Find an equation for the nth term where the first term in the sequence is a1

Answer: Θ = [tex]45[/tex]

Step-by-step explanation:

tan x=sinx/cosx

and tan x is negative in the first and third quadrants.

tan x=1 for 45 degrees so tan x=-1 in the first quadrant 135 degrees and the third quadrant= 315 degrees

Ill try my best to "show my work" in text

First, we need to calculate the total amount of time Ron spent watching TV over the weekend.

On Saturday, he watched TV for 1 hour and 0 minutes from 9:30-10:30AM, 2 hours and 30 minutes from 1:00-3:30PM, and 2 hours from 8:00-10:00PM, for a total of 5 hours and 30 minutes on Saturday.

On Sunday, he watched TV for 1 hour and 30 minutes from 1:00-2:30PM, and 2 hours from 8:00-10:00PM, for a total of 2 hours and 30 minutes on Sunday.

The total time he spent watching TV over the weekend is 5 hours and 30 minutes on Saturday + 2 hours and 30 minutes on Sunday = 8 hours.

Next, we need to calculate the time he spent watching sports programs and movies.

He watched sports programs for half of the total time he spent watching TV, so he spent 8 hours / 2 = 4 hours watching sports programs.

He watched movies for one third of the total time he spent watching TV, so he spent 8 hours / 3 = 2 hours and 40 minutes watching movies.

Finally, we can calculate the time he spent watching cartoons with his sister.

He spent 8 hours watching TV total, and 4 hours watching sports programs and 2 hours and 40 minutes watching movies, so he spent 8 hours - 4 hours - 2 hours and 40 minutes = 1 hour and 20 minutes watching cartoons.

Since there are 60 minutes in an hour, the total time Ron spent watching cartoons is 1 hour and 20 minutes = 80 minutes.

Answer:

So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.

Step-by-step explanation:

First, we need to calculate the total time that Ron spent watching TV. On Saturday, he watched TV for 1 hour in the morning, 2 hours and 30 minutes in the afternoon, and 2 hours in the evening, which adds up to 6 hours and 30 minutes. On Sunday, he watched TV for 1 hour and 30 minutes in the afternoon and 2 hours in the evening, which is a total of 3 hours and 30 minutes. So over the weekend, Ron watched TV for 6 hours and 30 minutes on Saturday and 3 hours and 30 minutes on Sunday, which adds up to a total of 10 hours.

Since Ron watched sports programs for half the time he watched TV, he spent 10 hours / 2 = 5 hours watching sports.

And since he watched movies for one-third of the time he watched TV, he spent 10 hours / 3 = 3 hours and 20 minutes watching movies.

Finally, we can calculate the time Ron spent watching cartoons by subtracting the time he spent watching sports and movies from the total time he spent watching TV:

10 hours - 5 hours - 3 hours and 20 minutes = 1 hour and 40 minutes

So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.

The factorization of the given polynomial is 10x²(x+1).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is 10x³+10x².

Here, factors of the terms 10x³ and 10x² are

10x³= 2×5×x×x×x

10x²= 2×5×x×x

GCF of the terms is 2×5×x×x=10x²

10x²(x+1)

Therefore, the factorization is 10x²(x+1).

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The value of the variables y and z are 18

From the question, we have the following parameters that can be used in our computation:

The special right triangle

The special right triangle has one of its angles to be 45 degrees

This means that

Legs = Hypotenuse/√2

Using the above as a guide, we have the following:

Legs = 18√2/√2

Evaluate

Legs = 18

Hence, the value of y and z are 18

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Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

ii

350x + 200y - 4200 = 0

Therefore, the equation in standard form that models the number of funnel cakes, x, and the number of deep-fried Oreos, y, Francis can buy if he spends $42.00 is:

350x + 200y - 4200 = 0

To find the x-intercept, we set y to zero and solve for x:

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

Therefore, the x-intercept is 12. This means that if Francis only buys deep-fried Oreos (y = 0), he can buy 12 funnel cakes with $42.00.

Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

3.50x + 2.00y = 42.00

3.50x + 2.00y - 42.00 = 0

Multiplying both sides by 100 to eliminate the decimals, we get:

350x + 200y - 4200 = 0

x-intercept means what is x when y is 0

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

y-intercept means what is y when x is 0

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

To find the y-intercept, we set x to zero and solve for y:

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

Therefore, the y-intercept is 21. This means that if Francis only buys funnel cakes (x = 0), he can buy 21 deep-fried Oreos with $42.00.

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

Answer: la response est 1,235 je pense

Step-by-step explanation: trois decimal veux dire trois chiffre après la virgule donc on decale la virgule de 3 vers la gauche

The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of each packet is given as,

v = 16 x 9 x 4

v = 576 cubic cm

The volume of the cubical box is given as,

V = (1.2 x 100) x (1.2 x 100) x (1.2 x 100)

V = 120 x 120 x 120

V = 1,728,000 cubic cm

Then the number of packets is given as,

n = V / v

n = 1,728,000 / 576

n = 3,000

The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

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Value of composite functions (g-f)(x)  and (f/g)(x) are x² - 2x - 8 and

(x+1)/(2x - 3) respectively.both of these functions don't have the same

domain and range.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given functions,

f(x) = x² - 3x - 4

g(x) = 2x² - 5x - 12

1. (g - f)(x)

= g(x) - f(x)

= 2x² - 5x - 12 - (x² - 3x - 4)

= 2x² - 5x - 12 - x² + 3x + 4)

= x² - 2x - 8

x is defined for all real numbers

Domain = (-∞, ∞)

let y = x² - 2x - 8

x = √y + 2(x) - 8

Function is defined for y ≥ 9

Range is {y∈R , y ≥ 9}

2. (f/g)(x)

= f(x)/g(x)

= (x² - 3x - 4)/(2x² - 5x - 12)

= (x² - 4x + x - 4)/(2x² - 8x + 3x - 12)

= (x(x - 4) + 1(x - 4))/(2x(x - 4) + 3 (x - 4))

= (x+1)(x-4)/(2x+3)(x-4)

= (x+1)/(2x - 3)

function is defined for x ≠ 3/2, Domain is {x ∈ R : x ≠ 3/2}

Let y = (x+1)/(2x - 3)

y.2x - 3y = x + 1

-3y - 1 = x - 2xy

x = (-1 - 3y)/(1 - 2y)

function is defined for y ≠ 1/2, Range is {y ∈ R : y ≠ 1/2}

Domain and range are not same for both functions.

Hence,  Value of composite functions (g-f)(x) = x² - 2x - 8 and

(f/g)(x) = (x+1)/(2x - 3), Domain and range is not same for both functions.

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The actual train is 957 inches long.

A ratio indicates the number of times one number contains another. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of the model train to the actual train is 1 : 87.

The model train is 11 inches long, therefore,

1=11

Then, the value of 87 is:

87 = 87×11

   = 957

Hence, the actual train is 957 inches long.

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The solution is, the remainder is 9.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

find the remainder in the synthetic division

1         4       6        -1

Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder

1         4       6        -1

        0        4        10

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

        4        10       9 -> Remainder

So the remainder is 9.

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Answer:

To add different quantities of liquids with different units of measurements, we need to convert them all to the same unit of measurement. In this case, let's convert everything to quarts since that is what we want the final answer to be in.

2 gallons = 8 quarts (since 1 gallon = 4 quarts)

5 quarts of pineapple juice = 5 quarts (no conversion needed)

4 pints of cranberry juice = 8 cups = 2 quarts (since 1 pint = 2 cups and 1 quart = 4 cups)

6 cups of apple juice = 1.5 quarts (since 1 cup = 0.25 quarts)

Now we can add up all the quantities:

2 + 5 + 2 + 1.5 = 10.5

Maya made 10.5 quarts of fruit punch in all

Answer: x = -7

explanation:

2(x+4)= -6

2x+8= -6

-8 -8

2x -14

Divide both sides by 2

X = -7

Answer:x=-7 I hope this helps

Step-by-step explanation:

2(x+4)=-6

Divide both sides of the equation by 2

X+4=-3

Move the constant to the right-hand side and change its sign

X=-3-4

Calculate the difference which means subtract-3 minus 4 which give you -7

X=-7

And that how you solve for X

The system of equations are y = ( 5/4 )x and y = 6 - 3x where the value of x and y are 1.4117 and 1.765 respectively

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first equation be P

y = ( 5/4 )x   be equation (1)

Let the second equation be Q

y = 6 - 3x   be equation (2)

Substituting the values in the equation , we get

( 5/4 )x = 6 - 3x

Adding 3x on both sides of the equation , we get

6 = ( 5/4 + 3 ) x

( 17/4 )x = 6

Multiply by 4 on both sides of the equation , we get

17x = 24

Divide by 17 on both sides of the equation , we get

x = 24/17 = 1.4117

Substitute the value of x in equation (1) , we get

y = ( 5/4 ) ( 24/17 )

y = ( 30/17 )

y = 1.765

Hence , the equations are solved and the value of x and y are 24/17 and 30/17 respectively

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Answer: To find the point on the directed line segment that partitions it into a ratio of 4 to 5, we can use the formula for a point on a line given two endpoints and a ratio. The formula is:

(x, y) = (1 - t) * (x1, y1) + t * (x2, y2)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and t is a value between 0 and 1 that determines the location of the point along the line.

In this case, (x1, y1) = (-1, -9) and (x2, y2) = (8, 9), and we want the point that partitions the line segment into a 4 to 5 ratio, so:

t = 4 / (4 + 5) = 4 / 9

Plugging in the values into the formula:

x = (1 - t) * x1 + t * x2 = (1 - 4/9) * (-1) + (4/9) * 8 = (5/9) * 8 - (4/9) * 1 = 44/9 - 4/9 = 40/9

y = (1 - t) * y1 + t * y2 = (1 - 4/9) * (-9) + (4/9) * 9 = (5/9) * 9 - (4/9) * (-9) = 45/9 + 36/9 = 81/9

So the point that partitions the line segment into a 4 to 5 ratio is (40/9, 81/9).

Step-by-step explanation:

We can find the variance of a uniform distribution, using the following formula: Variance = (b - a)² / 12. Here: a is the lower limit of the uniform distribution, b is the upper limit of the uniform distribution.

The formula for the variance of a uniform distribution is based on the fact that the variance of a continuous uniform distribution is equal to the square of the range (i.e., the difference between the upper and lower limits) divided by 12.

For example, let's say we have a uniform distribution between 0 and 10. To find the variance, we would use the formula:

Variance = (10 - 0)² / 12

Variance = 100 / 12

Variance = 8.33

Therefore, the variance of a uniform distribution between 0 and 10 is 8.33.

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The sum of all the angles of triangle is 180°

We have the following angles:

The sum of all these angles will be equal to 180°

[tex] \sf \: 70 + 90 + 2x + 6 = 180[/tex]

[tex] \sf166 + 2x = 180[/tex]

[tex] \sf2x = 180 - 166[/tex]

[tex] \sf2x = 14[/tex]

[tex] \sf2x \div 2 = 14 \div 2[/tex]

[tex] \boxed{ \tt \: x = 7}[/tex]

The given angle is 2x+6, So put the value of x in this and find the value of angle

Answer: c

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

I will assume they are all there on day 1

 then the LCM of  4  6  2  and 3   is 12 days

    every 12 days they are there together

       12 weeks = 12 x 7 = 84 days

                 84 / 12 = 7 times

day   1    13     25    37    49    62    74

Answer:

m∠6 = 142°

m∠7 = 38°

Step-by-step explanation:

You will be using postulates and theorems to solve this question.

Two parallel lines are cut by a transversal          (Given)

- m∠1 = 38°                         (Given)

- m∠1 ≅ m∠3                      (Vertical Angles Theorem)

  ∴ m∠3 = 38° (Definition of Vertical Angles Theorem)

- m∠3 ≅ m∠5                     (Alternate Angles Theorem)

 m∠3 = 38° ∴ m∠5 = 38° (Definition of Alternate Angles Theorem)

- m∠5 ≅ m∠7                     (Vertical Angles Theorem)

 m∠5 = 38° ∴ m∠7 = 38° (Definition of Alternate Angles Theorem)

m∠7 + m∠6 = 180°            (Corresponding Angles Postulate)

m∠7 = 38°                          (Given above)

Plug in 38 for m∠7 and solve for m∠6:

(38) + m∠6 = 180

Isolate m∠6. Note the equal sign, what you do to one side, you do to the other. Subtract 38 from both sides of the equation:

m∠6 + 38 = 180

m∠6 + 38 (-38) = 180 (-38)

m∠6 = 180 - 38

m∠6 = 142°

-

Answers:

m∠6 = 142°

m∠7 = 38°

~

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Answer:

I think its

Step-by-step explanation:

2^(n+1) is the explicit form

The Equation of Circle is (x+ 6)² + (y - 3)² = 9².

The equation for a circle is given by:

(x-h)² +(y-k)² = a²

Where (h,k) is the center and a is the radius of the circle.

Given:

We have the points A(-6, 3), B(-15, 3), and C(3,3).

Using Distance Formula

AB = √(-15 + 6)² + (3-3)²

AB = √9²

AB= 9 unit

BC= √(3 + 15)² + (3-3)²

BC = 18 unit

and, AC = √(3+6)² + (3-3)²

AC = 9 unit

As, AB = AC then A has to be the center (-6, 3) with radius 9 unit.

Thus, the Equation of Circle is

(x+ 6)² + (y - 3)² = 9²

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The length of the arc AB is 6 cm when BC is 2 cm, ∠BOC = 32°, and ∠AOB = 96°.

The arc length is the portion of the circumference of a circle. It is directly proportional to the central angle formed by an arc.

The center of the circle is O, where BC = 2 cm, ∠BOC = 32°, and ∠AOB = 96°. Draw the diagram as per the given data.

As 96° = 3×32°, it follows that ∠AOB = 3×∠BOC.

As the central angle formed by an arc is proportional to its length. It follows that AB = 3×BC.

Since, BC = 2 cm, it can be got that AB = 3×2 cm = 6 cm.

Therefore, the required answer is 6 cm.

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We can use the Pythagorean theorem to find the length of the short cut up the flight of stairs. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the short cut "x". Then, we can set up the following equation:

x^2 = 60^2 + 80^2

Expanding the squares:

x^2 = 3600 + 6400

x^2 = 10000

Taking the square root of both sides:

x = sqrt(10000)

x = 100

So, the length of the short cut up the flight of stairs is 100 meters.

To create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Yaseen can produce 15 kits, the cost per kit she should charge is

p = 10 + 0.5q

p = 10 + 0.5(15) (15)

p = $17.50

She can produce 15 kits, the cost per kit she should charge is:

p = 30 - 0.5(15) (15)

p = $22.50

She can provide 60 kits, the cost per kit should be as follows:

p = 10 + 0.5q

Here, q=60

p = 10 + 0.5(60)

p = $40

She can produce 60 kits, the cost per kit should be set at:

p = 30 - 0.5(60) (60)

p = $15

Therefore, to create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

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The main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).

Both exponential equations are in the form y = ab^x - c, where a is the vertical scaling factor, b is the horizontal scaling factor (also known as the growth factor), and c is the vertical translation. The difference between the two equations lies in the values of the parameters a, b, and c.

The first equation, 2 (1/5)x-5, has a vertical scaling factor of 2, a horizontal scaling factor of 1/5, and a vertical translation of -5. The graph of this equation will increase at a slower rate than the graph of the second equation.

The second equation, 3 (1/2)x-3, has a vertical scaling factor of 3, a horizontal scaling factor of 1/2, and a vertical translation of -3. The graph of this equation will increase at a faster rate than the graph of the first equation.

In summary, the main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).

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Answer:

Step-by-step explanation:

Number of guests who called for room service = 45

Total number of guests = 45 + 200 = 245

Percentage of guests who called for room service = (45/245) x 100% ≈ 18.4%

Therefore, approximately 18.4% of the hotel's guests called for room service.

4v + (9 x 7)= 4v +56

Answer:

1:8

Step-by-step explanation:

since the base and sides are equal, I'll use 2 as a value for them. since all square sides are equal, we can find the area of the square. 2(2)=4. this means that in the situation the area of the triangle is 16.

16=1/2(2)h

32=2h

16=h

the height of the triangle is 16, while the side of the square is 2. the ratio is 2:16, or 1:8

The balance amount when compounded daily at a rate of 4.075% after 6 months is  $269,320.60.

What is meant by compound interest?

The interest you earn on interest is known as compound interest. Compound interest, also known as interest on principal & interest, is the practice of adding interest to the principal amount of a loan or deposit. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even while the principal remains the same, the interest changes annually. We can observe that interest rises over time. Thus, we can infer that the interest the bank charges is compound interest rather than simple interest.

Given,

Principal amount P = $263,000

Rate of interest r = 4.075%

Time period t = 6 months = 0.5 years

Final amount =  [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

where n = 365

A = [tex]P(1 + \frac{r}{n})^{nt} =263000(1 + \frac{0.04075}{365})^{365*0.5}[/tex]  = $269,320.60

Therefore the balance amount when compounded daily at a rate of 4.075% is  $269,320.60.

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The correct option regarding the estimate of the percentage is of:

The answer should be close to 1/3 of 120, which is 40.

The percentage is estimated applying the proportions in the context of the problem.

To estimate 30% of 123, we must multiply the total amount of 123 by the decimal equivalent of the percentage of 30%, which is 30/100 = 0.3, hence the estimate is given as follows:

0.3 x 123 = 36.9.

This is close to 1/3 of 120, which is of 40, hence the last option is correct.

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