Does the infinite series converge or diverge? If it converges, what is the sum?

b. 1/3 - 1/9 + 1/27 - 1/81 + . . . .

Answer:

Q= ( -4 -9)

Step-by-step explanation:

Using the midpoint formula

X1 + X2 Y1 + Y1

----------, ---------

2. 2

The midpoint QR = (2, -5) and R = (-8, 1) Q =>(x, y)

= x + 8. y - 1

------------ = 2 and -------- = -5

2 2

=> (4 = x + 8) and( -10= y-1)

=> 4 -8 = x and -10+1= y

Q(x, y) = (-4, -9)

P'''( 1 , -2 )     Q'''( 0 , 1)   R'''( -1 , 3 )    S'''( -2 , 0) are the coordinates of P''' Q''' R''' S''' .

What does the term "coordinates" mean?

( x , y)  →  ( x + 3 , y - 2 )

p' ( -2, -1 )     Q' ( 1 , 0)    R'( 3, -3 )   S'(0, -4 )

( x , y )  →   ( x , -2 - y)

p''(-2 , - 1 )   Q''( 1 , 0 )     R''( 3 , 1 )      S''( 0,2 )

( X , Y ) →  ( -Y , X )

P'''( 1 , -2 )     Q'''( 0 , 1)   R'''( -1 , 3 )    S'''( -2 , 0)

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The interval using two different representations are (-∝, 11) ∪ (0, ∝) and {x | x < −11 or x > 0}

The interval is given as

x < −11 or x > 0

Inequalities like < and > are represented using the parenthesis ( and )

Also, the term "or" mean union and it is represented using ∪

So, one representation of the interval can be represented as

(-∝, 11) ∪ (0, ∝)

Another representation of the interval is {x | x < −11 or x > 0}

Hence, the interval using two different representations are (-∝, 11) ∪ (0, ∝) and {x | x < −11 or x > 0}

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Answer:

B.  -2  <  x  <  4

Step-by-step explanation:

The function is (x +2)/(x-4) and we are asked to determine the x interval when the inequality (x +2)/(x-4) < 0 is satisfied

1. Find the critical points

The critical points are

x = - 2 when the numerator becomes -2 + 2 = 0, and f(x) = 0

and

x = 4 when the denominator becomes 4 - 4 = 0 and (x + 2)/0 is undefined

So critical points are -2 and 4

2. Use these critical points to divide the number line into intervals
The intervals are -∞ < x < -2, -2 < x < 4 and 4 < x < ∞
these can be re-written as x < -2, -2 < x < -4 and x > 4

3. For each  of these intervals take a test point and see if it satisfies that inequality
(a) -∞ < x < -2    Take x = -3 which is less than -2
We get f(-3) =  (-3 + 2)/(-3 -4) = -1/-7 which is + 1/7 and does not satisfy the (x+2)/(x-4) < 0 inequality.

So we can discard this interval
(b) For interval -2 < x < 4, Let's take x = 0
(0+2)/(0-4) = 2/(-4) = -1/2 = -0.5 which does satisfy the inequality
(x+2)/(x-4) <0, so this is a valid interval

(c) For interval x > 4, take x = 5
(x+2)/(x-4 ) = (5 + 2)/(5-4) = 7/1 = 7 and does not satisfy (x+2)/(x-4 ) < 0

So the interval which satisfies the inequality is -2 < x < 4

ΔPRQ ≅ ΔTRS under both (side-side-side) SSS condition and (angle-side-angle) ASA condition.

So,

Given: ∠P ≅ ∠T, ∠S ≅ ∠Q, TR ≅ PR, RP ≅ RQ, RT ≅ RS, PQ ≅ TS

To Prove: Δ PRQ ≅ ΔTRS

So, ΔPRQ ≅ ΔTRS under both SSS condition and ASA condition.

Therefore, ΔPRQ ≅ ΔTRS under both SSS condition and ASA condition.

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The ratio of trick-or-treaters who were not dressed as snow white last Halloween is 5/9

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

On the other hand, proportion is the equality of two or more ratios.

example: a : b = c : d

If four out of every nine trick-or-treaters that came to your house last Halloween were dressed as snow white, then the rest were not dressed as snow white.

9 - 4 = 5

If five out every nine trick-or-treaters that came to your house last Halloween were not dressed as snow white, we can express the ratio as

5 out of 9 or 5 : 9 or 5/9

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The estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.

It follows from the task content that the estimated thickness of paper such that it is written using a single digit and a power of 10 as required in the task content is to be determined.

Given;

Thickness of sheet = 0.0013.

By rounding to one significant digit; the digit is considered and rounded down to zero which is added to 1 so that we have;

= 0.001.

On this note, since the number, 0.001 can be written via the laws of indices as;

= (1/1000)

= 1/10³

And ultimately, we have

= 1 × 10-³.

Ultimately, the estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.

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cot(55°) = 0.70021 ... cot(58°) = 0.62487 ... cot(77°) = 0.23087 ... cot(80°) = 0.17633

(1+cot55)(1+cot80)(1+cot77)(1+cot58).

In trigonometry, the cot or cotangent is one of the six trigonometric ratios. In a right triangle, the lattice of angles is equal to the ratio of the adjacent and opposite sides of the angle. Cot x is also equal to the reciprocal of tan x.

Therefore, the cotangent of the angle α of a right triangle is equal to the length of the adjacent side b divided by the opposite side a. To remove the crib, simply enter the length of the adjacent and opposite sides, then remove it. This formula can be very similar to the formula used to calculate the tangent.

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Option D is the correct answer.

Triangle Inequality Theorem states that the sum of two side lengths of a triangle is always greater than the third side.

If this is true for all three combinations of three combinations of side lengths.

i.e., a + b > c , b + c > a and c + a > b then the length form a triangle.

(A) 10 + 11 = 21 > 20

And 11 + 20 =31 > 10

And, 20 + 10 = 30 > 11

So, it forms a triangle

(B) 14 + 16 = 30 >28

And 16 + 28 = 44 >14

And 28 + 14 = 42 > 16

So, it forms a triangle

(C) 35 + 45 = 80 > 75

And 45 + 75 = 120 > 35

And 75 + 35 = 110 > 45

So, it forms a triangle

(D) 41 + 55 = 96 < 98

It does not form a triangle

because sum of two sides lengths is less than the third side length.

Hence, Option D is the correct answer

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Answer: 3 ft

Step-by-step explanation:

l=length. w=width. h=height. V=volume

V=l*w*h

24=4*w*2

24=8*w

8w=24

w=3 ft

Answer:

100 m/s

Step-by-step explanation:

divide by 3.6 to get km/h to m/s, multiply by 3.6 to get m/s to km/h!

Answer:

perimeter=4l then multiply with how many square are there

then area = l²

multiple with how many square are there

Answer:

Hello,

Step-by-step explanation:

Do you remember the formula

[tex]\boxed{a^3-b^3=(a-b)(a^2+ab+b^2)}\\\\\\27x^6y^9-64=(3x^2y^3)^3-4^3\\\\=(3x^2y^3-4)((3x^2y^3)^2+(3x^2y^3*4)+4^2)\\\\\\=(3x^2y^3-4)(9x^4y^6+12x^2y^3+16)\\[/tex]

The given equations are

[tex]x-2y=4[/tex]                               …(1)

[tex]3x+y=4[/tex]                               …(2)

Using Substitution method,

From the equation (1) [tex]x-2y=4[/tex] , the value of x is

= [tex]x=4+2y[/tex]

Putting the value of x in equation (2), we get

= [tex]3(4+2y)+y=4[/tex]

= [tex]12+6y+y=4[/tex]

= [tex]12+7y=4[/tex]

= [tex]7y=-8[/tex]

= [tex]y=-\frac{8}{7}[/tex]

Now, putting the value of y in equation (1), we get

= [tex]x-2(-\frac{8}{7}) =4[/tex]

= [tex]x+(\frac{16}{7}) =4[/tex]

= [tex]x =4-(\frac{16}{7})[/tex]

= [tex]x =(\frac{28-16}{7})[/tex]

= [tex]x =(\frac{12}{7})[/tex]

∴ The value of x is [tex]\frac{12}{7}[/tex] and the value of y is [tex]-\frac{8}{7}[/tex]

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The value of x is (12/7) and the value of y is (-8/7) for the given equation.

The given equations are

x - 2y = 4                              equation (1)

3x + y = 4                             equation (2)

Using Substitution method,

From the equation (1) i.e., x - 2y = 4 , the value of x is

x = 4 + 2y

Putting the value of x in equation (2), we get

3 ( 4 + 2y ) + y = 4

⇒ 12 + 6y + y = 4

⇒ 12 + 7y = 4

⇒ 7y = (-8)

⇒ y = (-8/7)

Now, putting the value of y in equation (1), we get

x - 2 ( -8/7 ) = 4

⇒ x + ( 16/7 ) = 4

⇒ x = 4 - ( 16/7 )

⇒ x = ( 28 - 16 )/ 7

⇒ x = 12/7

∴ The value of x is (12/7) and the value of y is (-8/7).

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What is Irrational Number?

An Irrational number is areal number that cannot be expressed as a ratio of integers; for example [tex]\sqrt{2}[/tex] is an irrational number. We cannot express any irrational number in the form of ratio, such as p/q, where p and q are integers, q[tex]\neq[/tex] 0. Again, the decimal expansion of an irrational number in neither terminating nor recurring.

Let us assume [tex]7\sqrt{56}[/tex] is rational.

So, we can write this number as

[tex]7\sqrt{56}[/tex] = a/b __(1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) divide by 7 both sides, we get

[tex]\sqrt{56}=\frac{a}{7b}[/tex]

Here, a and b are integers, so a/7b is a rational number, so [tex]\sqrt{56}[/tex] should be a rational number.

But [tex]\sqrt{56}[/tex] is a irrational number, so it is Contradictory.

Therefore, [tex]7\sqrt{56}[/tex] is irrational number.

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This is recursive sequence and -121,-108,-95,-82,-69,-56 these are the first five terms of sequence.

A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formulas:

1. The initial term in the series.

2. The general rule for determining any term from its preceding term.

Recursive Arithmetic Sequence Formula

The following is the recursive formula to determine the nth term in an arithmetic series:

an = an-1 + d for n ≥ 2

where

The common difference is d, and an is the nth term of an A.P.

given that

a₁ = -121

a (n) =a (n-1) +13 so, d = +13

For example, we need to extend the sequence term by term in order to find the first five terms:

a(1) = -121

a(2) = a(1) + d = -121 + 13 = -108

a(3) = a(2) + d = -108 + 13 = -95

a(4) = a(3) + d = -95 + 13 = -82

a(5) = a(4) + d = -82 + 13 = -69

a(6) = a(5) + d = -69 + 13 = -56

a(7) = a(6) + d = -56 + 13 = -43

Hence,this is recursive sequence and -121,-108,-95,-82,-69,-56 these are the first five terms of sequence.

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Answer:

2(x + 6) = 38

Step-by-step explanation:

First, we choose a variable to represent the unknown number.

1. Let x = the unknown number.

Then, we translate the sentence into an equation using the variable we chose.

"Twice the sum of six and a number is 38."

We do it piece by piece:

"the sum of six and a number":                        x + 6

"Twice the sum of six and a number":              2(x + 6)

"Twice the sum of six and a number is 38.":    2(x + 6) = 38

Now we have an equation that represents the sentence.

2(x + 6) = 38

Given events are independent events and the probability that getting an even number on die and getting odd number on a spinner numbered 1 to 5

In this question,

we have been given two events.

Let event A: rolling an even number on a die

event B: spin a spinner numbered 1 through 5 and get an odd number.

We can clearly observe that the occurrence of event A is not dependent on the other event B.

So, event A and event B are independent events.

The probability of event A is,

P(A) = n(A) / n(S)

here, sample space, n(S) = 6

n(A) = 3

So, P(A) = 3/6

P(A) = 1/2

The probability of event B is,

P(B) = n(B) / n(S)

here, sample space, n(S) = 5

n(B) = 3

So, P(B) = 3/5

Now we find the joint probability of these independent events.

⇒ P = P(A) × P(B)

⇒ P = 1/2 × 3/5

⇒ P = 3/10

Therefore, given events are independent events and the probability that getting an even number on die and getting odd number on a spinner numbered 1 to 5

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Based on the scale of the drawing, and the actual width, the width of a park in a drawing would be 14 inches.

A single inch of the width of a park in a drawing, is 5 yards of the width of the actual park.

This means that a single inch equates to 5 yards.

If there were therefore 70 yards in the actual park, the width of the drawing is:
= 70 / 5

= 14 inches

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Answer: x = 5, 7

Step-by-step explanation:

       This equation is already factored for us, so we can split it into two separate equations set equal to 0 and solve for x.

Given:

(x - 7)(x - 5) = 0

Equation #1:

x - 7 = 0

x = 7

Equation #2:

x - 5 = 0

x = 5

Solution:

x = 5, 7

Answer:

x = 5, x = 7

Step-by-step explanation:

(x - 7)(x - 5) = 0 ← in standard factored form

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x - 5 = 0 ⇒ x = 5

By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b

Given,

The algebraic expression = 7b-(3a-8b)

Expand the expression

7b-(3a-8b)= 7b-3a+8b

Rearrange the terms and combine like terms

7b-3a+8b= -3a+7b+8b

=-3a+(7+8)b

=-3a+15b

Hence, By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b

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Determine whether each infinite geometric series diverges or converges.The series converges.

If the series converges, state the sum. 1-1+1- . . . .

The sum of the infinite series is 1/2

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=1\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{-1}{1}=-1[/tex]

Since  [tex]\vert r\vert < 1[/tex] , the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{1}{1+1} =\frac{1}{2}[/tex]

The sum of the infinite series is 1/2

What is an infinite geometric series?

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Answer:

Step-by-step explanation:

58 + 66(x-1) + 50 = 1428cents

66(x-1) + 108 = 1428

66(x-1) =1320

x-1 = 20

x = 21 mins

The value for x = -2,0,1 and 4 is -5,1,4,13 respectively.

To "solve for x" is to determine the value of x that would result in the equation being true. Think about the following equation: x plus 1 = 3. You would have to figure out a value for x such that it produces three when one is added in order to try to solve it.

For x = -2,

3x+1

= 3(-2)+1

= -6 +1

= -5

For x = 0

3x+1

= 3(0) + 1

= 1

For x = 1

3x+1

= 3(1) + 1

= 4

For x = 4

3x+1

= 3(4) + 1

= 13

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The direct variation equation between x and y is 4x = y.

Here, we are given that x and y are in direct variation. In other words, this means that x and y are directly proportional to each other.

Thus, if k is a constant term, then the relation between x and y can be represented as-

x = ky

Now, we are given that if y = 12, x = 3

⇒ 3 = 12k

12k = 3

k= 3/12

k= 1/4

Thus, we found the value of k, the relation will become-

x = y/4

or 4x = y

Thus, the direct variation equation between x and y is 4x = y.

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Answer: 1st option

Step-by-step explanation:

Black to Red is the transformation

C to C'

I to I'

Q to Q'

G to G'

1st, graph is moved up by 1 unit(+1 in x direction)

Then, graph is moved to right by 5 units(+5 in y direction)

(1, 5) is the change ==> 1st option

Answer:

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

Reason:

In the first graph, it is possible to draw a single vertical line through more than one point on the blue graph. For instance, draw a vertical line through 1 on the x axis.

Because this happens, we consider the graph to "fail the vertical line test". This leads to the graph not being a function.

A function is only possible if any input in the domain leads to exactly one and only one output.

The input x = 1 leads to multiple outputs y = 3 and y = -3 simultaneously.

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

On the other hand, the second graph doesn't have this issue happening. It's impossible to draw a single vertical line through more than one point on the blue graph.

Therefore, this graph passes the vertical line test and it is a function. Whatever x input you pick, it leads to one y output only.

Answer:

561

Step-by-step explanation:

168/3=56 (10 percent of armandos pull ups)

56 x 10 = 560 (100 percent of armandos pull ups)

Now it is equal. We are looking for greater than armando. You would need 561 pull ups to have more

The measures of the angle and it's supplement are144°  and 36° respectively.

The measure of the supplement of an angle is four times the measure of the angle. (given)

Let us consider the value of the supplement be X°.

Therefore the value of the angle  is 4X°

 180 - X = 4X

  X = 36° (The value of supplement)

180°-X = 144°( The value of angle)

Hence the angles are 36° and 144° .

The measures of the angle and it's supplement are144°  and 36° respectively.

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