choose the appropriate postulate of the following pair lf triangles are congruent.

(i) 3 csc²(x) - 4 = 0

3 csc²(x) = 4

csc²(x) = 4/3

sin²(x) = 3/4

sin(x) = ± √3/2

x = arcsin(√3/2) + 2nπ  or   x = arcsin(-√3/2) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ

where n is any integer. The general result follows from the fact that sin(x) is 2π-periodic.

In the interval 0 ≤ x ≤ 2π, the first family of solutions gives x = π/3 and x = 4π/3 for n = 0 and n = 1, respectively; the second family gives x = 2π/3 and x = 5π/3 for n = 1 and n = 2.

(ii) 4 cos²(x) + 2 cos(x) - 2 = 0

2 cos²(x) + cos(x) - 1 = 0

(2 cos(x) - 1) (cos(x) + 1) = 0

2 cos(x) - 1 = 0   or   cos(x) + 1 = 0

2 cos(x) = 1   or   cos(x) = -1

cos(x) = 1/2   or   cos(x) = -1

[x = arccos(1/2) + 2nπ   or   x = 2π - arccos(1/2) + 2nπ]   or   x = arccos(-1) + 2nπ

[x = π/3 + 2nπ   or   x = 5π/3 + 2nπ]   or   x = π + 2nπ

For 0 ≤ x ≤ 2π, the solutions are x = π/3, x = 5π/3, and x = π.

Answer:

t =3

Step-by-step explanation:

24t = 72

Divide each side by 24

24t/24 = 72/24

t=3

Answer:

A

Step-by-step explanation:

24 t = 72

divide both sides by 24

Thus, t = 72/24

t = 3

Bye ! :-)

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

Explanation:

Let x be the net winnings the customer gets

Saying something like x = 24 means you've walked away with $24. This occurs when you pay $1, and get $25 back in prizes, so 25-1 = 24 dollars overall.

The probability of this event occurring is 1/100 since there's only one ticket with the $25 prize

Make a table as shown below. It represents all the possible x values which are all the possible net winnings. Note how 1/100 = 0.01, 3/100 = 0.03 and 95/100 = 0.95

The third column is x*p(x) which is the product of the first two columns. Adding everything in the third column (that isn't highlighted in yellow) gets us the value -0.45 which is the expected value for the customer.

This represents a loss of $0.45, aka a loss of 45 cents. This is from the perspective of the customer.

Flipping things around, the pizza company will see this is as a gain of $0.45 or a gain of 45 cents.

----------------

Here's another way to see why this works:

The pizza company earns $100 in revenue since 100 tickets are sold for a dollar each. The company pays out 25+15+3*5 = 55 dollars in prizes overall. That means the company will make a profit of 100-55 = 45 dollars. So the average profit per ticket is 45/100 = $0.45 aka 45 cents and this is from the viewpoint of the pizza company (not the customer). The positive average profit represents a gain.

Answer:

What is the answer you're looking for?

Step-by-step explanation:

Answer:

b = 55

Step-by-step explanation:

The two angles add to 90 degrees

b+35 = 90

Subtract 35 from each side

b +35-35 = 90-35

b = 55

Answer:

90-35=55

Answer is D

Step-by-step explanation:

As evident, the line is bisecting the right angle. One side of the bisection is given as 35. Thus by deduction:

90-35=b

90-35=55

55=b

Answer:

this statement is true because then the triangles will be congruent by rhs axiom

Answer:

Step-by-step explanation:

343: = 7 * 7 * 7

x^9: = x^3 * x^3 * x * x * x = x^3 * x * √x

y^12: = y^6 * y^6

z^6: = z^3 * z^3

So the square root  is

√343 = 7 √7

√x^9 = x^4√x

√y^12 = y^6

√z^6 = x^3

The rule is for every pair of equal factors, you take one outside the root sign and throw the other one away.

So z^6 for example is z^3 * z^3 Take one of the pair outside the root sign and throw the other one away.

x^9 is rather tricky. You take x^4 out and there is still one x left over. You leave it under the root sign.

So the answer is

7  * x^4 * y^6 * z^3 * √7x

Answer:

14 (B)

Step-by-step explanation:

Area = L * h

L = 7 in^2

h = 2

Area = 7 * 2

Area = 14 in^2

Answer:

14

Step-by-step explanation:

Did lesson

It can save time from doing number crunching and analysis because it's an easy to see visual.

Answer:

A.

[tex] = > \: 2 \times {10}^{ - 3} [/tex]

Answer:

C = 1390

equation :

C=760+21g

Variables understanding

g = guest

c= cost

We are Finding C

If C is unknown

and c = 30.

C=760+21 x 30

C = 760+630

C = 1390

Answer:

1389

Step-by-step explanation:

hope this helps alot

Answer:

A

Step-by-step explanation:

The table represents a proportional function which has a rate of proportionality equal to 5

In fact

5:1 = 5

15 : 3 = 5

25 : 5 = 5

35 : 7 = 5

If we make 90 : 18, the result is 5, so this dates can be part of the table

Answer:

4th option is correct

Step-by-step explanation:

[tex]8 x - 4 = 6 - 3 x[/tex]

[tex]8x−4+3x=6[/tex]

[tex]11x−4=6[/tex]

[tex]11x=6+4[/tex]

[tex]11x=10[/tex]

Answer:

option 4 ,

x=10/11

is the answer of your question

explanation is attached below .

hope it is helpful to you

Answer:

The answer is (3 ,5)

Step-by-step explanation:

Please give brainliest!!!

Answer:

(3,5)

Step-by-step explanation:

order pair of A is (3,5)

3 is x component.

5 is y component.

Answer:

good question

Step-by-step explanation:

Answer:

The answer is "Option 5"

Step-by-step explanation:

Please find the complete question in the attached file.

Throughout the above output the regression equation is:

Delivery cost [tex]=0.469\times weight +9.617[/tex]

Answer:

592 Votes

Step-by-step explanation:

According to the Question,

                                 A        B       С

Candidates Votes     67      57     54

And, There are 1571 students in the school.

⇒(1571/178)×67

⇒591.33 ≈ 592 Votes(Approximately)

Answer:

She earned 1500 in interest

Step-by-step explanation:

10,000 × 0.03 × 5 = 1500

Your welcome :)

Answer:

47/60

Step-by-step explanation:

Find the LCM and multiply to get there.

LCM is 60

63/60-16/60

47/60

Answer:

-2

Step-by-step explanation:

The integer of - 2 is - 2 only as integers can be positive and negative whole numbers

Answer:

a

Step-by-step explanation:

1/2x-30aaaaaaaaaaaaaaaa

Answer:

10*9*8*7*6*5*4*3 = 10!/2 = 1814400 Cheers

Step-by-step explanation:

hope it works.

Answer:

answer in picture
c, b, d

Step-by-step explanation:

Answer:

b = 3.8

Step-by-step explanation:

- b/0.1 +2.9= -35.1

Subtract 2.9 from each side

- b/0.1 +2.9-2.9= -35.1-2.9

-b/.1 = -38

Multiply each side by -.1

-b/.1 * (-.1) = -38 *(-.1)

b = 3.8

Answer:

10 cups

Step-by-step explanation:

we can set up a proportion of cups of water over cups of apple juice

2/3 = w/15

if you cross-multiply you will get:

3w = 30

w = 30/3

w = 10

Answer:

a) G

b) C

Step-by-step explanation:

Triangle A is congruent to triangle G

Triangle D is congruent to Triangle C

Answer:

9 did not hit the bulls eye

Step-by-step explanation:

If 40% did hit the bulls eye, 100-40 = 60% did not hit the bulls eye

15 * 60%

15 *.6

9

9 did not hit the bulls eye

Answer:

Therefore, 9 darts did not hit the bull's-eye.

Step-by-step explanation:

Equivalent ratio states that the two ratios are express the same relationship between numbers

As per the given statement: Curtis threw 15 darts at a dashboard.

40% of his darts hit the bull's eye

then;

60 % of his darts did not hit the bull's eyes.

By definition of equivalent ratio;

x/15= 600/100

Multiply both sides by 15 we have;

x= 60/100 *15= 60*15/100= 900/100=  9 Darts