Determine the next 2 terms if it is a geometric sequence, then write a recursive definition that matches the sequence in the form f(1)=120,f(n)=_*f(n-1) for n>2

Answer:B. The number is composite. Its prime factors written as a product are (5*3^3*2^2)

Step-by-step explanation:

Since 540 is an even number, that means it can be divided by 2. This means that the number is composite.

You can keep dividing it by 2 until you can't anymore.

Once you divide 540 by 2 twice, then you get 135.

You can divide it by 5 because the ones digit is 5.

Then you get 27, which is 3 times itself 3 times.

You finally multiply the numbers you divided by, and you get 2*2*5*3*3*3, which is 5*3^3*2^2.

Answer:

17

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}9-6\\\end{array}\right]+\left[\begin{array}{ccc}-5-(9)\\\end{array}\right][/tex]

=3+14

=17

Answer:

[tex]5\sqrt{5}[/tex] = ~11.18

Step-by-step explanation:

[tex](x+4)(2x+5)\\\\2x^2+5x+8x+20\\\large\boxed{2x^2+13x+20}[/tex]

Answer:

Step-by-step explanation:

cos(30) x tan (60) + sin (30) = (√3)/2 x √3 + 1/2 = 3/2 + 1/2 = 4/2 = 2

The constant of variation in  y = (3/2)x is (3/2)

y = kx                           (Where k is the constant)

Here, y = (3/2)x

so k = (3/2)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -1 , [tex]y_{1}[/tex] = -5 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = -3 .

On substituting the values of variables in equation1, we will get

m = ( (-1)-(-5) ) / ( (-3)-(3) ) = (4/0) = Infinity.

As the slope of a line is Infinity, so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

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  955°C is  temperature (in celsius) is the rate constant equal to 0.08857 sec-1.

What is the short definition of activation energy?

The least amount of energy necessary to bring atoms or molecules into a state where they can undergo chemical transformation or physical transport is known as the activation energy .

K = [tex]A . e^{\frac{-Eq}{RT} }[/tex]

logk = logA = Eq/RT

log0.02629 = log5.57 × [tex]10^{10}[/tex] sec-1  -  [tex]\frac{125.6 * 10^{3} }{8.314 * T}[/tex]

                   = log5.57  + [tex]log 10^{10}[/tex]  - [tex]\frac{12.56 * 10^{3 J} }{8.314 * T}[/tex]

                   = log5.57  + 10log10 - 15.10 * 10³ J/T

   -1.5483 = 0.7458 + 10 - 15.10 * 10³/ T

  -1.5483 = 10.7458 - 15.10 * 10²/T

 - 15.10 * 10³/ T   = -1.5483 - 10.7458

   15.10 * 10³ /T = 12.2941

 T = 15.10 * 10³/ 12.2941

       = 1228K

       = 955°C

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Answer:

5/6

Step-by-step explanation:

Get LCD of 30 and add

9/30 + 16/30

25/30

Reduce

5/6

Answer:

Step-by-step explanation:

simplify

6/7x + 7= 31

6/7x+7-7=31-7

6/7x=24

6/7x=24/6/7

28

6/7(28)+15-8=31

24+15-8=31

39-8=31

Answer:

5 50bw syfnauw dux fyq euw eywvr6b

The dimensions of the decks increased by the 11 feet.

According to the statement

We have to find that the length by which we increase the dimensions.

So, For this purpose, we know that the

The Area is the amount of space occupied by a two-dimensional figure.

From the given information:

Ashley has a deck that measures 22 feet by 11 feet. She wants to increase each dimension by equal lengths so that its area is tripled.

Then

The shape of the deck is the rectangle then dimensions is 22 feet by 11 feet.

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  22* 11

Area of the deck with the given dimensions =  242.

Then the dimensions increased by the x

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  (22+x)* (11+x)

Area of the deck with the given dimensions =  242 + 22x+11x+x^2

Area of the deck with the given dimensions =  242 + 33x+x^2

Then according to given details:

x^2 + 33x + 242 = 3*242

x^2 + 33x + 242 = 726

x^2 + 33x = 726 - 242

x^2 + 33x = 484

x^2 + 33x - 484 = 0

After solving

The value of the x become

x = 11 and x = -44

Then second option be neglected.

Then the length increased by the 11 feet.

So, The dimensions of the decks increased by the 11 feet.

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The maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively

Here, we have

Weight = 35 pounds

Labeled weight = within 8 ounces

Convert ounce to pounds

So, we have:

Labeled weight = within 0.5 pound

The equation is then represented as

|x - 35| = 0.5

Where x represents the labeled weight

In (a), we have

|x - 35| = 0.5

Expand

x - 35 = 0.5 and x - 35 = -0.5

Add 35 to both sides

x = 36 and x = 35

Hence, the maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively

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Natalie’s current available balance is $116.07.

To find current available balance, we need to subtract pending deposits/ credits with pending withdrawals/ debits.

Account Balance = Pending deposits / credits – Pending Withdrawals /debits

= $126.02- $97.68 = $28.34

Available Balance = Account Balance + Current Posted Balance

= $28.34 +$87.73 = $116.07

Current Available Balance = $116.07

The balance in checking or demand accounts that is available for use by the client or account holder is known as the available balance. The accessible balance of an account holder may not match the current balance. Any unfinished transactions are often included in the current balance.

Pending Deposit Credits: Pending check deposits that haven't been processed, haven't been credited to your account, or didn't have availability when we got them.

Pending Deposit Debits: Your account is put on hold for the transaction's amount until it is processed.

Hence Natalie’s current available balance is $116.07.

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Step-by-step explanation:

we must want to find C

Answer:

55 sq ft

Step-by-step explanation:

okay so the are of the lil square is 9 sq ft and the area of the big square is 64 sq ft so j subtract the small from the big

Answer: 55cm ^2

Step-by-step explanation:

Area of a square is A=a^2

Area of small square is 3cm^2 = 9cm^2

Large square has an area of 8cm^2 = 64cm^2

64 - 9 = 55 cm^2

Therefore the remaining area is 55 centimeters squared

Answer:

slope = -4

Step-by-step explanation:

slope = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{-10 - (-2)}{-2 - (-4)}[/tex] = [tex]\frac{-10 + 2}{-2 + 4}[/tex] = [tex]\frac{-8}{2}[/tex] = -4

The volume of pyramid is 9.16×10⁷ feet³.

We are given the measure of each side of Great Pyramid, which will be it's length and width. Also, we are given height. The formula for calculation of volume of pyramid is -

Volume = (length×width×height)÷3

Keep the values in formula to find the volume of Great Pyramid

Volume = (756×756×481)÷3

Performing multiplication on Right Hand Side of the equation to find the volume of Great Pyramid-

Volume = 274908816÷3

Solving the Right Hand Side of the equation, by performing division, we get the volume of Great Pyramid -

Volume = 9.16×10⁷ feet³

The volume of Great Pyramid is 9.16×10⁷ feet³.

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The fraction for 0.1515... is 5/33

It is possible to convert non terminating decimals to fraction. Because decimals are originally obtained from fractions itself.

If we have a terminating decimal number, by multiplying and dividing with powers of 10 gives a fraction.

For example, for the decimal 0.25, multiply and divide it with 100 which gives, 25/100 = 1/4.

Now we need to find the fraction corresponding to the decimal 0.1515..

Let x = 0.1515...

First we take 100x = 15.1515...

Now we can subtract the decimal part completely from 15.1515... since it is non terminating.

Now, 100x - x = 15.1515..- 0.1515.. = 15

Therefore, 99x = 15

and x = 15/99 = 5/33

So 5/33 is the fraction for the decimal 0.1515...

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The inequality that represents the number of nights he can stay in Dallas is 155n+ 99 ≤ 850 (option d).

Here are inequality signs and what they mean:

Since his budget is $850, he can spent a total of $850 or less than $850 on the trip. The sign that would be used to represent this is ≤.

(Total hotel stay cost) + cost of flight ≤. budget

(cost per night x number of hotel stays) + $99 ≤ $850

155n + $99 ≤ 850

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Answer:

Answer is D

Step-by-step explanation:

In the given triangle the statement that holds true is [tex]b^2+c^2 < a^2[/tex]. Therefore, the option (c) is the correct option.

In the cosine formulas, the cosine (cos) function is discussed. Consider a right-angled triangle with one acute angle, x. The cosine formula is cosx = (adjacent side) / (hypotenuse), where "adjacent side" refers to the side adjacent to angle x and "hypotenuse" refers to the longest side of the triangle.

As per cosine rule fore given [tex]$\triangle$[/tex]ABC:

[tex]$\cos \theta=\frac{b^2+c^2-a^2}{2 b c}$$$[/tex]

According to the question;

For a given [tex]$\triangle$[/tex]ABC;

cos e < 0.

Therefore, [tex]\quad \frac{b^2+c^2-a^2}{2 b c} < 0 \\[/tex]

[tex]b^2+c^2 < a^2[/tex]

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Step-by-step explanation:

or, x + 65° = 180° [ Being Straight line]

or, x = 180° - 65°

or, x = 115°

Therefore the value of x is 115° .

Now,

or, 4x = 4 × 115° = 460° .

The distance of AO and BO are the same so the given triangle will be an isosceles triangle.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

The given vertices are making a triangle as shown below in the figure.

Distance between A(5,12) and O(0,0) is

⇒ [tex]\sqrt{(5 - 0)^2 + (12 - 0)^2}[/tex]

⇒ 13

Distance between B(13,0) and O(0,0) is

⇒ [tex]\sqrt{(13 - 0)^2}[/tex]

⇒ 13

Since the two sides are the same so triangle will be isosceles.

Hence "The distance of AO and BO are the same so the given triangle will be an isosceles triangle".

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Answer:

Option B

Step-by-step explanation:

→ Find the option with the smallest power

Option B

The value of X in the equation that allows a solution with the values of "a" and "b" is x = 16

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

   We write the given equation

b = 3x + 4a

 and we have the values of the coefficients a and b, and these are:

  We substitute these values in the equation:

b = 3x + 4a

(12) = 3x + 4(-9)     :::: We solve the equation

12 = 3x -36

3x = 12 + 36

3x = 48

x = 48/3

x = 16

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