Match each trigonometric function with its right triangle definition. Note that opp = side opposite Angle A, adj = side adjacent to Angle A, and hyp = hypotenuse.

1. hyp/opp
2. hyp/adj
3. opp/adj
4. adj/hyp
5. adj/opp
6. opp/hyp

a. sec A
b. cot A
c. sin A
d. tan A
e. csc A
f. cos A​

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AI = 32,36 m

IE = 30,78 m

Explication étape par étape:

Utilisation de Pythagore:

Cosθ = adjacent / hypoténus

AI = hypoténus

θ = 72 °

Adjacent = 10 m

Cos 72 = 10 / AI

0,3090169 = 10 / AI

AI = 10 / 0,3090169

AI = 32,36 m

De la trigonométrie;

IE = opposé

Adjacent = 10m

Tanθ = opposé / adjacent

Tan 72 = IE / 10

IE = Tan 72 * 10

IE = 3,0776835 * 10

IE = 30,78 m

Answer:

20.5

Step-by-step explanation:

AB= Sqare root of 15^2 + 14^2

USe pythagoras' theorum

Answer:

B: 60,000

Step-by-step explanation:

Since there was a total of 200,000 votes, we can create this equation, since we also know the ratio between the two candidates:

7x + 3x = 200,000

x can be seen as a common factor between the two candidates that can be used to express their difference

We can now further simplify this equation by combining like terms and solving for x:

10x = 200,000

x = 200,000/10

x = 20,000

Now, to find the total number of votes cast for Bob Tanks, we multiply x by 3, since it says that Julie Sanders won by a ratio of 7:3, which means she had 7 in the ratio and Bob had the 3.

3x = 3(20,000) = 60,000

The answer is B: 60,000.

Answer: 60,000

Step-by-step explanation:

The easiest way to solve this problem is to use equations

Since we know the ratio of Julie's votes to Bob's votes is 7:3 and the total is 200,000 we can use this equation 200,000 (number of votes)  = 7x(Julie's votes) + 3x(Bob's votes)

After you solve it you get x=20,000

Then,

You put that back into Bob's votes and you get 60,00

Hope this helps :)

Answer:

(8, 10)

Step-by-step explanation:

He is at (11, 12). He moves three to the left, so 11 - 3 = 8. He then moves two down. 12 - 2 = 10. Therefore, he is at point (8, 10).

Answer:

4 bags will be required.

Step-by-step explanation:

Patio is in the shape of a parallelogram.

Formula for the area of a parallelogram is,

Area = [tex](\text{Base})(\text{Height})[/tex]

        = 16.2 × 12

        = 194.4 square feet

∵ 50 square feet area is covered by 1 bag of concrete mix.

∴ 1 square feet area will be covered by [tex]\frac{1}{50}[/tex] bag of concrete mix

∴ 194.4 square feet patio will require the concrete mix = [tex]\frac{194.4}{50}[/tex]

                                                                                           = 3.888

                                                                                           ≈ 4 bags

Therefore, 4 bags of concrete mix will be required by Dave to add a new patio.

Answer:

The statue is 22ft tall.

Step-by-step explanation:

Here we will have two similar triangle rectangles.

One is made between the girl's feet, the mirror, and the girl's eyes.

So in this case the catheti are:

the distance between the girl and the mirror (3 m) and the height of the girl (5.5 ft)

The other triangle rectangle has the vertices:

The mirror, the base of the statue, and the top of the statue.

Such that the catheti of this triangle are the distance between the base of the statue and the mirror (12m) and the height of the statue (we want to know this, let's call this X for the moment).

Because the triangles are similar, this means that there is a proportionality constant between each correspondent side, let's call this k.

Then the distance between the girl and the mirror must be k times the distance between the base of the statue and the mirror:

3m = k*12m

And the height of the girl must be k times the height of the statue.

5.5ft = k*X

You can see that we have different units, this does not matter because k is a dimensionless constant.

With the first equation we can find the value of k

3m = k*12m

3m/12m = k

(3/12) = 1/4 = k

Now we can replace this in the other equation to get:

5.5ft = (1/4)*X

Solving this for X we get:

(5.5ft)*4 = X

22ft = X

The height of the statue is 22ft.

Answer:

the probability of not winning is 0.9946

Step-by-step explanation:

The computation of the probability of not winning is shown below:

The Probability of winning is

= 7 ÷ 1302

So, the probability of not winning is

= 1 - 7 ÷ 1302

= (1302 - 7) ÷ 1302

= 1295 ÷ 1302

= 165 ÷ 186

= 0.9946

Hence, the probability of not winning is 0.9946

The same is considered

Answer:

20, 90 and 100

Step-by-step explanation:

Total number of statues = 210

Assuming that a large statue = x, medium statue = y and a small statue = z

Then, x + y + z = 210........i

Also, we're told that the monthly cost is $760, so

5x + 4y + 3z = 760.........ii

Cost of selling is $3640, so then

26x + 18y + 15z = 3640.........iii

Solving i and ii simultaneously, we have

5x + 5y + 5z = 1050

5x + 4y + 3z = 760

Subtracting, we have

y + 2z = 290.........iv

Again, solving ii and iii simultaneously, we have

130x + 104y + 78z = 19760

130x + 90y + 75z = 18200

On subtracting, we have

14y + 3z = 1560.........v

And finally, solving iv and v simultaneously, we also have

14y + 28z = 4060

14y + 3z = 1560

On subtracting,

25z = 2500

z = 2500 / 25

z = 100

Substituting for z = 100 in iv, we have

y + 2(100) = 290

y + 200 = 290

y = 290 - 200

y = 90

Substituting for y = 90, and z = 100 in i

x + 90 + 100 = 210

x + 190 = 210

x = 210 - 190

x = 20

Therefore, large statues has to be 20, medium statues has to be 90, and small statues has to be 100

Answer:

16%

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

None of the angles in the two triangles match, so it is impossible for them to be congruent.

Answer:

Your answer would be:

[tex]x=6[/tex]

Step-by-step explanation:

[tex]5x + 30 = 110[/tex]

[tex]5x + 30 - 30 = - 30[/tex]

[tex]5x = 80[/tex]

[tex]x = 16[/tex]

Hope this helped! UwU

Answer:

$405,44

Step-by-step explanation:

Equation: 499.99 - (499.99 x 15/100) - 1/10[499.99-(499.99 x 15/100)] + 6/100{1/10[499.99-(499.99 x 15/100) = x

Steps: x = (15 x 499.99)/100 = $74.9985

499.99 - 74.9985 = $424,9915

x = (424,9915 x 10)/100 = $42,49915

424,9915 - 42,49915 = $382,49235

x = $22,949541

382,49235 + 22,949541 = $405,441891

That can be rewritten as $405,44.

I hope that helped :)

Answer:

a) 20[tex]\sqrt{35}[/tex]

b) 7[tex]\sqrt{5}[/tex]

c) 18[tex]\sqrt{2}[/tex]

d) 5[tex]\sqrt{2}[/tex]

e) 36[tex]\sqrt{3}[/tex]

f) 72

g) 10[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

492.87cm^3

Step-by-step explanation:

Given data

Diameter= 4.9cm

The expression for the volume is

V= 4/3 πr^3

Substitute

V= 4/3*3.142*4.9^3

V= 4/3*3.142*117.649

V=1478.612632 /3

V=492.87 cm^3

Hence the volume is 492.87cm^3

Answer:

it would be 9 cause with start counting the 7- to 2 its gonna be nine

Step-by-step explanation:

Answer: 50

Step-by-step explanation:

400 ÷ 8 = 50

Answer:

50 or A

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Answer: the tip you should leave is 4.2

14 is 0.04

do 0.04 times 30 and you get 4.2 which is 14 % of 30

Step-by-step explanation:

A mortgage loan is termed as a loan that is used to purchase or maintain a home, land or other pieces of real estate.

The borrower agrees to repay the amount of loan to the lender over a period of time, usually in a series of regular installments divided into principal and interest. The property is used as security for the loan.

Calculation of the amount of mortgage is as follows:

[tex]\text{Interest}= \text{Mortgage amount} \times\frac{0.05}{12}\times3[/tex] = 1875

[tex]\text{Principal Pay }= 1000 \times3[/tex] = 3000

Total amount paid = Interest + principal pay = 1875 + 3000 = 4875

Initial balance = 150000

The remaining balance for the mortgage amount = initial balance - the total amount paid.

Amount of mortgage = $ 145125.

Therefore the closest to the mortgage balance after 3 months of payments is

(1) $145,165.

To know more about the calculation of the mortgage amount, refer to the link below:

https://brainly.com/question/24913140

Answer:

hey it is 15.71 thanks for points

Answer:

36

Step-by-step explanation:

.4 x 90

Answer:

36

Step-by-step explanation:

40/100 = x/90

100x div 100         3600div 100

             x  =  36

Answer:

if you wanted it in equation form the it'll be :  9 < 4 x n = 15

~ i hope this has helped you out, have a gr8 day/night my friend!~

Step-by-step explanation:

Answer:

Six / 6

Step-by-step explanation:

Fifteen less than 4 times a number is 9, meaning we have to find the number.

Let the required number be x

4 times the number = 4x

15 less than 4 times the number = 4x-15

⇒ 4x – 15 = 9

⇒ 4x = 9 + 15

⇒ 4x = 24

⇒ x = 6

meaning the number is 6.

Hope this helps!

Answer:

b. 0.25

Step-by-step explanation:

40 + 120 = 160

40 / 160

Answer:

6 e (*2)x

Step-by-step explanation:

i hope this helps and the 2 is a square unit

Answer:

y = 0

Step by step explanition:

Answer: x=10; y=-1

Step-by-step explanation:

To solve this via elimination:

get rid of the y's like this:

4x+2y=38 + 2x-2y=22

6x=60

x=10

20-2y=22

y=-1

The value of x which is included in terms of both the angles ∠PRM and ∠NRP is given by: Option  D: x = 18

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

Here, we're specified that:

They are adjacent and line segments MR and RN are forming a straight line MN, so these angles are supplementary. That means:

(7x -11)° +  (4x -7)° = 180°

Opening the brackets, and solving in terms of magnitude, we get:

[tex]7x - 11 + 4x -7 = 180\\11x - 18 = 180\\11x = 180+18 \\\\x = \dfrac{198}{11} = 18[/tex]

Thus, the value of x which is included in terms of both the angles ∠PRM and ∠NRP is given by: Option  D: x = 18

Learn more about supplementary angles here:

https://brainly.com/question/2882938