator by √3: [tex]\frac{-\sqrt{2} }{\sqrt{3} } = - \frac{\sqrt{6}}{3}[/tex]Find the measure of x in each figure
Answers
Step-by-step explanation:
40+2x=90°(given in question)2x=90-40x=50/2x=25°stay safe healthy and happy...Find the missing measurements.
Area: ?
Length: 13 cm
Width: 15 cm
Answers
Answer:
13 x 15 = 195
Find the distance between the points (1, 4) and (- 2, - 1).
Answers
5.83
Use the distance formula i attached an example of another problem same formula different numbers, you can use it for future reference just switch out the points and you’ll have your answer
PLZ HELP ASAPPP I just need with 1 and 2 this is my very last assignment! Thank you guys for all your help this yr!
Answers
Answer:
1. a = 32.96 m∠B = 21° b = 12.74
2. x = 24.99
Step-by-step explanation:
1. Use the law of sines:
a/sin 112 = 26/sin 47
a = 26 sin 112/sin 47
a = 32.96
m∠B = 180 - 47 - 112 = 21°
b/sin 21 = 26/sin 47
b = 26 sin 21/sin 47
b = 12.74
2. Use the law of cosines
[tex]x^{2} = 17^{2} + 11^{2} - 2(17)(11) cos 125[/tex]
= 289 + 121 - 374 cos 125
= 624.5175....
x = [tex]\sqrt{624.5175...}[/tex]
= 24.99
subtract -2/15 from -3/5 and add the result to 5/6
Answers
Answer:
6/5
Step-by-step explanation:
-3/5-(-2/15)+5/6
-3/5+2/15+5/6
=-3+2×5/15 + 5/6. (taking lcm)
=-3+6/15+5/6
=3/15+5/6
=3+5×3/15 (taking lcm)
=18/15
=6/5
Answer:
Step-by-step explanation:
-3/5-(-2/15)+5/6
=-3/3+2/15(take lcm of 3 and 15)+5/6
=-3*3+2*1/15+5/6
=-9+2/15+5/6
=-7/15+5/6(take lcm of 15 and 6)
=-7*2+5*5/30
=-14+25/30
=11/30
=11/30
Drag the sliders.
Shape A
Shape B
Which slider creates scale copies of the shape?
Choose 1 answer:
Slider for Shape A
Slider for Shape B
Answers
Find the value of each variable in the figure on the right.
What is x and y?
Answers
What is
[tex] {5}^{7} [/tex]
Answers
Answer:
78,125
Step-by-step explanation:
5 × 5 × 5 × 5 × 5 × 5 × 5 = 78125
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Have a good day :)
I WILL GIVE BRAINLESS IF YOU HELP ME PLZ
S.O.S I HAVE MATH
Answers
slope is rise/over run, with the y-intercept being on 1
When looking at rate of change, it's really just telling you to look at the slope and how steep it is. The more steeper it is, the higher the rate of change. (as close as it is to being a vertical line). Since the slope here is 2. Look for one that has a slope greater than 2, which is 3. Therefore the answer
A. 3x-1
Hope this helps!
Una escalera de 30 pies de longitud está apoyada contra una pared de modo que su extremo superior se desliza hacia abajo con una velocidad de 1/2 pies/seg ¿cuál es la tasa de variación de la medida del ángulo formado por la escalera y el piso cuando el extremo superior está a 18 pies del piso?
Answers
Answer:
dα /dt = - 0.028 rad /sec or dα /dt = - 1.59 °
El signo menos significa que el angulo va decresiendo
Step-by-step explanation:
La escalera, la pared vertical y el pié de la escalera y la pared forman un triangulo rectangulo. En ese triangulo
cos α ( α angulo que forma la escalera con el piso )
cos α = x / L
Tomando derivadas con respecto al tiempo (L es constante ) se tiene:
- sen α * dα / dt = dx/ dt / L
Cuando el extremo superior de la escalera está a 18 pies del piso, entonces sen α = 18 / 30 = 0.6
dx/dt = 1/2 pie/sec
dα/dt = - (1/2)/ L* 0.6
dα /dt = - 0.5 / 18
dα /dt = - 0.028 rad /sec or dα /dt = - 1.59 °
El signo menos significa que el angulo va decresiendo
HELPPP ME PLEASE IT’S A VERY IMPORTANT TESTTTTT
Answers
Answer:
B also have a great day today
Answer:
D, Between 5.4 and 6.5
Step-by-step explanation:
anything less than .5 gets rounded down and anything higher gets rounded up so it'll end up with 6
Tyra, Ella, Tran and Ann share equally in the rental of a car. If the total cost of the rental is C dollers which expression represents Tyras share of cost
Answers
Answer:
C/4
Step-by-step explanation:
The amount divided by the amount of people will show how much each person owes
PLEASE HELP!!! IL MARK BRAINLIEST
Which transformation results in a similar geometric figure rather than a congruent one?
A. Relation
B. Transformation
C. Dilation
D. Rotation
Answers
Answer: C dilation
Step-by-step explanation:
CORRECT TO ONE DECIMAL PLACE
[tex]2x(x - 3)[/tex]