Use each recursive definition to write an explicit formula for the sequence. a₋₁ = 1, a n =a n ₋₁ +4

The equation of the circle with radius 6 and center at (0 , 0) is x^2 + y^2 = 36.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 6

(x - 0)^2 + (y - 0)^2 = 6^2

x^2 + y^2 = 36

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Answer:

decimal is the number system of 10base .

The point of intersection for the function is  (2, 2)

Considering to the line passing through the points (0,6) and (3,0)  to be f(x).Therefore the slope intercept of the function is

m = 0-6/3-0 = -2

So, the functions F(x) in the slope-intercept form f(x)= -2x+6  ......1

interchanging the variable x to y and y to  x

=> x =-2y + 6

=> 2y = -x + 6

=> y= -0.5x + 3

let  f⁻¹(x)= y

f⁻¹(x) =-0.5x+3   ......2

Solving the equation  1 and 2, we get

=> -0.5x + 3 = -2x + 6

=> 2x - 0.5x = 6 - 3

=> 1.5x = 3

=> x = 2

Substituting the values of x in the function  we get,

f( x) = -2(2) + 6 = 2

Thus, the outcome is (2,2)

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The explicit formula for give sequence an = n² + 1:

An arithmetic sequence has the explicit formula a = a + (n - 1)d, and each term of the series may be calculated without knowing the values of the previous terms. The nth term in an arithmetic, geometric, or harmonic series is usually the explicit formula.

a1 = (1) + 1 = 2

a2 = 2.2 + 1 = 5

a3 = 3.3 + 1 = 10

a4 = 4.4 + 1 = 17

a5 = 5.5 + 1 = 26

and so on.

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Answer:

y = 1

if you need answer of x

x = 2

Step-by-step explanation:

Let's solve your system by substitution.

4x+2y=10;3x+5y=11

Step: Solve4x+2y=10for x:

4x+2y=10

4x+2y+−2y=10+−2y(Add -2y to both sides)

4x=−2y+10

4x/4 = −2y+10/4

(Divide both sides by 4)

x= −1/2y+5/2

Step: Substitute −1/2y+5\2 for x in3x+5y=11:

3x+5y=11

3(−1/2y+5/2)+5y=11

7/2y+15/2=11(Simplify both sides of the equation)

7/2y+15/2+−15/2=11+/−152

(Add (-15)/2 to both sides)

7/2y=7/2

7/2y/7/2 = 7/2/7/2

(Divide both sides by 7/2)

y=1

Step: Substitute1for y in x= −1/2y+5/2:

x=−1/2y+5/2

x=−1/2(1)+5/2

x=2(Simplify both sides of the equation)

Answer:

12 oranges

Step-by-step explanation:

The ratio is K/L where K = Kudi's oranges and L = Ludi's oranges

K/L = 2/3

To find the number of oranges that Kudi has, divide the numerator by the sum of numerator and denominator.Then multiply by total number of oranges

For Ladi, divide the denominator by the sum of numerator and denominator. Then multiply by total number of oranges

[tex]K = 20\cdot \dfrac{2}{2+3} = 20 \cdot \dfrac{2}{5} = 8 \; \mathrm {oranges}\\\\L = 20\cdot \dfrac{3}{2+3} = 20 \cdot \dfrac{3}{5} = 12 \; \mathrm {oranges}[/tex]

So answer is Ladi has 12 oranges

Answer:

x = -14

Step-by-step explanation:

Solve:

7x - 28 = 2(4x - 7)

7x - 28 = 8x - 14

Substrate 8x from both sides.

7x - 28 - 8x = 8x - 14 - 8x

-x - 28 = -14

Add 28 to both sides.

-x - 28 + 28 = -14 + 28

-x = 14

Divide both sides by -1.

-x/-1 = 14/-1

x = -14

Therefore x = -14

Answer:

they would need a 98 on the next math test.

The operator *= is called  multiple assignment operator.

The operator is given as

*=

Take for instance, we have the following statement in Python

a *= b

The meaning of the above statement is

a = a * b

Assume the following values for the variables

a = 6 and b = 3

The value of the operation a *= b would be

a *= b --- given expression

a = a * b --- expanded expression

a = 6 * 3 ---- when the values are substituted

a = 18 --- the result

This implies that the operator represents an assignment and a multiply operator

Hence, the operator *= is called  multiple assignment operator.

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The total amount that debtors are overcharged is 360 million dollars.

The unitary method is a technique to find the necessary value by multiplying the single unit value by finding the value of single unit value. We will use the same technique to solve this problem

According to question, $6 is charged per month for 5 years period from 1 million credit card holders

so, the total amount will be

1000000 × $6 × 12 × 5 = $360000000

Final answer: amount will be 360 million dollars

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Answer:

11/11 is an improper fraction.

Step-by-step explanation:

In order for a fraction to be considered "Proper" a < b, when a/b. Meaning that the numetator must be less than the denominator.

In the case for 11/11, it does not follow these qualifications.

Hope this helps!

Using the graph of g we get (a) value of function g at x=0 is 5

(b) [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist

(c) value of function g at x=1 is 4

(d) [tex]\lim_{x \to \11} g(x)[/tex]  or  limit of g(x) at x=1 is 4

What is limit of a function how can limit be interpreted using graph of that function?

Limit : Limit is the value that a function output approaches as the input  approaches to a certain value.

For any function g(x) ,[tex]\lim_{x \to \22} g(x)[/tex] means that the value g(x) approaches as the x approaches to 2 .

From any graph we can easily see that to what value g(x)=y  on the curve is approaching when the x  is approaching to some value on x axis and if the graph is breaking on the value where x is approaching then the limit does not exist for that value of x.

For given graph

We can see value of value of function g at x=0 is 5 and value of function g at x=1 is 4

As the graph is breaking on x=0 into two functions then [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist

As the graph is not breaking at x=1 or we can say that graph of g(x)is approaching to 4 as x approaches to 1 then   [tex]\lim_{x \to \11} g(x)[/tex]  or  limit of g(x) at x=1 is equal to g(1) that is  4

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Answer:

Step-by-step explanation: First row, first column 500 * 7 = 3500

1st row , second column 7 * 60 = 420

1st row, third column 7 * 3 = 21

Do similary for the others

2nd row, 40,000                  4800                  240

3rd row , 100000                  12000                6000

Answer:

[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]

Step-by-step explanation:

For each box, multiply the number of the row by the number of the column:

[tex]\large\text{ \quad \quad \quad \quad \quad 500 \quad \quad \quad\;\;60 \quad \quad \quad \;\;\;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{7 \times 500} &\boxed{7 \times 60} & \boxed{ 7 \times 3}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{80 \times 500} & \boxed{80 \times 60} & \boxed{80 \times 3}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{200 \times 500} & \boxed{200 \times 60} & \boxed{200 \times 3}\\\cline{2-4} \end{array}[/tex]

When multiplying numbers ending in zeros (multiples of 10, 100, etc.), first multiply the numbers as if they didn't have zeros, then add all the zeros to the final answer.

For example:

200 × 500 has a total of 4 zeros.

Multiply 2 × 5 = 10

Then add 4 zeros: 10 0000

Therefore, 200 × 500 = 100000

Final Solution

[tex]\large\text{ \quad \quad \quad \quad 500 \quad \quad\;\;\;60 \quad \quad \;3}\\\\\large\begin{array}{r|c|c|c|}\cline{2-4} \phantom{\dfrac12}7 & \boxed{3500} &\boxed{420} & \boxed{21}\\\cline{2-4} \phantom{\dfrac12}80 & \boxed{40000} & \boxed{4800} & \boxed{240}\\\cline{2-4} \phantom{\dfrac12}200 & \boxed{100000} & \boxed{12000} & \boxed{600}\\\cline{2-4} \end{array}[/tex]

I believe it's 3ײ - 6x - 7.56

Sorry if this isn't helpful!

The other option would be -6x + 3ײ-7.56 (but this is the problem in a simplified form and not when it is evaluated).

The total number of matches played will be 46. matches.

From the information, there are 24 baseball teams in a league each team plays two matches against each of the other teams.

The total number of matches that will be played will be:

= (24 - 1) × 2

= 23 × 2

= 46 matches.

Therefore, the total number of matches played will be 46. matches.

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Answer: not possible

Step-by-step explanation:

I think you're doing quadratics and if that's the case probably go and rework the problem because that doesn't work.

The measures of the indicated angles are

m ∠EFH = 59.5°

m ∠GFH = 59.5°

From the question, we are to determine measures of the indicated angles

The angles are ∠EFH and ∠GFH

From the given information,

FH bisects ∠EFG

Since FH bisects ∠EFG,

Then,

m ∠EFH  = m ∠GFH

and

m ∠EFH  + m ∠GFH = m ∠EFG

Then,

We can write that

m ∠EFH  + m ∠EFH = m ∠EFG

2 × m ∠EFH = m ∠EFG

2 × m ∠EFH = 119°

m ∠EFH = 119°/2

m ∠EFH = 59.5°

Thus,

m ∠GFH = 59.5°

Hence, the measures of the indicated angles are

m ∠EFH = 59.5°

m ∠GFH = 59.5°

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Answer: The answer is x = 6.5

2 m/s^2 is the acceleration in the given graph .

Acceleration is the general term for any process where the velocity changes. There are only two ways to gain speed: by changing your speed or direction, or by doing both. This is thus because speed and direction both affect velocity.

Since we formula for acceleration is =
(v - u) / t

where u represents initial velocity , v represents final velocity

  so acceleration from graph will be = (7 - 0)/3.5  

                                                            = 7/3.5

                                                            = 2 m/s^2

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  For numbers 5 and 45 the value of the geometric mean of these numbers is

Gm (5, 45) = 15

   The geometric mean is defined as a type of measure that is calculated as the root of a product between a set of numbers, it can be expressed as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

Gm (5, 45) = √5×45

Gm (5, 45) = √225  ;    In this case the square root is direct-

Gm (5, 45) = 15

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The explicit formula of arthmetic sequence is [tex]a_{n}[/tex] = a + (n-1)d

Here is an explicit formula of the sequences 62, 59, 56, and 53...

  [tex]a_{n}[/tex] = 62 + (n-1)(-3)

In the formula, n is any term number and [tex]a_{n}[/tex] is the nth term.

This formula allows us to simply plug on the number of the term we are interested in, and we will get the value of that term.

In order to find the fifth term, for example, we need to plug n = 6

     [tex]a_{6}[/tex] = 62 + (6-1)(-3) = 62 + 5× -3

      = 62- 15

      = 47

In this way, we can find any term by using the explicit formula of an arithmetic sequence.

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The relationship between the ∠4 and ∠5 is that both are consecutive interior angles

Given,

The angles =∠4 and ∠5

Here, ∠4 and ∠5 are interior angles.

Both are lies on the opposite sides of the transversal.

So, ∠4 and ∠5 are consecutive interior angles

Hence, The relationship between the ∠4 and ∠5 is that both are consecutive interior angles

The complete question is :

Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠4 and ∠5

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According to the given statement

The area of Colorado is 67.43 times greater than the area of Rhode Island

Area is typically thought of as a specific instance of volume for two-dimensional regions. By applying axioms, one can define area as the relationship between a set of real numbers and a collection of particular plane figures.

Area is a mathematical concept that describes the size of a region on a planar or curved surface. The area of an open surface or the border of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

According to the given values;

The area of Rhode Island = 43.07 billion square feet.

The area of Colorado = 2.9045 trillion square feet.

43.07 billion =43,070,000,000

2.945 trillion =2,9045,000,000,00

Now we have to find how many times as great is the area of Colorado than the area of Rhode Island.

For this ,we divide area of Colorado by area of Rhode Island.

=2,9045,000,000,00/43,070,000,000

=67.43

So, the area of Colorado is 67.43 times greater than the area of Rhode Island.

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The value of the function at an input of 50 will be 36.95.

Since the pressure at the surface is 14.7 psi, a function to represent water pressure will be:

= 14.7 + (0.445 × p)

where p is the increase in pressure for each foot

= 14.7 + 0.445p

Therefore when the input is 50, the amount will be:

= 14.7 + 0.445p

= 14.7 + 0.445(50)

= 14.7 + 22.25

= 36.95

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

Work Shown:

[tex]SA = 2\pi r^2 + 2\pi r h\\\\SA \approx 2*3.14*15^2 + 2*3.14*15*40\\\\SA \approx 5181\\\\[/tex]

The cylinder has a surface area of about 5181 square feet.

Side notes:

Answer:

Step-by-step explanation:

3768 feet. Is this right?