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
How do this I can’t do it?
Answers
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, scaled copy to original
scale factor = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]
Need the answer please help
Answers
the answer is -7, -5 its the answer check it
A tool box has the dimensions of 10 in by 4 in by 7 in. If Magnus plans to double all three dimensions to build a larger tool box, he believes he would double the volume of the tool box. Is he correct?
Answers
Answer: No. He's wrong.
Step-by-step explanation:
Since the tool box has the dimensions of 10 in by 4 in by 7 in. The volume will be:
= 10 × 4 × 7
= 280in³
When the dimensions are doubled, the new dimensions will be:
10 in = 10in × 2 = 20in
4in = 4in × 2 = 8 in
7in = 7in × 2 = 14in
The volume will now be:
= 20 × 8 × 14
= 2240in³
He is wrong, the volume isn't the double of the former tool box. The double of the former tool box will give (280in³ × 2) = 560in³. This is different from the new volume.
What is the length of the hypotenuse of the triangle when x=11?
Answers
Answer:
hypotenuse = 93.06
Step-by-step explanation:
[tex]x = 11\\\\base = 4 \times 11 = 44\\\\height = 7x + 5 = 7 \times 11 + 5 = 77 + 5 = 82\\\\hypotenuse ^2 = base^2 + height^2\\[/tex]
[tex]=44^2 + 82^2\\\\=8660[/tex]
[tex]\\\\hypotenuse=93.06[/tex]
This question is worth 20 points and I will mark brainliest
which expressions are equivalent to 2 (3h + 7) choose "equivalent" or "Not equivalent" for each expression.
6h+7
2+3h+7
6h+7+7
3h+3h+14
(3h+7) + (3h+7)
Answers
Answer:
2(3h+7)
=6h+14
6h+7+7 (True)
3h+3h+14 (True)
Determine the length of the radius of the circumscribed circle to the right triangle with the legs 7 cm and 4cm.Round your answer to the nearest hundredth
Answers
Answer:
4.03cm
Step-by-step explanation:
Note that the diameter of the circumscribed circle to the right triangle is the hypotenuse of the triangle.
To get the diameter, we will use the pythagoras theorem as shown;
d² = 7² + 4²
d² = 49 + 16
d² = 65
d = √65
d = 8.0622577
Since radius = d/2
radius = 8.0622577/2
radius = 4.0311288
Hence the radius of the circumscribed circle to the nearest hundredth is 4.03cm
please help!! i need help asap <33
Answers
Answer:
9
Step-by-step explanation:
What is the area of this triangle?
Answers
Now that you know how long it will take to buy your house from Assignment 4 and how much you need to save for retirement given different start times in your life (Assignment 5), you will now determine the time you will start saving for retirement. Add the savings time it takes to buy your house (2 years or the months you calculated, whichever is greater) to the age 22. By using the new budget from assignment 4, determine if you can afford the savings it takes from assignment 5 to retire with $1,000,000 based on your new age after buying your house. If you cannot, you have a choice, change your budget, or retire will less money.
For your answer, tell me your age, if you can afford in your budget to retire with $1,000,000. If you can, write your budget with the retirement savings added in. If you cannot, write that you cannot afford it and tell me if you are going to change your budget to afford it or simply retire with less money. Then write your budget with what savings you can afford. Remember, retiring with less money does not mean that you will have a smaller retirement income, it just means that you will pass on less than a million dollars to your children.
Answers
Answer:
You have to answer this yourself because i believe this quesstion is directed to you and your teacher want's to know your answer
Step-by-step explanation:
what multiples to -52 but also adds to 24
Answers
Answer:
-2 and 26
Step-by-step explanation:
-2*26=-52
-2+26=24
The Martinez family picked 3 lb of apples. Ana picked for those apples,
How many pounds of apples did Ana pick?
Answers
Answer:
C. 7/8
Step-by-step explanation:
The Martinez family picked 3 and one-half pounds of apples. Ana picked one-fourth of those apples. How many pounds of apples did Ana pick?
options
A. 1/4
B. 3/4
C. 7/8
D. 1 1/4
E. 3 1/8
Total apples the Martinez family picked = 3 1/2 pounds
Ana picked one-fourth of those apples.
Number of apples Ana picked = 1/4 × 3 1/2 pounds
= 1/4 × 7/2 pounds
= (1 * 7) / (4 * 2) pounds
= 7/8 pounds
Ana picked 7/8 pounds of apples
Jackie has 54 fewer beads then sally. If B stands for the number of beats Jackie has, write an expression that represents the number of beats Sally has?
Answers
Answer:
B+54
Step-by-step explanation:
If Jackie has B beads, and Sally has 54 more than that, then you are adding 54 to B
i will give brainliest!! please help me, i appreciate it !!
Answers
Answer:
-4050
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
6x²y³ - 2x + 10
x = 5
y = -3
Step 2: Evaluate
Substitute in variables: 6(5)²(-3)³ - 2(5) + 10Exponents: 6(25)(-27) - 2(5) + 10Multiply: -4050 - 10 + 10Add: -4050A. 7/24
B. 24/7
C. 24/25
D. 7/25
Answers
Answer:
d
Step-by-step explanation:
find the circumference of a circle with a radius of 2.5 cm
Answers
2*3.141592654*2.5
Answer: 15.7 cm
Given the equation ab= c where a=2.
Select an equation that is equivalent.
A. ax2=c
B. bx2=c
C. cxa= b
D. b x C = a
Answers
(PLEASE HELP) 17. Jon read 3/8 of a book the
first day. 1/3 the second day.
and 1/4 the third day. On the
fourth day he finished the book.
What part of the book did Jon
read on the fourth day?
Answers
Answer:
[tex]\frac{1}{24}[/tex]
Step-by-step explanation:
24 is a common multiple so ill just use that as a denominator:
3/8 = 9/24
1/3 = 8/24
1/4 = 6/24
so then adding those up:
[tex]\frac{9}{24}[/tex] + [tex]\frac{8}{24}[/tex] + [tex]\frac{6}{24}[/tex] = [tex]\frac{23}{24}[/tex]
then whats left is 1/24 left to read, which cant be simplified so [tex]\frac{1}{24}[/tex]
Answer:
[tex]\frac{1}{24}[/tex]
Step-by-step explanation:
Let x be the part of the book he read on fourth day.
[tex]\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1[/tex]
[tex]LCM \ of \ 8, 3 , 4 = 24.\ Therefore , \\\\[/tex]
[tex]\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1\\\\\frac{9 + 8 + 6 + 24x}{24} = 1\\\\23 + 24x = 24\\24x = 1\\x = \frac{1}{24}[/tex]
[tex]On\ the\ fourth\ day\ he\ read\ \frac{1}{24} \ of\ the\ book\ to\ finish\ it.[/tex]
reduce 50/80 to the simplest terms in fractions
Answers
Answer:
5/8
hope this helps
have a good day :)
Step-by-step explanation:
A circle of radius 1 is inside a circle of radius 5. The smaller circle is rotated clockwise
on the larger circle without slipping until it arrives back at its starting point P. How
many revolutions (turns) will the small circle make? Be careful. The answer is not 5.
Answers
9514 1404 393
Answer:
4
Step-by-step explanation:
Consider the arcs PQ and P'Q. When turns are made without slipping, these have the same measure. The length of arc PQ is ...
PQ = CP·θ
The length of arc P'Q is ...
P'Q = O₂Q·(∠PO₂Q)
Segment O₂A is parallel to CP, so angle AO₂Q is θ. Then ∠PO₂Q = θ+α, where α is the angle by which P' has rotated counterclockwise from A.
We are given that ...
CP = 5, O₂Q = 1
Using the above relations, we can write ...
5θ = 1(θ+α)
α = 4θ
That is, for every full turn θ = 2π, the smaller circle makes turns totalling 4(2π) = 8π, or 4 full turns.
The small circle makes 4 revolutions to arrive at its starting point.
17. Jing has $800 to deposit into two different savings accounts.
•She will deposit $600 into an account that earns simple interest annually at a rate
of 2.75%.
•She will deposit $200 into an account that earns 2.5% interest compounded
annually.
Jing will not make any additional withdrawals or deposits. Which amount is closest
to the total balance of the two accounts at the end of 3 years?
Answers
Answer:
$864.88
Step-by-step explanation:
(1. $600 + $49.50 = $649.50
(2. $200 + $15.38 = $215.38
$649.50 + $215.38 = $864.88
A = $864.88
the table shows some of the solutions for an inequality related to the line shown in the graph. which inequality describes the solution set?
Answers
Answer:
Option B
Step-by-step explanation:
By plotting the points given in the table,
All points lie below the dark red line.
Let the equation of the line is,
y - y' = m(x - x')
Here, m = Slope of the line
(x', y') is a point lying on the given line.
Slope of the line passing through two points (-1, 3) and (0, 1) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{3-1}{-1-0}[/tex]
m = -2
Therefore, equation of the line passing through (0, 1),
y - 1 = -2(x - 0)
y = -2x + 1
Since all the points given in the table lie below the dark red line so the solution are will be,
y ≤ -2x + 1
Option B will be the correct option.
On a map, the distance between two towns is 12 centimeters. If 3 centimeters represents 90 miles, what is the actual distance between the cities in miles?
Answers
PLEASE HELP 30 POINT AND BRAINLIEST
Answers
Answer:
first is 2 second is 3
Step-by-step explanation:
Help. I don't understand..
Answers
Answer:
3
Step-by-step explanation:
Answer:
75.4
Step-by-step explanation:
All angles in a triangle should equal 180, so the lil dash on K's side means angle K is the same as J
so 52.3+52.3=104.6
and 180-104.6 is 75.4
hope i helped and feel free to ask questions
What is the factorization? x2 + x – 12
Answers
Answer:
(x+4)(x-3)
Step-by-step explanation:
Which statement is correct?
Answers
Answer:
Fresh water is evenly distributed throughout the earth.
Step-by-step explanation:
Freshwater exists on Earth's surface in lakes, rivers, and ice, as well as below the surface as groundwater.
Hope this answer helps you :)
Have a great day
Mark brainliest
30 Points I NEED HELP ASAP MATH PROBLEM 7th Grade
Answers
Answer:
-45 =x
Step-by-step explanation:
1/5(4x-2.5) = 5(.4x+10) +3 1/2
Change all to decimal form
.2(4x-2.5) = 5(.4x+10) +3.5
Distribute
.8x - .5 = 2x +50 + 3.5
Combine like terms
.8x - .5 = 2x +53.5
Subtract .8x from each side
.8x-.8x - .5 = 2x-.8x +53.5
-.5 = 1.2x +53.5
Subtract 53.5 from each side
-.5 -53.5 = 1.2x +53.5-53.5
-54 = 1.2x
Divide each side by 1.2
-54/1.2 = 1.2x /1.2
-45 =x
Jorge has saved $15.50. Janet saved 15 of the amount that Jorge saved. Rob saved 12 times as much as Janet. What is the total saved amount of all three?
Answers
Answer: 45.725 ( i think)
Step-by-step explanation: 2.325 + 27.9 + 15.50
An article is bought for Rs 8600 and is sold at a profit of 20 %. Find its selling price.
Answers
Selling price = 8600 + Profit
Selling price = 8600 + ( 8600 × 20/100 )
Selling price = 8600 + ( 86 × 20 )
Selling price = 8600 + 1720
Selling price = Rs 10,320
2) La expresión 7∙7∙7∙7 es igual a:
a) 47
b) 4+7
c) 47
d) 74
Answers
because 7•7•7•7 is 7 to the power of 4
Answer:
d) 7⁴
Step-by-step explanation:
7 ∙ 7 ∙ 7 ∙ 7
cuatro sietes = siete elevado a cuatro
d) 7⁴