Write one solution to the inequality 7(3-x)>14. Explain your reasoning.​

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:

I will help you figure it out. Multiply all the numbers together: And you'll get; 21,120 in.

Hope this helps! Rate Brainiest!

-Aslina

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:

B

Step-by-step explanation:

(g - f)(x)

= g(x) - f(x)

= log(x - 3) + 6 - ([tex]\sqrt[3]{12x+1}[/tex] + 4)

= log(x - 3) + 6 - [tex]\sqrt[3]{12x+1}[/tex] - 4 ← collect like terms

= log(x - 3) - [tex]\sqrt[3]{12x+1}[/tex] + 2

Value of the given function[tex](g-f)x = log(x-3)-\sqrt[3]{12x+1} +2[/tex].

" Function is defined as the relation between the given variables is such that every input has exactly one output each."

According to the question,

Given functions are,

[tex]f(x) = \sqrt[3]{12x+1} +4\\\\g(x) = log(x-3) +6[/tex]

Substitute the value in the function (g -f)x we get,

[tex](g-f)x = g(x) -f(x)[/tex]

             [tex]= log(x-3) + 6 -( \sqrt[3]{12x+1} +4)\\\\= log(x-3) + 6 -\sqrt[3]{12x+1} -4\\\\= log(x-3) -\sqrt[3]{12x+1} +2[/tex]

Hence, Option(B) is the correct answer.

Learn more about function here

https://brainly.com/question/12431044

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Answer:

The answer should be 273

Answer: 225 tiles

Step-by-step explanation:

Side of tile = 20 cm = 0.2 m

Side of bathroom = 3 m

Area of tile = 0.04 m²

Area of bathroom = 9 m²

No. of tiles = Ar (bathroom) / Ar (tile)

= 9 / 0.04

= 9 x 25

= 225 tiles

Answer:

Step-by-step explanation:

13.05

Answer:

13.05

Step-by-step explanation:

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%

Answer: 14I + 15t ≤ 170

Step-by-step explanation:

Let I be the number of hours life guarding, and t be the number of hours tutoring(stated in the questions). At least is means this number is greater or equal to, which used the symbol ≤.

14I + 15t ≤ 170

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: 16/24

Step-by-step explanation:

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

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:

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:

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:

Step-by-step explanation:

Reflection about the y-axis followed by a translation left by 2 units

Reflection about the x-axis followed by a translation left by 2 units

Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units

Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units

i hope it can help. thanks

Answer: The answer is C

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

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

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:

Step-by-step explanation:

Hope this helps! <3

Answer:500

Step-by-step explanation:

√250000=500

Answer:

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

Thank you ☺️☺️

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: 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

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:

the second picture answer is F.56

Step-by-step explanation:

if you add 16 + 40=56

yes 831 is divisible by 3

One way I know this is because when adding all the digits in the number you get 12 which is divisible by 3

Also if you do divide 831 ÷ 3 it would equal 277

Answer:

yes or true

Step-by-step explanation: