a sequence is defined by a term to term rule

iteration help please

Step-by-step explanation:

use formula

[tex](x - y) {2} = x {}^{2} - 2xy + y {}^{2} [/tex]

After simplification, the equivalent expression is 18(p-2). So the option D is correct.

In the given question,

We have to find factor 18p-36 equivalent expressions.

The given option is

A. 3(9p-12)

B. 9(2p-4p)

C. 2(9p-18)

D. 18(p-2)

The given expression is 18p-36.

We simplify the given expression to find their equivalent expression.

To simplify the expression we take out the common term from both terms.

We can see that 18 is a common multiply of both number 18 and 36. SO we take out 18 from both terms.

Taking common 18

18p-36 = 18(p-2)

Hence, the equivalent expression is 18(p-2). SO the option D is correct.

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The number of extra tables that you need to double the original seating capacity will be 7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The seating capacity y for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need.

If the no extra table is there. Then the value of 'y' will be

y = 8 (0) + 56

y = 56

Then the number of extra tables do you need to double the original seating capacity will be

8x + 56 = 2 × 56

8x = 56

x = 7

Then the number of extra tables that you need to double the original seating capacity will be 7.

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The annual rate of interest have to be 3.87%.

Mathematically, compound interest can be calculated by using this formula:

A = P(1 + r/n)^{nt}

Where:

Making the interest rate (r) the subject of formula, we have:

r = n[(A/P)^{1/nt} - 1]

Note: A = SI + P = 600 + 30,000 = $36,000

Substituting the given parameters into the formula, we have;

Interest rate, r = 1[(36,000/30,000)^{1/1 × 4.8} - 1]

Interest rate, r = [(1.2)^{0.20833333333} - 1]

Interest rate, r = [1.0387 - 1]

Interest rate, r = 0.0387

Interest rate, r = 3.87%.

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As per the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .

As given in the question,

Number of stacks of program to be divided = 1

Number of friends = 3

Number of people among whom stack of program is to be divided = 4

Let us consider stack of program divided equally

Fraction of stack of program each friend will get = 1 /4

As

( 1 / 4 ) +  ( 1 / 4 ) + ( 1 / 4 ) + ( 1 / 4 )

= ( 1+ 1+ 1+ 1) / 4

= 4/4

= 1

Therefore, for the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .

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Answer:

A= 6n

B= 9n

C= 15n

Step-by-step explanation:

It's just adding.

A= 6n

B= 9n

C= 15n

The graph of this proportional relationship would look like this: A line passes through the point (0, 0) and continues through the point (14, 7).

In Mathematics, a graph simply refers a type of chart that is typically used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) increases or decreases, the values on the y-coordinate (y-axis) increases or decreases simultaneously.

By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it passes through both points (0, 0) and (14, 7).

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Answer:

1. Plot x = 0

(A. IF YOU CAN EASILY FIND IT, PLOT Y = 0)

(B. BONUS: PLOT A FEW EASY TO CALCULATE POINTS LIKE X = 1 & X = -1)

2. Figure out what happens when x is really big (in the positive and negative direction)

3. Optional: look for any “significant” x-values

4. Connect the dots and finish!

Step-by-step explanation:

1. Plot x = 0

The first thing we want to do is get some points up on our graph, so we want to pick the ones that will be easy to calculate. For almost any equation, plugging in x = 0 and solving for y is fast and easy to do by eye, and almost always doable without a calculator. For our example equation:

So, the first point we’ll put on our graph is (0, -4).

Answer: its 18,0000

Step-by-step explanation: Be smart  2x9= 18+ three 0,s?

2/3 is the unit rate of the relationship

A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e.  $5 for one orange.

On a linear graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:

Slope = y2-y1 / x2-x1  

Thus, we can any two convenient points on the graph and use it calculate the slope as shown in the attached image:

Slope = y2-y1 / x2-x1

Slope = 6-2 / 9-3 = 4/6 = 2/3

Therefore, the unit rate for this relationship is 2/3. The 2nd option is the answer

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Answer:

If the coordinates of at least two points in the line are given, the slope (m) may be calculated by,                               m = (y2 - y1) / (x2 - x1

By using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 62.

In the image, we can see two supplementary angles, where by definition, two angles are supplementary if their addition is equal to a plane angle (an angle of 180°).

With that in mind, we can write the linear equation:

x + 118 = 180

So we just need to isolate x in that simple linear equation.

If we subtract 118 in both sides, we will get:

x + 118 - 118 = 180 - 118

x = 62

So the unknown angle has a measure of 62°.

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Answer:

θ = 64.98310506 degrees (65 degrees rounded to unit)

Step-by-step explanation:

4.2 * tanθ = 9

4.2 * tanθ/ 4.2 = 9/4.2

tanθ = 2.142857

θ = arctan 2.142857

θ = 64.98310506

Step-by-step explanation:

using the SOH CAH TOA Rule,

tan 0=opp÷adj

tan 0=9÷4.2

tan 0=2.14

0=tan inverse of 2.14

The value of f(9) is 13

The function f(x) = x + 4

The function g(x) = 3x / x+1

The function is the mathematical statement that show the relationship between one variable and another variable. If one variable is independent variable and another variable will be dependent variable. Also the function is the equation that shows the relationship between the input  and output.

The function

f(x) = x + 4

We have to find the value of f(9)

We have to substitute the value of x = 9 in the function

f(9) = 9 + 4

Add the terms

f(9) = 13

Hence, the value of f(9) is 13

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The exponential model for the lily pad colony is L(t) = A[tex](1+r)^{kt}[/tex] and the values of A=5 and k=1.2.

Over time, anything grows in quantity through an exponential growth process. When a quantity's rate of change over time (or derivative) is proportional to the quantity itself, this phenomenon takes place. A number that is increasing exponentially is referred to as a function, and the exponent, which stands for time, is the variable that represents time (in contrast to other types of growth, such as quadratic growth).

When a quantity decrements with time, it is considered to be experiencing exponential decay rather than a positive constant of proportionality. It is also known as geometric growth or geometric decay when the definition's discrete domain has equal intervals since the values of the function form a geometric progression.

Given, there are 5 lily pads that are found in a pond

And after 30 days, there are 16 lily pads in that pond

Here, a=5

r=(11-5)/5=1.2

f(x)=a(1+r)ˣ

f(x)=5(1+1.2)³⁰

From the above equation, A=5, and k=1.2

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Answer:

j = 9

Step-by-step explanation:

Given equation,

→ -3(j - 8) + (-6) = -9

Let's solve for the value of j,

→ -3(j - 8) + (-6) = -9

→ -3j + 24 - 6 = -9

→ -3j + 18 = -9

→ -3j = -9 - 18

→ j = (-27)/(-3)

→ [ j = 9 ]

Hence, the value of j is 9.

Answer:

j = -9

Step-by-step explanation:

[tex] - 3(j - 8) + - 6 = - 9 \\ open \: brackets \\ - 3j + 24 + - 6 = - 9 \\ 3j + 24 = - 9 + 6 \\ 3j + 24 = - 3 \\ 3j = - 3 - 24 \\ 3j = - 27 \\ divide \: by \: 3 \\ j = - 9[/tex]

The horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

Let f(x) = [tex]\frac{9x^{3}-5x-9}{4x^{3}-9x+4}[/tex]

Line y = L is a horizontal asymptote of the function y=f(x), if either [tex]\lim_{x \to \infty} f(x) = L[/tex] or, [tex]\lim_{x \to -\infty} f(x) =L[/tex] and L is finite.

We will calculate limits :

[tex]\lim_{x \to \infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

[tex]\lim_{x \to -\infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]

Hence, horizontal asymptote is y = [tex]\frac{9}{4}[/tex].

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Answer:

x=y , x-3y=4. x = y x = y , x − 3y = 4 x - 3 y = 4. Replace all occurrences of x x with y y in each equation. Tap for more steps... −2y = 4 - 2 y = 4. x = y x = y. Divide each term in −2y = 4 - 2 y = 4 by −2 - 2 and simplify. Tap for more steps... y = −2 y = - 2.

Step-by-step explanation:

Just smart

Answer:

C) 29

Step-by-step explanation:

1st equation - 2nd equation,

x+y - (x-3y) = 40-(-4)

x+y-x+3y = 40+4

4y = 44

y = 44÷4

y = 11

substituting y into the first equation,

x + 11 = 40

x = 40-11 = 29

answer is C

hope it helps. :)

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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Step-by-step explanation:

a + b + c + d = 125

a + 4 = b - 4 = 4c = d/4

a + 8 = b

a = b - 8

16c = d

b = 4c + 4

4a + 16 = d

b - 8 + 4c + 4 + c + 16c = 125

4c + 4 - 8 + 4c + 4 + c + 16c = 125

25c = 125

c = 5

d = 16c = 80

4a + 16 = d = 80

4a = 64

a = 16

b = a + 8 = 16 + 8 = 24

so, the numbers are

16, 24, 5, 80

Answer:

Step-by-step explanation:

Which graph represents the solution set of - 4x - y ≤ - 6?

Answer: 0.000089

Step-by-step explanation: 0.000089 is already in standard form, if you want 0.000089 in the scientific form then that would be...

8.9 x 10⁻⁵

The probability that the mean actual weight for the 100 weights is greater than 25.2 is equal to 0.0136%.

In order to determine the probability that the mean actual weight for the 100 weights is greater than 25.2, we would have to calculate the mean and standard deviation.

In a uniform distribution, the mean of a data set can be calculated by using this formula:

Mean, E(x) = [a + b]/2

Where:

Substituting the given parameters into the formula, we have;

Mean, E(x) = [24 + 26]/2

Mean, E(x) = 50/2

Mean, E(x) = 25.

For the standard deviation, we have:

Standard deviation, S(x) = √((b - a)²/12)

Standard deviation, S(x) = √((26 - 24)²/12)

Standard deviation, S(x) = √((2)²/12)

Standard deviation, S(x) = √(4/12)

Standard deviation, S(x) = 0.5774.

For the sample standard deviation, we have:

Standard deviation = S(x)/√n

Standard deviation = 0.5774/√100

Standard deviation = 0.5774/10

Standard deviation = 0.05774.

By applying the central limit theorem, we would determine the z-score as follows:

Z-score = (x - μ)/σ

Z-score = (25.2 - 25)/0.05774

Z-score = 0.2/0.05774

Z-score = 3.64

Therefore, the p-value is equal to 0.000136.

Probability (x > z) = 0.0136%.

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The volume of the fish tank required = 0.154 m^3.

A fish tank has a capacity = 154L.

Capacity of fish tank in Litre = Volume of the fish tank in meter cube

So the volume of the fish tank required in cubic meter.

For the volume we required a conversion of litre into meter cube.

Cubic meters and liters are two common metric units of volume.

1 cubic meter is 1000 liters.

To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters.

1L = 0.001 m^3

So 154L = 0.154 m^3

So the volume of the fish tank required = 0.154 m^3.

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Using division operations and based on the rates of production, given, Machine D works the fastest.

The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).

The rate of production is the number of goods that can be produced during a given period of time.

The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.

There are, therefore, two ways of determining production rate.  Firstly, we can divide the total production by the hours consumed.

Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.

                           Units          Production     Rate of

                       Produced          Hours      Production

Machine A        10,000               15             667 cups per hour

Machine B       25,000              20           1,250 cups per hour

Machine C       30,000              30           1,000 cups per hour

Machine D       15,000               10            1,500 cups per hour

Thus, using division operation, Machine D produces at the fastest rate than the other three machines.

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                           Units          Production

                       Produced          Hours

Machine A        10,000               15

Machine B       25,000              20

Machine C       30,000              30

Machine D       15,000               10

Step-by-step explanation:

e⁰ = 1

so, we have

(f² / (f³gh⁶))⁸ = f¹⁶ / (f²⁴g⁸h⁴⁸) = 1 / (f⁸g⁸h⁴⁸)

FYI - depending on what your teacher wants to see as simplified answer, it could be also

1 / (fgh⁶)⁸

or

(1 / (fgh⁶))⁸

but normally it should be the first result form above

1 / (f⁸g⁸h⁴⁸)

2y(xy+4)

Hope this answers your question!

Answer:

2y(xy+4)

Step-by-step explanation:

First, Distribute

you get 2y(xy+4) because you have to isolate the like terms than find a gcf of the terms

Answer:

5/48

Step-by-step explanation:

The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given,

James shares 5/8 of a cake between 6 people.

Now, 1/6 of 5/8 will be as,

1/6(5/8) = 5/48

Hence "The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48".

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