Please Solve this, it would be extremely helpful for me.
[tex]{\tt{\fbox{\red{Trigonometry}}}}[/tex]

In the figure given below,

AB ll EF ll CD. If AB = 22.5 cm,

EP = 7.5 cm, PC =15 cm and

DC = 27 cm. Calculate:

(i) EF (ii) AC

​

Answer:

[tex]120^{0}[/tex]

Step-by-step explanation:

Given: pentagon (5 sided polygon), two interior angles = [tex]90^{0}[/tex] each, other three interior angles are congruent.

Sum of angles in a polygon = (n - 2) × [tex]180^{0}[/tex]

where n is the number of sides of the polygon.

For a pentagon, n = 5, so that;

Sum of angles in a pentagon = (5 - 2) × [tex]180^{0}[/tex]

                                                = 3  × [tex]180^{0}[/tex]

                                                = [tex]540^{0}[/tex]

Sum of angles in a pentagon is [tex]540^{0}[/tex].

Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;

[tex]540^{0}[/tex] - (2 × [tex]90^{0}[/tex])  = [tex]540^{0}[/tex] - [tex]180^{0}[/tex]

                       = [tex]360^{0}[/tex]

So that;

the measure of the interior angle = [tex]\frac{360^{0} }{3}[/tex]

                                                        = [tex]120^{0}[/tex]

The measure of one of its three congruent interior angles is [tex]120^{0}[/tex].

Answer:

Question 2;

A. 25·x²·y²²

Question 3;

f(g(x)) = 4·x, represents the amount Aurora earns per hour

Step-by-step explanation:

Question 2;

(5·x·y⁵)²(y³)⁴ = (25×x²×y¹⁰)×y¹²

(25×x²×y¹⁰)×y¹² = 25×x²×y¹⁰⁺¹² = 25×x²×y²²

Therefore, the correct option is A. 25·x²·y²²

Question 3;

The given functions are;

The function f(x) = 0.5·x is the earnings of Aurora per ticket sold

The function g(x) = 8·x is the number of tickets Aurora sells per hour

Therefore, we have;

f(g(x)) = 0.5 × g(x) = 0.5 × 8·x = 4·x

The value of the function of a function f(g(x)) = 4·x, represents the amount Aurora earns per hour.

Answer:

Step-by-step explanation:

[tex]\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4[/tex]

put x=7 in the given equation

[tex]\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7[/tex]

which is true .

∴ x=7 is a solution of the given eq.

now put x=4 in the given eq.

[tex]\sqrt{4-3} +5=7\\1+5=7\\6=7\\[/tex]

which is not true.

∴x=4 is an extraneous solution.

Answer:

Perimeter: 88m

Step-by-step explanation:

Area of the square plot = (Side) X (Side)

And we are given the area is 484m²,

therefore, (Side) X (Side) = 484m²

or,

(Side)² = 484, taking square root on both the sides,

[tex]\sqrt{(Side)^{2} }[/tex] = [tex]\sqrt{484}[/tex]

Side = 22m.

And we know that, perimeter of a square is = 4 X (Side)

Therefore, Perimeter = 4 X 22 = 88m

:-)

Answer:

88m

Step-by-step explanation:

Area = 484m^2

A= s^2

484= s^2

s=[tex]\sqrt{484}[/tex]=22m

∴22m=s

⇒So, Perimeter= 4a=22*4= 88m

Answer:

[tex]\huge\boxed{f = 5\ Hz}[/tex]

Step-by-step explanation:

Given:

Time period = T = 0.2 sec

Required:

Frequency = f = ?

Formula:

f = 1/T

Solution:

f = 1/0.2

f = 5 Hertz

Answer:

[tex] \boxed{\sf Frequency \ (f) \ of \ the \ wave = 5 \ Hz} [/tex]

Given:

Time Period (T) = 0.2 s

To Find:

Frequency (f) of the wave

Step-by-step explanation:

[tex] \sf Frequency (f) = \frac{1}{Time Period (T)} [/tex]

[tex] \sf f = \frac{1}{0.2} [/tex]

[tex] \sf f = \frac{1}{0.2} \times \frac{10}{10} [/tex]

[tex] \sf f = \frac{10}{2} [/tex]

[tex] \sf f = \frac{ \cancel{2} \times 5}{ \cancel{2}} [/tex]

[tex] \sf f = 5 \: Hz[/tex]

Answer:

This is multiplicative identity in which 4✖️1=4

Step-by-step explanation:

Hope it will help you:)

Answer:

The product renders: [tex]-9-7\,i[/tex]

Step-by-step explanation:

Recall that the product of the imaginary unit i by itself renders -1

Now proceed with the product of the two complex numbers using distributive property:

[tex](1-5\,i)\,(1-2\,i)=1-2\,i-5\,i+10\,i^2=1-7\,i-10=-9-7\,i[/tex]

Answer:

64

Step-by-step explanation:

khan acadamy

Answer:

64

Step-by-step explanation:

Answer:

The probability of friend A winning with HH = 1/4.

Step-by-step explanation:

The probability of an event, A is P(A) given by the relationship;

P(A) = (The number of required outcome)/(The number of possible outcomes)

The parameters given are;

The condition of friend A winning = Coin toss sequence HH shows up

The condition of friend B winning = Coin toss sequence TH shows up

The number of possible outcomes = TT, TH, HH, HT = 4

(TH and HT are taken as different for the game to be fair)

The number of required outcome = HH = 1

Therefore;

The probability of friend A winning with HH = 1/4.

Answer:

-17.3

Step-by-step explanation:

To solve for x, we can divide both sides by -3:

x = -52 / 3 which = -17.3

Answer:

Step-by-step explanation:

[tex] \sf{ - 3x = 52}[/tex]

Divide both sides of the equation by -3

⇒[tex] \sf{ \frac{ - 3x}{ - 3} = \frac{52}{ - 3} }[/tex]

Calculate

⇒[tex] \sf{x = - 17.33}[/tex]

Hope I helped!

Best regards!!

Answer:H2+Br2-->2HBr

Step-by-step explanation:

The amount of atoms on the left side must be equal to the amount of atoms on the right side for each element.

On the left you got 2xH and 2xBr.

This means you must have the same amount on the right.

2HBr =2xH + 2xBr

Answer:-80

Step-by-step explanation:f(x)=2*2+4*-10

Answer:

420

Step-by-step explanation:

We need to find the LCM of 1, 2, 3, 4, 5, 6 and 7. The LCM of 1, 2, and 4 is 4 and the LCM of 3 and 6 is 6 so the list becomes the LCM of 4, 5, 6 and 7. The LCM of 4 and 5 is 20, the LCM of 20 and 6 is 60 and the LCM of 60 and 7 is 420.

Answer:

420

Step-by-step explanation:

Prime factorization:

7 = 7

6 = 2 × 3

5 = 5

4 = 2 × 2

3 = 3

2 = 2

1 =  1

LCM: 7, 6, 5, 4, 3, 2, 1

2 × 2 × 3 × 5 × 7  = 420

Answer:

The missing value is -9

Step-by-step explanation:

Given

[tex]-7 = _ -(-2)[/tex]

Required

Determine the missing value

Represent _ with a variable

[tex]-7 = x -(-2)[/tex]

Open the bracket

[tex]-7 = x -1*-2[/tex]

[tex]-7 = x + 2[/tex]

Subtract 2 from both sides

[tex]-7 - 2 = x + 2 - 2[/tex]

[tex]-9 = x[/tex]

Reorder

[tex]x = -9[/tex]

Hence, the missing value is -9

Answer:

The answer is 4=−2+6

Step-by-step explanation:

I checked on khan

Answer:

i dont know if you want me to solve for m

Step-by-step explanation:

Let's solve for m.

Answer:

x² + 4x + 4 = 0

Step-by-step explanation:

x² + 4x + 4 = 0

( x + 2 )² = 0

x + 2 = 0

x = -2

x² + x = 0

x ( x + 1 ) = 0

x = 0 or x = -1

x² - 1 = 0

x² = 1

x = 1 or x = -1

Answer:

9

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

We will use x instead of theta

● cos^2 x *(1+tan^2x)

We khow that: 1+ tan^2 x = 1/cos^2 x

Replace 1+tan^2 x by the new expression

● cos^2 x (1/cos^2 x)

● cos^2x/ cos^2 x

● 1

Answer:

M contains 3,4,7,9

M bar is 2 ,5 ,6 ,8

Step-by-step explanation:

The set for M is what is in the circle labeled M

M contains 3,4,7,9

The question in the picture asks for M bar which is what is not contained in M

M bar is 2 ,5 ,6 ,8

2+3i, x=2−3

Explanation:

Answer:

Scouts are on the third side in the sense they are running

Step-by-step explanation:

A regular hexagonal shape of perimeter 270 has each side of                 270/6 = 45  

Let´s call d  the run distance  then

d = 2/5 * 270      d = 108 m

We don´t have fig 9 available therefore if  X is a vertex in the hexagon or at the middle point of one side, scouts are 108 m from the starting point which means they had run 2,4 sides of the hexagon. If X is not either a vertex or a middle point of a side then, we have two solutions for the question depending on the sense the scouts took when began the run (clockwise or counterclockwise)

Answer:

  sin(θ) = (2/5)√6

Step-by-step explanation:

The sine and cosine are related by the formula ...

  [tex]\sin{(\theta)}^2+\cos{(\theta)}^2=1\\\\\sin{(\theta)}=\pm\sqrt{1-\cos{(\theta)}^2}[/tex]

Filling in the given value for cos(θ), we find the sine to be ...

  [tex]\sin{(\theta)}=\pm\sqrt{1-\left(\dfrac{1}{5}\right)^2}=\pm\dfrac{\sqrt{24}}{5}=\pm\dfrac{2}{5}\sqrt{6}[/tex]

__

The cosine function is positive for angles in both the first and fourth quadrants. The restriction on θ tells us this is a first-quadrant angle. The sine is positive in the first quadrant, so the desired value is ...

  sin(θ) = (2/5)√6

Hey there! I'm happy to help!

to find the volume of a sphere, you cube the radius, multiply it by 4/3, and then multiply it by π.

First, we have to find the radius. To find the surface area you square the radius and multiply it by 4 and then π.

Let's do that formula backwards on our surface area to find the radius.

We divide by π

100÷π=100

We divide by 4.

100÷4=25

We find the square root.

√25=5

Now, we use our radius in the volume formula.

5³=125

125×4/3=500/3

We multiply by π.

500/3π

Therefore, the volume of a sphere if its surface area is 100π ft² is 500/3π ft³.

Have a wonderful day! :D

Answer:

V=166.66[tex]\pi[/tex] ft³

Step-by-step explanation:

The surface area of a sphere is 4[tex]\pi[/tex]r²

100[tex]\pi[/tex]=4

100[tex]\pi[/tex]/4

25=r²

r=5

Now that we know the radius is 5, we can find the volume.

v=4/3[tex]\pi[/tex](5)³

v=(5*5*5*4)/3*[tex]\pi[/tex]

V=166.66[tex]\pi[/tex]

Answer:

Step-by-step explanation:

Amount charges by plumber =  £ 167.00

Call out fee = £ 18.50

Charge excluding the call out fee = 167 - 18.50 = £ 148.50

Total hours worked = 9 hours

Charge per hour = charge excluding the call out fee ÷ total hours

                           = 148.50 ÷ 9

                          = £ 16.50

Answer: Line EF=2

Step-by-step explanation: 11 minus 9 is equal to 2. So line EF is equal to 2.

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:

Answer:

$2 per pound = $0.125. per pound

Step-by-step explanation:

The unit of weight conversion from pound to ounce is given as follows;

1 pound weight  = 16 ounces weight

1 ounce weight = 1/16 pound weight

Therefore, whereby the cost of 1 pound weight of an item is two dollars, we have;

The cost of one ounce weight of the item will be the cost of 1 pound weight, divided by 16 and given as follows;

$2 per pound = $2/16 per pound  = $0.125. per pound

Therefore;

$2 per pound = $0.125. per pound.

Answer:

Sine, Cosine and Tangent are  main functions used in Trigonometry .

They  are based on a Right-Angled Triangle.

It helps to give a name to each side of a right triangle:

"Opposite" ;  side opposite to the angle θ

"Adjacent"; side adjacent (next to) to the angle θ,

"Hypotenuse" ; the longest side

Step-by-step explanation:

Sine, Cosine and Tangent (are often shortened as sin, cos and tan)

They are used in calculation by;

[tex]Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Cos \alpha = \frac{Adjacent}{Hypotenuse}\\ \\Tan \alpha = \frac{Opposite}{Adjacent}[/tex]

To remember how to apply them , we use

SOHCAHTOA

soh

cah

toa