1 .9 times 42 .5
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Answer:  see proof below

Step-by-step explanation:

Use the Cofunction Identity: sin (90 - A) = cos (A)

Use the Double Angle Identity: sin(2A) = 2 sinA cosA

Use the Triple Angle Identity: cos (3A) = 4cos³A - 3cosA

Use the Zero Product Property: If a · b = 0, then a = 0 or b = 0

Use Pythagorean Identity: cos²A + sin²A = 1  → cos²A = 1 - sin²A

Use Quadratic Formula:   [tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Proof LHS → RHS:

Assumption:                 Let A = 18°

Multiplication:               then 5A = 5(18°)

                                         →   5A = 90°

Expand:                         2A + 3A = 90°

                                  →  2A = 90° - 3A

Apply sin:                  sin (2A) = sin (90° - 3A)

Cofunction:               sin (2A) = cos (3A)

Double Angle:          2 sinA cos A = cos (3A)

Triple Angle:             2 sin A cos A = 4cos³A - 3cos A

                             → -4cos³A + 3cos A + 2sinA cos A = 0

Factor:                      cos A(-4cos² A + 3 + 2sin A) = 0

Zero Product Property: cos A = 0    or   -4cos² A + 3 + 2sin A = 0

                                             ↓

                                     Disregard (since cos A ≠ 0)

Pythagorean:                                           -4cos² A + 3 + 2sin A = 0

                                                            →  -4(1 - sin² A) + 3 + 2sin A = 0

                                                           →   -4 + 4sin² A + 3 + 2sin A = 0

Simplify:             4sin² A + 2sin A - 1 = 0

                      a=4         b=2      c= -1

[tex]\text{Quadratic Formula:}\qquad \sin A=\dfrac{-(2)\pm \sqrt{2^2-4(4)(-1)}}{2(4)}[/tex]

                                              [tex]=\dfrac{-2\pm \sqrt{4+16}}{8}[/tex]

                                              [tex]=\dfrac{-2\pm \sqrt{20}}{8}[/tex]

                                              [tex]=\dfrac{-2\pm 2\sqrt{5}}{2(4)}[/tex]

                                             [tex]=\dfrac{-1\pm \sqrt{5}}{4}[/tex]

                                             [tex]=\dfrac{ \sqrt{5}-1}{4}[/tex]

[tex]\text{Substitute A = 18:}\qquad \sin 18=\dfrac{ \sqrt{5}-1}{4}[/tex]

Answer:

(14,12)

Step-by-step explanation:

Answer:

144cm^2

Step-by-step explanation:

This is a cube which means it has 6 sides

The dimensions of one side is 5cm by 5cm

So the area of one side is 5*5=25cm

25cm * 6 sides = a total surface area of 144cm^2

Hope this helps! :)

Answer:

MNO ~ OPQ by AAA (Angle angle angle)

Step-by-step explanation:

1. angle POQ is equal to angle NOM because they are both vertical angles

2. angle OPQ and angle OMN are equal because parallel lines cut by a transversal form congruent alternate interior angles.

3. angle PQO and angle ONM are equal becase of the same reason as reason 2 (parallel lines cut by a transversal form congruent alternate interior angles. )

4. triangles MNO ~ OPQ through AAA (angle angle angle)

Answer:

Step-by-step explanation:

13.05

Answer:

13.05

Step-by-step explanation:

Answer:

The answer should be 273

Answer:

The value of the expression for x=3 is 51

Step-by-step explanation:

Evaluating expressions

To evaluate a given expression, we simply substitute the value of the variables and complete the operations.

The expression to evaluate is:

P=3(2+5x)

We will evaluate for x=3:

P=3(2+5*3)

The product must be done first:

P=3(2+15)=3*17=51

The value of the expression for x=3 is 51

The number of apple in each basket is as follows:

First basket = 25 apples

Second basket = 37 apples

Third basket = 16 apples

Fourth basket = 29 apples

Fifth basket = 13 apples

total apples = 120

let

the number of apples in the first basket = a

the number of apples in the second basket = b

the number of apples in the third basket = c

the number of apples in the fourth basket = d

the number of apples in the fifth basket = e

Therefore,

a + b = 62

b + c = 53

c + d = 45

d + e = 42

a + b + c + d + e = 120

62 + 45 + e = 120

e = 120 - 62 - 45

e = 13

d = 42 - 13

d = 29

c = 45 - 29

c = 16

b = 53 - 16

b = 37

a = 62 - 37

a = 25

Therefore,

the number of apples in the first basket = 25

the number of apples in the second basket = 37

the number of apples in the third basket = 16

the number of apples in the fourth basket = 29

the number of apples in the fifth basket = 13

learn more on algebra here: https://brainly.com/question/21318615

Answer:

75

Step-by-step explanation:

angles on a straight line always add up to 180 degrees so 180-105 =75

Answer:

The larger fish weigh 231 pounds and the smaller fish weigh 77 pounds

Step-by-step explanation:

Here is the complete and correct question:

A fish market bought two swordfish at a rate of $12 per pound. The cost of the larger fish was three times as great as the cost of the smaller fish. The total cost of the two fish was $3,696. How much did each fish weigh?

Step-by-step explanation:

Let the cost of the larger fish be x, and the cost of the smaller fish be y.

From the question,

The cost of the larger fish was three times as great as the cost of the smaller fish, that is

x = 3y

Also, from the question,

The total cost of the two fish was $3,696, that is

x + y = $3,696

Since x = 3y, we can write that

3y + y = $3696

Now, we can determine y

3y + y = $3696

4y = $3696

y = $3696/4

y = $924

Hence, the cost of the smaller fish is $924

From x = 3y; we can determine x

y = $924

∴ x = 3y becomes

x = 3 × $924

x = $2772

Hence, the cost of the larger fish is $2772

Now, to determine how much each fish weigh,

From the question, A fish market bought two swordfish at a rate of $12 per pound

To determine the weight of each fish, we will divide the cost by the rate ($12 per pound)

For the larger fish

Cost = $2772

∴ Weight = $2772 ÷ $12 per pound = 231 pounds

Hence, the larger fish weigh 231 pounds.

For the smaller fish

Cost = $924

∴ Weight = $924÷ $12 per pound = 77 pounds

Hence, the smaller fish weigh 77 pounds.

Price per hour of first case :

[tex]P_1 = 24 + 9a[/tex] ( Here, a is number of hours )

Price per hour of second case :

[tex]P_2 = 18 + 11b[/tex] ( Here, b is number of hours )

Let, after x hours both company charges the same.

[tex]P_1=P_2\\\\24+9x = 18 + 11x\\\\2x=6\\\\x = 3\ hours[/tex]

Hence, this is the required solution.

Answer:

3.4

Step-by-step explanation:

both angles are equal, i.e 16x - 9 = 45.

the value of x is 3.375

Answer:

The value of x is 9.

Step-by-step explanation:

i used the equation (16x-9) + 45 = 180

1. i added -9 +45 i got 36

2. 16x + 36 = 180

3. i subtract 36 from 36 and 180

4. 16x=144

5. i divide 16 from 16x and 144

6. x=9

I hope this helped! :)

Answer:

she has 12 - D quarters.

She has 24 (12-D) cents in quarters

Step-by-step explanation:

You know that the number of coins, and you know the number of dimes - even if the amount is a variable - you can find the amount of quarters with an equation.

If you knew that Lina had 6 dimes instead of D, you would say 12 - 6 and get the number of quarters. You can do the same thing here.

and If you know Lina has 6 quarters, you could find the amount of money in cents by multiplying 6 by 25. You can do that here too, but with variables and an equation.

Answer:

she has 12 - D quarters.

Step-by-step explanation:

Answer: NO it is not a unit rate

Step-by-step explanation:

No, a unit rate is the amount for 1 item or unit. and 1/ 1/3, 1/3 is on the bottom

1/3≠1 so no

Answer:

trapezoid

Step-by-step explanation:

since the figure has only 1 pair of parallel sides then it is a trapezoid

Answer:

rhombus

Step-by-step explanation:

Answer:

100 people.

Step-by-step explanation:

25% of 400

= 0.25 * 400

= 100.

Answer:

16

Step-by-step explanation:

844.80 ÷ 52.80

Answer:

$0.25 for 1 juice box

Step-by-step explanation:

Divide $2.00 by 8

The answer is 0.25

Hope I helped :)

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The unit price of each box will be $0.25 per box.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

It costs $2.00 for eight juice boxes.

The unit rate is given by the division of the numbers 2 and 8. Then the units rate is given as,

Rate = $2 / 8

Rate = $0.25 per box

The unit price of each box will be $0.25 per box.

More about the rate link is given below.

https://brainly.com/question/14731228

#SPJ2

Answer:

Step-by-step explanation:

Hope this helps! <3

Answer: 16/24

Step-by-step explanation:

Answer:500

Step-by-step explanation:

√250000=500

Answer:

[tex] \sqrt{250000} \\ \sqrt{500} \times \sqrt{500 } \\ { \sqrt{500 } }^{2} \\ 500[/tex]

Thank you ☺️☺️

The sides RS and ST are equal because they are the side of the congruent triangle that is RS ≅ ST. Then the correct option is D.

It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

In circle Q, ∠RQS ≅ ∠SQT.

In ΔRQS and ΔTQS

∠RQS ≅ ∠SQT (Given)

QS = QS (Common side)

RQ = QT (Radius of the circle)

The ΔRQS and ΔTQS triangles are congruent to each other. That is given as ΔRQS ≅ ΔTQS.

The sides RS and ST are equal because they are the side of the congruent triangle that is RS ≅ ST. Then the correct option is D.

More about the circle link is given below.

https://brainly.com/question/11833983

Answer:

D. rs≅st

Step-by-step explanation:

i did it

Answer:

corey can wash 48 dogs in 8 hours

Step-by-step explanation:

we know  that he can wash 12 dogs in 2 hours. we need to know how many dogs he can wash in 1 hour, to do that we take the 12 dogs divided by 2 hours

12/2 = 6 dogs

he can wash 6 dogs in 1 hour

to find out how many dogs he can was in 8 hours you take number of dogs  per hour times amount of time given.

6dogs * 8 hours= 48 dogs

Answer:

discount = 25%

Step-by-step explanation:

discount is calculated as [tex]\frac{reduction}{original}[/tex] × 100%

reduction = 2800 - 2100 = 700

discount = [tex]\frac{700}{2800}[/tex] × 100%  = 0.25 × 100% = 25%