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.

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

The probability of getting prime number is 2/7.

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:

https://brainly.com/question/11234923

#SPJ2

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:

https://brainly.com/question/30398551

#SPJ6

Answer:

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

Answer:

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

Step-by-step explanation:

took the test

Answer:

2.5 hours

Step-by-step explanation:

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

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.

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.

Answer:

90000

Step-by-step explanation:

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!

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

Answer:

1

Step-by-step explanation:

2 /9÷   6/ 27=1

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.

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]

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

Answer:

The Q³ of this data set is 9.5

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!

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)

If there is no more informations, then:

Answer: They were able to use 665 pencils

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

                  Give Brainliest please :)

Answer:

ithink its a or c

Step-by-step explanation:

not sure but dang what grade u in??

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

Answer:3x-x+2=4

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

Answer: 148

Step-by-step explanation:

180-32 = 148

B=C

P=X

Answer:

x = 148 degrees

Step-by-step explanation:

180 - 32 = 148

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.

Answer:

the answer wouldbe 8585434930.123

Step-by-step explanation: