sin( x+ π/4) + sin( x− π/4 ) = 1
Expand using the Sum Difference formula
Choose the correct set of possible solutions for X in the interval [0, 2\pi ]

To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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Answer:

terms:  'k' and '-3d'

coefficient of 'k' is 1

coefficient of '-3d' is -3

Step-by-step explanation:

if a variable exists by itself then its coefficient is 1, otherwise

whatever value precedes a variable is its coefficient

Answer:

\(5x\leq 20\)

\($4\) \(dollars\)

Step-by-step explanation:

For the first question, since the maximum cost is $20, it has to be \(5x\leq 20\) because less than or equal to 20 is the maximum.

For the second question, we solve:

\(5x\leq 20\)

\(\frac{5x}{5} \leq \frac{20}{5}\)

\(x\leq 4\)

\(Answer\) \(is\)\(:\) \(4\) \(dollars\)

Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Answer:

6.8 gallons per day vhuwhbehkq i had to put those random letter because it had to be 20 letters or more

Answer:

104ft

Step-by-step explanation:

First - find the area of triangles.

h = hight

b = base
h • b / 2

5 • 8 /2 = 20ft

And

4 • 6 /2 = 12ft

And then area of the rectangle.
l • w

9 • 8 = 72 ft

Than add. Them all together

Answer:

C . neither 8500 nor 850,000

Answer:

false

true

true

sorry i just need more characters

Answer:

0.9973 or 364/365

Step-by-step explanation:

Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.

Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:

P(not on 1st day) = 1 - P(on 1st day)

P(not on 1st day) = 1 - 1/365

P(not on 1st day) = 364/365

So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.

Check the picture below.

Answer:

  x = 2

Step-by-step explanation:

When a transversal crosses parallel lines, it creates 8 angles. Pairs of angles that are in the same direction from the points of intersection are called "corresponding angles." Corresponding angles are congruent.

__

In the given diagram, the marked angles are both "southeast" of their respective points of intersection. That means they are corresponding angles, and have the same measure.

  (9x -7)° = (7x -3)°

  2x = 4 . . . . . . . . . . . divide by °, add 7-7x

  x = 2 . . . . . . . . . divide by 2

_____

Check

The measures of the angles are ...

  (9(2) -7)° = (18 -7)° = 11°

  (7(2) -3)° = (14 -3)° = 11° . . . . same as the first angle, as it should be

Answer:

bro theres nothing there

Step-by-step explanation:

Answer:

(-1, 1)

Step-by-step explanation:

-1 is the opposite of 1, and the point is located in quadrant ll.

Answer:

1.equilateral

2.isosceles

3.isosceles

4.isosceles and right

5.scalene

6.scalene and right

7.isosceles and right

8.isosceles

9.equilateral

Answer:35x^3 + 15x^2 + 42xz + 28x + 18z + 12

Step-by-step explanation:

(7x + 3) (5x^2 + 6z + 4)

7 (5^2 + 6 + 4) +3 (5^2 + 6 + 4)

35^3 +42 + 28 + 15^2 + 18 + 12

35^3 + 15x^2 + 42xz + 28x + 18z + 12

Answer: 12

Step-by-step explanation: Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.

Answer:

Step-by-step explanation:

Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.

The standard forms of the quadratic equations are listed below:

Case 6: z² - 4 · z - 5

Case 8: 2 · x² - 18

Case 10: 2 · l² - 3 · l - 20

Case 12: 5 · q² + 24 · q - 5

Case 14: 6 · m² - 6

Case 16: 10 · a² - 19 · a + 6

Case 18: 2 · x² - 3 · x · y + y²

The standard forms of the cubic equations are listed below:

Case 20: t³ + 3 · t² + 6 · t + 4

Case 22: m³ + 6 · m² + 14 · m + 15

In this problem we find eight quadratic equations in factor form, whose standard form must be determined. Each form is introduced below:

Factor form

a · (x - r₁) · (x - r₂)

Standard form

a · x² + b · x + c

Where:

The transformation can be done by algebra properties:

Case 6

(z - 5) · (z + 1)

z² - 4 · z - 5

Case 8

(2 · x - 6) · (x + 3)

2 · (x - 3) · (x + 3)

2 · (x² - 9)

2 · x² - 18

Case 10

(2 · l + 5) · (l - 4)

2 · l · (l - 4) + 5 · (l - 4)

2 · l² - 8 · l + 5 · l - 20

2 · l² - 3 · l - 20

Case 12

(q + 5) · (5 · q - 1)

q · (5 · q - 1) + 5 · (5 · q - 1)

5 · q² - q + 25 · q - 5

5 · q² + 24 · q - 5

Case 14

(2 · m + 2) · (3 · m - 3)

2 · (m + 1) · 3 · (m - 1)

6 · (m + 1) · (m - 1)

6 · (m² - 1)

6 · m² - 6

Case 16

(5 · a - 2) · (2 · a - 3)

(5 · a - 2) · 2 · a - (5 · a - 2) · 3

10 · a² - 4 · a - 15 · a + 6

10 · a² - 19 · a + 6

Case 18

(x - y) · (2 · x - y)

2 · x · (x - y) - y · (x - y)

2 · x² - 2 · x · y - x · y + y²

2 · x² - 3 · x · y + y²

The following two cases belong to cubic equations:

Case 20

(t + 1) · (t² + 2 · t + 4)  

t² · (t + 1) + 2 · t · (t + 1) + 4 · (t + 1)

t³ + t² + 2 · t² + 2 · t + 4 · t + 4

t³ + 3 · t² + 6 · t + 4

Case 22

(m + 3) · (m² + 3 · m + 5)

(m + 3) · m² + 3 · (m + 3) · m + 5 · (m + 3)

m³ + 3 · m² + 3 · m² + 9 · m + 5 · m + 15

m³ + 6 · m² + 14 · m + 15

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Answer:

\((-\infty, 0) \cup (0,2) \cup (2,\infty)\)

Step-by-step explanation:

Remember that the domain of the product of functions is the intersection of domains, therefore when you intercept them you get the following interval.

\((-\infty, 0) \cup (0,2) \cup (2,\infty)\)

The 19th term of a geometric sequence is 1048576.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

a = 4 and r = 2

The nth term of a geometric sequence.

= a\(r^{n-1}\)

Now,

The 19th term of a geometric sequence.

= a\(r^{n-1}\)

Substituting a and r values.

= 4 x \(2^{19 - 1}\)

= 4  x \(2^{18}\)

= 4 x 262144

= 1048576

Thus,

The 19th term of a geometric sequence is 1048576.

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Let a represent the cost of adult tickets and c represent the cost of children's tickets.

On the first day, $138.50 worth of tickets were sold by selling 5 adult tickets and 2 child tickets. This means that:

On the second day, $185.50 worth of tickets were sold by selling 7 adult tickets and 2 child tickets. This means that:

We can solve the simultaneous equations by subtracting the two equations:

We can solve for c by substituting for a into the first equation:

Therefore, an adult ticket costs $23.50 and a child ticket costs $10.50.

Answer:

6 2/3

Step-by-step explanation:

Answer:

area of parllelogram=base×height=(4+8)×7=12×7=

84m²

Answer:

2/3x-4

Step-by-step explanation:

2/3*x=2/3x

2/3*6=4

The difference in the production levels will be 3x + 8.

The amount that Jackson spent more will be 5.20 - p.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Based on the information, a company has two manufacturing plants that had levels of 5x + 11 and 2x - 4.

The difference in the production levels will be:

= 5x + 11 - 2x - 3

= 3x + 8

The amount that Jackson spent more will be:

= 7.65 + 5p - 2.45 - 4p

= 5.20 - p.

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Answer:

x = 10

Step-by-step explanation:

y = 2x + 1

21 = 2x + 1

21 - 1 = 2x

2x = 20

x = 10

The number of labor hours required to install the ceiling is 24.528 labor hours.

What is ceiling?

Ceiling is the overhead surface of a room, typically flat and finished with paint, wallpaper, or tiles. It is the highest point or top part of a room, and can be made up of different materials including drywall, plaster, tiles, or even wood. Ceilings also help to separate the room from the outside air and create a space that is more comfortable and insulated. Ceilings can be used to add visual interest to a room, as they can be decorated with different colours and textures. Ceilings can also be used to conceal mechanical and electrical systems, such as wiring, piping, and ductwork.

The number of labor hours required to install the ceiling is 24.528 labor hours. This is determined by multiplying the area of the ceiling (1,856 square feet) by the productivity rate (0.013 labor hours per square foot) and then multiplying that result by the productivity factor (0.95).

1,856 square feet x 0.013 labor hours per square foot x 0.95 productivity factor = 24.528 labor hours.

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