Angle α is acute such that cos α = 53
Angle β is obtuse such that sin β = 12
(a) Find the exact value of
(i) tan α
(ii) tan β
(b) Hence show that
tan(α + β) = (m rt3 − n) / (n rt3 + m)
where m and n are positive integers whose values are to be found.

Answers

Answer 1

Answer:

Do You have a picture?

Step-by-step explanation:


Related Questions

ASAPPPPP
Fill in the blank
When lit, a candle loses 5% of its original height every hour. Jennifer lit a candle with
an original height of 8 inches. Until the candle had been burning for at least _______ hours, the height of Jennifer's candle will be more than 7 inches.

Answers

Answer:

2.5 hours

Step-by-step explanation:

It would be 6.8 I did this earlier

What is the area of B

Answers

If there is no more informations, then:

A  =  ¹/₃(6 + x)

You pick a card at random. 4 5 6 6 7 8 9 )) What is P(prime)? Write your answer as a fraction or whole number.​

Answers

It’s 6....... bc just bc its 6

The probability of getting prime number is 2/7.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Outcome = 4, 5, 6, 6, 7, 8, 9.

Number of outcome = 7.

a) The prime numbers from the outcome are 5 and 7.

So, the probability of getting prime number

= 2/7

Hence, the probability is 2/7.

Learn more about Probability here:

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There were 8,454 pencils that were produced in the factory. When inspecting the pencils they noticed that 1,789 pencils were cracked. How many pencils were they able to use

Answers

Answer: They were able to use 665 pencils

Step-by-step explanation: You would simply do 8,454 - 1,789=665

                  Give Brainliest please :)

The diameter of a circle is 6 feet find its area to the nearest 10th

Answers

Answer:

The area of the circle is 113.0 ft²

Step-by-step explanation:

To solve this problem we need to use the area formula of a circle:

a = area

r = radius = 6ft

π = 3.14

a = π * r²

we replace with the known values

a = π * (6ft)²

a = π * 36ft²

a = 113.04ft²

The area of the circle is 113.04ft²

round to the nearest tenth

a = 113.04ft²  = 113.0 ft²

A rectangle has a perimeter of 60 inches and a length of 22 inches. What is the width of the rectangle?​

Answers

Answer:

8in

Step-by-step explanation:

I hope this helps. have a great dsy

Answer:

perimeter of a rectangle = 2( l+b )

perimeter = 60 inches

length = 22 inches

∴ width =

2 ( 22 + b ) = 60

22 + b = 60/2 = 30

22 + b = 30

b = 30 - 22 = 8 inches

∴ width = 8 inches

hope this answer helps you..

please mark as brainliest .. thank you!

1/7 done! Starting off strong! Let’s try and keep it up!

Answers

Answer: 148

Step-by-step explanation:

180-32 = 148

B=C

P=X

Answer:

x = 148 degrees

Step-by-step explanation:

180 - 32 = 148

What are the solutions for the given equation?
x^2+ 2x + 7 = 0

Answers

the solutions are 899-72 becuasee of the =o

Answer: 2 imaginary solutions

Step-by-step explanation:

x^2+2x+7=0

a=1, b=2, c=7

2^2-4*1*7

-24 (The discriminant is less than 0 , so the quadratic equation has 2 imaginary solutions)

Find the area of each sector. Use exact answers

Answers

Answer:

B) 54π in²

Step-by-step explanation:

area of full circle = πr² = 81π in²

area of 4π/3 segment = (81)(4π/3)/2π = 54π in²

The size and shape of a figure will stay the same after a translation is performed.
o True
o False

Answers

Answer: true

Step-by-step explanation:

True, because translation means just to move a figure, not to change a shapes's size, width, height, or any other property of the shape.

Help plz need answers less than 10 minutes

Answers

Answer:

the answer wouldbe 8585434930.123

Step-by-step explanation:

9. Plot A(8,-4), B(3, -4), C(7, 1), and D(7.-3) in a coordinate plane.
Then determine whether AB and CD are congruent.

Answers

Answer:

Just put it into Geogebra Classic. It's an app that really helps with this kinda stuff

The mass of an adult North Pacific right whale is about 70,000 kg, or 7 x 104
kg.
The mass of a male African elephant is about 7000 kg, or 7 x 103 kg.
About how many times more massive is the right whale than the African
elephant?

Answers

10 times more massive.

Can someone please help me
p.s. round to the nearest tenths

Answers

Answer:

Apothem:

radius is the same length as the base/length of each side of the hexagon.

r = 8

use pythagorean theorem to calculate the apothem

[tex]4^2+a^2=8^2\\\\16+a^2=64\\\\a^2=48\\\\a= 6.928[/tex]

≈ 6.9

Area

[tex]A = \frac{3\sqrt{3} }{2} *a^2\\\\=\frac{3\sqrt{3} }{2}(6.928)^2\\\\=124.7[/tex]

Find the area of each composite figure.
Round to the nearest TENTH if necessary.

Answers

The area of the composite figure is 54.

A poll asks shoppers at the mall how many cups of water they typically drink in a day. The results of the poll are listed below.
3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11
A five number summary was found. What is value of the 3rd quartile?
9

9.5

8

10

Answers

Answer:

The Q³ of this data set is 9.5

What are the solutions to the equation (10−x)(3x−9)=0?

Answers

Answer:

10−x)(3x−9)=0

−3x2+39x−90=0

−3(x−3)(x−10)=0

x=3 or x=10

The solutions to the equation (10 - x)(3x - 9) = 0 are x = 10 and x = 3.

Given that the equation (10 - x)(3x - 9) = 0

The factors will have the form (ax + b)(cx + d), where a, b, c, and d are constants.

To find values for a, b, c, and d such that (ax + b)(cx + d) is equal to 0

To determine the solutions of (ax + b)(cx + d),  equate each term to zero and solve for x which gives the solutions.

The two solutions of (ax + b)(cx + d) are -b/a and -c/d.

To find the solutions to the equation (10 - x)(3x - 9) = 0, set each factor equal to zero and solve for x.

Setting (10 - x) = 0 gives:

10 - x = 0

To isolate x, subtract 10 from both sides of the equation:

10 - x - 10 = 0 - 10

Simplifying gives:

-x = -10

Multiplying both sides by -1 to solve for x:

(-1)(-x) = (-1)(-10)

x = 10

So, one solution is x = 10.

Now, setting (3x - 9) = 0, gives:

3x - 9 = 0

To isolate x, we add 9 to both sides of the equation:

3x - 9 + 9 = 0 + 9

Simplifying gives:

3x = 9

Dividing both sides by 3 to solve for x:

(1/3)(3x) = (1/3)(9)

x = 3

Therefore, the second solution is x = 3.

The solutions to the equation (10 - x)(3x - 9) = 0 are x = 10 and x = 3.

Learn more about solving quadratic equations and factoring, click here:

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Cómo trazar Polígonos regulares utilizando material geométrico como la regla, compas y el graduador porfa ayuda

Answers

Answer:

En matemática, un polígono construible es un polígono regular que puede ser construido con regla y compás. Por ejemplo, un pentágono regular es construible con regla y compás mientras que un heptágono regular no lo es.En matemática, un polígono construible es un polígono regular que puede ser construido con regla y compás. Por ejemplo, un pentágono regular es construible con regla y compás mientras que un heptágono regular no lo es.

A house has increased in value by 35% since it was purchased. If the current value is 648,000, what was the value when it was purchased?

Answers

Answer:

Purchase rate of the house is $480000.

Step-by-step explanation:

Let the purchase rate of the house = $p

Current value of the house = $648000

If the current rate of the house has increased by 35% of the purchase rate,

Current rate = Purchase rate +  35% of the purchase rate

648000 = p + (35% of p)

648000 = p + [tex]p\times \frac{35}{100}[/tex]

648000 = p + 0.35p

648000 = (1.35)p

p = [tex]\frac{648000}{1.35}[/tex]

p = $480000

Therefore, purchase rate of the house is $480000.

one summer, the average price of a gallon of gas in Cleveland was $1.094 while the average price of gas in New York was 1.332. to the nearest penny (round to the nearest penny or hundredths) how much more did a gallon of gas cost in New York than in Cleveland?

Answers

Answer:

$0.24

Step-by-step explanation:

1.332 - 1.094 = 0.238

Answer: 0.24

It cost $0.24 more in New York, than in Cleveland

You can find the answer by subtracting the larger price from the smaller price like so

[tex]1.332 - 1.094= 0.238[/tex]

Since it says to round to the nearest hundredths

[tex]0.238[/tex] becomes [tex]0.24[/tex]

If this helped you a Brainliest would be much appreciated!

45 workers can complete a piece of work in 12 days.how many workers should be removed so that it takes 6 more days to complete the work

Answers

Answer:

90000

Step-by-step explanation:

I NEED HELP LIKE ASAP I NEED TO PASS THIS CLASS >:PILL GIVE 20 POINTS

Answers

Answer: (-2,4) to (2,-2)

go up 1 from the origin

then 2 to left since it’s -2

3 up since it’s 3

go up 1 from the origin

then 2 right since it’s 2

3 down since it’s -3

DaJuan has a photo that is 4 inches in width by 6 inches in length that
he wants to enlarge for his mother's birthday. The width of the enlarged
photo is 10.5 inches. What is the length of the enlarged photo?

please help if u can! thx

Answers

Answer:3x-x+2=4

Step-by-step explanation: source: (Too much work) srry

about liner equations!! please help with answer

Answers

Answer:

There are infinitely many solutions

Step-by-step explanation:

The expressions on both sides of the equation are the same, that is

[tex]\frac{1}{2}[/tex] (b + 14) is the same as [tex]\frac{b+14}{2}[/tex]

Thus the equation has infinitely many solutions

please help
Mofor and Shanice are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Mofor sold 12 small boxes of oranges and 3 large boxes of oranges for a total of $96. Shanice sold 6 small boxes of oranges and 6 large boxes of oranges for a total of $84. Find the cost each of one small box of oranges and one large box of oranges.​

Answers

Answer:

$6 = cost of small box

$8 = cost of large box

Step-by-step explanation:

Let s = cost of small box

     l  = cost of large box

(1)    12s + 3l = 96            (2)     6s + 6l = 84

    Multiply by -2                     -24s - 6l = -192

                                                -18s   = - 108

                                                     s = $6 = cost of small box

      12(6) + 3l = 96

         72 + 3l = 96

                 3l = 24

                   l = $8 = cost of large box

2/9 divided by 6/27 fill the box with a fraction that makes the equation true

Answers

Answer:

1

Step-by-step explanation:

2 /9÷   6/ 27=1

What was an effect of the Second Punic War?

ФCarthage remained a major trading center.
ФRome gained control over Sicily and Greece.
ФRome maintained control of Egypt and Spain.
ФCarthage became a major military rival to Rome.

please answer ASAP!!!!! I'm on a times unit test on edge please help ASAP!!!!!

Answers

Answer:

ithink its a or c

Step-by-step explanation:

not sure but dang what grade u in??

a. Find the value of x from given figure​

Answers

X = 45 , you have to look at the graph and notice it’s a 90 degree angle, then devide by 2 hahaha ik

Toby has made 298 goals out of 347 goals attempted.
About what percent of his attempts were successful?

Answers

Answer:

Convert fraction (ratio) 298 / 347 Answer: 85.878962536023% so round it up to 86%

Step-by-step explanation:

took the test

What is the area in square meters of the trapezoid below​

Answers

Given:

Bases of the trapezoid are 5.2 m and 14.6 m.

The height of the trapezoid is 7 m.

To find:

The area of the trapezoid.

Solution:

The area of a trapezoid is:

[tex]A=\dfrac{a+b}{2}\times h[/tex]

Where, a,b are bases and h is the height of the trapezoid.

Putting [tex]a=5.2,b=14.6,h=7[/tex] in the above formula, we get

[tex]A=\dfrac{5.2+14.6}{2}\times 7[/tex]

[tex]A=\dfrac{19.8}{2}\times 7[/tex]

[tex]A=9.9\times 7[/tex]

[tex]A=69.3[/tex]

Therefore, the area of the trapezoid is 69.3 square meters.

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