Evaluate each infinite geometric series. 3+1+1/3 +1/9+ . . . .

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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Answer:

1) x≤10.33

2) x≤5

Step-by-step explanation:

Question: 3x−8≤23

1) 3x≤31

2) x≤10.33

Question: -4x + 26≥6

1) -4x ≥-20

2) x ≤5

1) 3x < 23 + 8

3x < 31

x < 31/3

x < 10.33

x value will be more than equal to 10.33

2) -4x > 6 - 26

x > -20/-4

x < 5

x value will be less than and equal to 5

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

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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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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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?

Answer:

x = -3

Step-by-step explanation:

-10 + 5x = 7x - 4

      -7x    -7x

-10 - 2x = -4

+10          +10

- 2x = 6

÷-2   ÷-2

x = -3

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 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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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:

decimal is the number system of 10base .

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: The answer is x = 6.5

The equation in slope-intercept form for the line given (-3,12) and (15,0) is

[tex]y=-\frac{2}{3}x+ 10[/tex]

Given,

The points = (-3,12) and (15,0)

We know,

Slope of the equation m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Substitute the values and find the value of m

m= [tex]\frac{0-12}{15--3}[/tex]

m=[tex]-\frac{12}{18}=-\frac{2}{3}[/tex]

Slope intercept form of the equation is y= mx + b

where b is y intercept form.

Consider one point and substitute the values.

[tex]0=-\frac{2}{3}(15)+b \\0=-10+b\\b=10[/tex]

Then the slope intercept form is

[tex]y=-\frac{2}{3}x+ 10[/tex]

Hence, The equation in slope-intercept form for the line given (-3,12) and (15,0) is [tex]y=-\frac{2}{3}x+ 10[/tex]

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Given that when Q = 2, P = 24 the value of P when Q = 10 is 120.

It should be noted that given that when Q = 2, P = 24, the constant will be;

= 24/2 = 12

Therefore, the value of P when Q is 10 will be:

= 12 × 10

= 120

The value of P is 120.

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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.

Two diagrams have been drawn that could be proved congruent by the ASA condition.

So,

Therefore, two diagrams have been drawn that could be proved congruent by the ASA condition.

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The final price after all discounts is $62.74.

A discount is when the price of an item is decreased. An item becomes cheaper when a discount is applied.

Percentage is the fraction of an amount expressed as an amount out of 100. Percentage is a measure of frequency. The sign used to represent percentage is %.

Price of the skateboard after the first discount = (1 - discount) x initial price

(1 - 0.30) x 119.50

0.70 x 119.50 = $83.65

Price of the skateboard after the second discount = (1 - discount) x discounted price

(1 - 0.25) x $83.65

0.75 x $83.65 = $62.74.

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The center of a circle is the point at which the tip of our compass is placed when drawing a circle. It is the center of the circle's diameter.

A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "centre."

The center of a circle is the point at which the tip of our compass is placed when drawing a circle. It is the center of the circle's diameter. The radius of a circle is the distance from the center to any point on its circumference that is always the same.

The center of the circle that is internally tangent to all three triangle sides; the orthocenter, the intersection of the triangle's three altitudes; and the nine-point center, the center of the circle that passes through nine key triangle points.

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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]

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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each input is mapped into only one output, then this relation is a function.

The correct option is "Yes, because each input value has only one output value"

A relation maps elements from a set (called the domain, which is the set of the inputs) into elements from another set (called the range, which is the set of the outputs). Such that these mappings generate coordinate pairs (x, y) or (input, output)

A relation is a function only if all the elements in the domain are mapped into only one value in the range.

On the given relation, we have the coordinate pairs:

(6, 3)

(1, 2)

(-1, -1)

(4, 3)

So we can see that each input is mapped into only one output, then this relation is a function.

The correct option is "Yes, because each input value has only one output value"

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Answer:

C. Yes, because each input value has only one output value

Step-by-step explanation:

The option (B) (2, 5), (3, 6), (6, 9) is a function.

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

"f(x) = ... " is the classic way of writing a function.

For the given situation,

The list of ordered pairs are given in option.

A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate.

According to the definition, the ordered pair should not have same x value.

Thus in option B (2, 5), (3, 6), (6, 9), each input is related to exactly one output.

Hence we can conclude that the list of ordered pairs of option (B) (2, 5), (3, 6), (6, 9) is a function.

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