If a and b are acute angles such that tan (a+b)= 1.73 and tan(a-b) =1/1.73, find a and b

Answers

Answer 1

[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]

Given,

tan (a + b) = 1.73 [tex]\approx[/tex] √3tan (a - b) = 1 / 1.83 [tex]\approx[/tex] 1 / √3

To find:

Value of a and b in degrees....?

Solution:

☃️ Refer to the trigonometric table....

Then, proceeding

⇛ tan 60 ° = √3

⇛ tan 60° = tan (a + b)

⇛ 60° = a + b

Flipping it,

⇛ a + b = 60° --------(1)

And,

⇛ tan 30° = 1 / √3

⇛ tan 30° = tan (a - b)

⇛ 30° = a - b

Flipping it,

⇛ a - b = 30° ---------(2)

Now adding eq.(1) and eq.(2),

⇛ a + b + a - b = 60° + 30°

⇛ 2a = 90°

⇛ a = 90° / 2

⇛ a = 45°

Putting value of a in eq.(1),

⇛ 45° + b = 60°

⇛ b = 15°

☄ So, Our Required answers:

a = 45°b = 15°

━━━━━━━━━━━━━━━━━━━━

If A And B Are Acute Angles Such That Tan (a+b)= 1.73 And Tan(a-b) =1/1.73, Find A And B

Related Questions

What is the width of the rectangle shown below?
4x + 3
A = 8x2 – 10x – 12

Answers

Answer:

2x-4

Step-by-step explanation:

Area of a rectangle = Length * Width

Given parameters

Area A = 8x2 – 10x – 12

Length of the rectangle = 4x+3

Required

Width of the rectangle.

Substituting the given parameters into the formula

8x2 – 10x – 12  = (4x+3)*width

width = 8x2 – 10x – 12 /4x+3

S

Factorizing the numerator

8x² – 10x – 12

= 2(4x²-5x-6)

= 2(4x²-8x+3x-6)

= 2(4x(x-2)+3(x-2))

= 2(4x+3)(x-2)

Width = 2(4x+3)(x-2)/4x+3

Width = 2(x-2)

Width = 2x-4

Hence the width of the rectangle is 2x-4

Which is the simplified form of the expression ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline) (3 squared)) squared?

Answers

Answer:

[tex]\dfrac{1}{6561}[/tex]

Step-by-step explanation:

Given the expression [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex], Using the laws of indices to simplify the expression. The following laws will be applicable;

[tex]a^m*a^n = a^{m+n}\\(a^m)^n = a^{mn}\\[/tex]

[tex]a^{-m} = 1/a^m[/tex]

Given [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex]

open the parenthesis

[tex]= (2^{-2})^{-3}(3^{4})^{-3}* (2^{-3})^2(3^2)^2\\\\= 2^{-2*-3}* 3^{4*-3} * 2^{-3*2} * 3^{2*2}\\\\= 2^6 * 3^{-12} * 2^{-6} * 3^4\\\\collecting \ like \ terms\\\\= 2^6 * 2^{-6} * 3^{-12} * 3^4\\\\= 2^{6-6} * 3^{-12+4}\\\\= 2^0 * 3^{-8}\\\\= 1 * \frac{1}{3^8}\\ \\= \frac{1}{6561}[/tex]

Kelly bought a crate of floor tiles for $95.94. The crate had 6 boxes of floor tiles. Each box contained 20 floor tiles.

Write and solve an equation to determine the cost per box, b. Then write and solve a second equation to determine the cost per tile, t, to the nearest cent.

Answers

Answer:

$1.60 a crate

Step-by-step explanation:

t= 95.94/(6x20)

(6x20)= 60

95.94/60

$1.60

Answer:

Step-by-step explanation:

i) Cost per box = cost of a crate ÷ Number of boxes in the crate

b = 95.94 ÷ 6

b = $ 15.99

ii) Cost per tile = Cost per box ÷ Number of tiles in a box

 t = b ÷ 20

 t = 15.99 ÷20

t = $ 0.7995

What is the solution to 7 × p = -56? A. -49 B. -8 C. 8 D. 49

Answers

Answer:

-8

Step-by-step explanation:

Hello!

What we do to one side of the equation we do to the other side

7 * p = -56

Divide both sides by 7

p = -8

The answer is -8

Hope this helps!

New York City is a popular feild trip destination. This year the senior
class at High School A and the senior class at High School B both
planned trips there. The senior class at High School A rented and filled
8 vans and 4 buses with 220 students. High School B rented and filled 12 vans and 4 buses with 228 students. Every van had the same
number of students in it as did the buses. How many students can a
van carry? How many students can a bus carry?​

Answers

Step-by-step explanation: look so if you have

shcool A its 8v+4b=12

and

School B: 12v+4b= 16

since both classes used 4 busses we can use elimination by subtracting the A class Equation from the b class equation to solve from v for its value Then, use either equation and the now found value for v to solve for b.

You should find part of the process to be

12v+4b-(8v+4b)=12-16 which shows the van holds only a few people even before continuing the solution.

Answer -4

What is the result when the number 90 is decreased by 10%

Answers

Answer:

81

Step-by-step explanation:

First find the amount decrease

90 * 10 %

90 * .10

9

90 decreased by 9

90 -9

81

Answer:

81

Step-by-step explanation:

Turn into decimal.

10% = 0.1

Multiply

90 * 0.1 = 9

Subtract

90 - 9 = 81

Best of Luck!

what do you think you’d like most about working as a forensic scientist? why

Answers

Answer:

i think its very interesting and pretty cool,  because there is so much to learn  and so much to explore

i wouldn't like the fact that you have to study so much though

Step-by-step explanation:

Can someone pls help me &THANK YOU



SLATTTT!!!

Answers

BABYYYY SOSAAAAA CASH CARTIIII

math now..!! Help..?

Answers

Answer:

2p + 12

2 (p = +6) + 12 = 20

Answer:

I think its 6

Step-by-step explanation:

because you have to add 9 and 3 together then you get 12 and you have to divide 2p with 12 and you'll get 6

what is the coefficient of x in the equation of 32+2x=10
solve after finding the coefficient

Answers

Answer:

x= -11

Step-by-step explanation:

the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .

the value of x is:

>32+2x=10

>2x=10-32

>2x= -22

>x= -11

Answer:

Step-by-step explanation:

Coefficient of x = 2

32 + 2x  = 10

Subtract 32 from both side

32 + 2x -32 = 10 - 32

              2x =  - 22

Divide both sides by 2

            2x/2 = -22/2

x = -11

Line m and point P are shown below. Part A: Using a compass and straightedge, construct line n parallel to line m and passing through point P. Leave all construction marks. Part B: Explain the process that you used to construct line n.

Answers

Answer:

  see the attached

Step-by-step explanation:

In the attachment, we will refer to the circles, bottom-to-top, as circles 1, 2 and 3. The black points of intersection, bottom-to-top, will be referred to by the letters A, B, C, D. The transversal line through the white point (W) and pink point (P) will be line q.

Step 1. Draw line q through point P so it intersects line m at some convenient point. Label that point W.

Step 2. Choose an arbitrary radius for your compass. Here, we have chosen it to be the length WB. It happens to be less than half the length of WP, but that is not a requirement.

Step 3. Draw an arc of the chosen radius centered at W and intersecting line q and line m. Label the intersection points A (on line m) and B (on line q). These intersection points are on circle 1.

Step 4. Draw an arc of the same radius centered at P. It should be a long enough arc that it would intersect the proposed line parallel to m. Label the intersection point on line q with label C. This intersection point is on circle 3.

Step 5. Adjust the compass width (radius) to the distance from A to B. This is the radius of circle 2.

Step 6. Draw an arc centered at C so that it intersects the arc of Step 4. This is circle 2, and you want it to intersect circle 3. Label that point of intersection D.

Step 7. Draw line PD parallel to m.

_____

The point of the construction is to create congruent alternate interior angles AWB and CPD, so that lines AW and PD are parallel.

Combine the radicals. 2√24+5√54 A) 53√6 B) 5√6 C) 19√6 D) 93√6

Answers

Answer:

The answer is option C

Step-by-step explanation:

2√24 + 5√54

To combine the radicals first make sure the radicals have the same square root

That's

For 2√24

[tex]2 \sqrt{24} = 2 \sqrt{4 \times 6} = 2 \times 2 \sqrt{6} [/tex][tex] = 4 \sqrt{6} [/tex]For 9√54

[tex]5 \sqrt{54} = 5 \sqrt{9 \times 6} = 5 \times \sqrt{9} \times \sqrt{6} [/tex][tex] = 5 \times 3 \times \sqrt{6} [/tex][tex] = 15 \sqrt{6} [/tex]

Since they have the same square root we can combine them

That's

[tex]4 \sqrt{6} + 15 \sqrt{6} = (4 + 15) \sqrt{6} [/tex]

We have the final answer as

[tex]19 \sqrt{6} [/tex]

Hope this helps you

What is the decimal equivalent of 16/3 ?
A. 5.3
B. 0.1875
C. 53333...
D. 16.3

Answers

Answer:

c. 5.333...

Step-by-step explanation:

When converting fractions into decimals, all you have to do is that you have to divide the numerator by the denominator. In this case, we will get 16 divided by 3. If we do this, we will get 5 and 1/3. One third in decimals is 0.3333... so the answer is 5.333...

The decimal 5.33 will be equivalent to 16/3 so option (A) will be correct.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given the fraction of 16/3

So divide 16 by 3

16/3 = (15 + 1 )3

⇒ 15/3 + 1/3

⇒ 5 + 0.333

⇒5.3

Hence "The decimal 5.33 will be equivalent to 16/3".

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PLEASE HELP!!!
10. Write the formula of the function f(x) whose graph is shown.
A
f(x) = 4 - 4
х
B
f(x)=
1
= - +4
X
с
f(x) = 24
D
1
f(x) =
X +4

Answers

Step-by-step explanation:

c

Which equation can be used to find x, the length of the hypotenuse of the right triangle?

Answers

Answer:

[tex] \boxed{\sf {18}^{2} + {24}^{2} = {x}^{2}} [/tex]

To Find:

Length of hypotenuse of the right triangle i.e. x

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore [/tex]

[tex] \sf \implies {18}^{2} + {24}^{2} = {x}^{2} [/tex]

Answer:

18²+24²=x²

Step-by-step explanation:

to answer this question you must know Pythagorean theorem

a^ 2+b^2 =c^2

a and b stands for the sides with length 24 and 18 and c stands for the HYPOTENUSE . so the correct answer for the above question is 18²+24²=x²

3 sides of the triangle are consecutive odd numbers. What is the smallest possible perimeter of the triangle ?

Answers

The sides are 3, 5, and 7 because 7 is less than 3 + 5, so it equals a triangle.

The smallest possible perimeter of such triangle would be 8.

What is triangle inequality theorem?

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]

Given; 3 sides of the triangle are consecutive odd numbers.

The sides are 3, 5, and 7 because 7 is less than 3 + 5 so it equals a triangle.

The smallest consecutive odd numbers are 1, 3 and 5

Therefore, the smallest possible perimeter of such triangle = 8

Learn more about triangle inequality theorem here:

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The physician orders 1500 flu injections. There were 300 shots given in September, 450 shots given in October, and 665 shots given in November. What percentage of flu vaccine has been given?

Answers

Answer:

94.33

Step-by-step explanation:

add up all numbers then input into a percentage calculator

Percentage of flu vaccine has been given 94.33%

What is percentage?

Percentage is defined as ratio expressed as a fraction of 100.

The physician have total 1500 flu injections

300 shots given in September,

450 shots given in October,

and 665 shots given in November,

Total flu vaccine has been given = 300+450+665 = 1415

Percentage of flu vaccine has been given = (1415/1500)×100%

Percentage of flu vaccine has been given = 0.9433×100%

Percentage of flu vaccine has been given = 94.33%

Hence, percentage of flu vaccine has been given 94.33%

Learn more about percentage

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Review what you know about products and sums represented by rectangular area models. [5 points] Use algebra tiles to multiply (x-1)(3x+2).

Answers

(x - 1)(3x + 2)
= 3x^2 + 2x - 3x - 2
= 3x^2 - x - 2

3x^2 - x - 2

What are some ways to solve an equation?

Different ways to solve equations. We have 4 ways of solving one-step equations: Adding, Substracting, multiplication, and division. If we add the same number to both sides of an equation, both sides will remain equal.

How do you evaluate an equation?

∫ y2+y−2dy ∫ y 2 + y − 2 d y∫ 2 1 y2 +y−2dy ∫ 1 2 y 2 + y − 2 d y∫ 2 −1 y2 +y−2dy ∫ − 1 2 y 2 + y − 2 d y

= (x - 1)(3x + 2)

= 3x^2 + 2x - 3x - 2

= 3x^2 - x - 2

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Write in standard 7.125×10^-9

Answers

Answer:

7.125*10⁻⁹ = 0.000000007125

Step-by-step explanation:

7.125*10⁻⁹ = 0.000000007125

There are 45 eighth graders and 20 seventh graders in a school club. The president of this club wants 40% of the club’s members to be seventh graders. How many more seventh-graders must join the club in order to meet the president’s wishes? (Assume that the number of eighth-graders remains the same.)

Answers

Answer: Please Give Brainliest. Thank You!

10 more

The number of seventh-graders that must join the club in order to meet the president's wishes is 10.

Since there are 45 eighth graders and 20 seventh graders in a school club and the president of this club wants 40% of the club’s members to be seventh graders, we need to find the number of seventh graders that will be added to the school club to make their percentage 40 %.

Let the number of seventh-graders to be added be x.

So, the new number of seventh-graders is 20 + x and the new number of people in the club is 45 + 20 + x = 65 + x

Thus, the percentage of seventh graders in the club is thus

[tex]\frac{20 + x}{65 + x} X 100[/tex] %

Since this percentage equals 40 %, we have that

[tex]\frac{20 + x}{65 + x} X 100[/tex]% = 40 %

[tex]\frac{20 + x}{65 + x} = \frac{40}{100} \\\frac{20 + x}{65 + x} = 0.4[/tex]

Cross-multiplying we have

[tex]20 + x = 0.4(65 + x)[/tex]

Expanding the bracket, we have

[tex]20 + x = 26 + 0.4x[/tex]

Subtracting 20 from both sides we have

[tex]x = 26 - 20 + 0.4x\\x = 6 + 0.4x[/tex]

Subtracting 0.4x from both sides, we have

[tex]x - 0.4x = 6\\0.6x = 6[/tex]

dividing both sides by 0.6, we have

x = 6/0.6

x = 10

So, the number of seventh-graders that must join the club in order to meet the president's wishes is 10.

Learn more about percentages here:

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What does this mean? 20 points + brainleist! What other angle measures or side lengths can you determine using these added figures? List all the concepts and facts you use.

Answers

Step-by-step explanation:

The question has asked you to have another concepts or facts that can be used to find the other angles and measure of side length.

by looking the fig we can determine various sides and angles as all are joined together.

Rebecca is saving money to purchase a laptop, which costs $1,099.51. She has already saved $354.20 and plans to continue
saving $50.60 per week. Which inequality could be used to find w, the number of weeks that Rebecca must save in order to
purchase the laptop?
OA $354.20 + $50.60w < $1,099.51
OB. $354.20w+ $50.60 $1,099.51
OC $354.20 + $50.60w< $1,099.51
OD. $354.20 + $50.60w $1,099.51

Answers

Answer:

354.20 + 50.60w ≥ 1099.51

Step-by-step explanation:

354.20 + 50.60w ≥ 1099.51

FACTOR THIS EXPRESSION -385y LOOK AT THE SCREENSHOT THANKS AND BRAINLIST IF CORRECT PLEASE HELP

Answers

Answer:

-1*5*7*11*y

Step-by-step explanation:

This is the prime factorization of 385y times -1.

Pls answer I really need help
Brainlist and thank you will be the reward thank you so much!!!

Answers

Answer:

0.667 ✅

Step-by-step explanation:

This is best solved using a proportion.

The formula is soy/vinegar = soy/vinegar where one of these is a variable.

Here we have:

[tex]\frac{150}{100} = \frac{1}{x}[/tex]

Now, we solve this by cross multiplying.

150x = 100

Dividing both sides by x, we get x = 2/3 or about 0.667.

Checking:

[tex]\frac{150}{100} = \frac{1}{0.667}[/tex]

1.5 = 1.5 ✅

I'm always happy to help :)

Please answer question now

Answers

Answer:

90

Step-by-step explanation:

Tangents drawn to a circle from an external point are equal, thus

IH = IJ = 7

ON = OH = 19 - 7 = 12

MN = ML = 26 - 7 = 19

Summing the 4 sides for perimeter (P)

P = 26 + 19 + 7 + 7 + 12 + 19 = 90

Work out the value of angle x

Answers

Answer: 166 degrees

======================================================

Explanation:

The given exterior angle 97 is adjacent to the interior angle 180-97 = 83. This is the base angle of the isosceles triangle. The other base angle is directly above it. The base angles are always opposite the congruent sides.

The missing interior angle (adjacent to the blue angle x) is unknown, so we'll call it angle y. This angle adds to the other two base angles (83 each) to get a sum of 180. Adding any three interior angles of a triangle always gets you 180

y+83+83 = 180

y+166 = 180

y = 180-166

y = 14

Angle x and y are supplementary. They form a 180 degree angle

x+y = 180

x = 180-y

x = 180-14

x = 166

As you can see, the base angles combine to form the exterior angle we're after. This is because of the remote interior angle theorem.

cual es el area de un rectangulo

Answers

Answer:

Use this formula:

a = b * h

Where: "a", the area of the rectangle is equal to its "b" (base), multiplied by "h" (height)

Step-by-step explanation:

Usa esta formula:

a = b * h

Donde: "a", el área del rectángulo es igual a su "b" (base), multiplicado por "h" (su altura).

There are approximately fifty five million metric tons of apples grown each year. It has been estimated that half of all the apples grown are eaten fresh. Approximately how many metric tons of apples are eaten fresh

Answers

Answer:

Twenty-seven and a half million metric tons of apples are eaten fresh.

Step-by-step explanation:

The amount of metric tons of apples that are eaten fresh is equal to the half of the total amount of metric tons. That is:

[tex]m = \frac{55,000,000\,m-ton}{2}[/tex]

[tex]m = 27,500,000\,m-ton[/tex]

Twenty-seven and a half million metric tons of apples are eaten fresh.

WILL MARK BRAINLIEST!!!!20 POINTS!!!!URGENT!!!

Answers

Answer:

the firsts third and last one

Step-by-step explanation:

hope this helped

A set of circular cups are placed so that they are touching rim to rim, as close together as possible. It is not possible to fit more cups inside the group if the longest straight line is five cups long, how many cups are there altogether?

Answers

Answer:

The total number of cups in arranged in an hexagonal area = 19 cups

Step-by-step explanation:

The pack the most circles within an area, the arrangement with the densest packing is the hexagonal lattice structure similar to the bee's honeycomb as has been proved Gauss and Fejes Toth.

Therefore, we pack the circles in an hexagonal lattice structure in an assumed hexagonal area where we have;

The longest straight line is five cups the next on either side are four cups and the final line on either side has three cups

The total number of cups = 3 + 4 + 5 + 4 + 3 = 19 cups

The total number of cups = 19 cups.

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