Two students start a club the first week of school. Each member invites three new members the second week of school. Each of these new members then invites three additional members the following week. If the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks?
80 students
121 students
242 students
363 students

The derivative of the given equation is x = −3√2 ≈−1.259921049894873.

In mathematics, the derivative is the rate of variation of a function given respect to a variable. Derivatives are essential for solving calculus related differential equation issues.

The derivative is defined as the slope of a straight line that is tangent towards the curve at a certain location. An additional derivative definition is the limit of the function's instantaneous rate of evolution as the time between observations approaches zero. activity, such as currency and interest rate risk, for a set length of time.

It is significant because many physical phenomena, such as velocity, acceleration, and force, are defined with an instantaneous rate of change of some other quantity.

Given :

9x^2(1+2x^-3).

= [tex]9\left(\frac{2}{x^3}+1\right) x^2[/tex]

= [tex]\frac{\mathrm{d}}{\mathrm{d} x}\left[9\left(\frac{2}{x^3}+1\right) x^2\right][/tex]

= [tex]=9\left(\frac{\mathrm{d}}{\mathrm{d} x}\left[\frac{2}{x^3}+1\right] \cdot x^2+\left(\frac{2}{x^3}+1\right) \cdot \frac{\mathrm{d}}{\mathrm{d} x}\left[x^2\right]\right)[/tex]

=  [tex]=9\left(\left(2 \cdot \frac{\mathrm{d}}{\mathrm{d} x}\left[\frac{1}{x^3}\right]+\frac{\mathrm{d}}{\mathrm{d} x}[1]\right) x^2+\left(\frac{2}{x^3}+1\right) \cdot 2 x\right)[/tex]

= [tex]=9\left(\left(2(-3) x^{-4}+0\right) x^2+\left(\frac{2}{x^3}+1\right) \cdot 2 x\right)[/tex]

= [tex]=9\left(2\left(\frac{2}{x^3}+1\right) x-\frac{6}{x^2}\right)[/tex]

= [tex]=18\left(\frac{2}{x^3}+1\right) x-\frac{54}{x^2}[/tex]

= [tex]\frac{18 x^3-18}{x^2}[/tex]

x = −3√2 ≈−1.259921049894873.

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Answer:

£1.6

Step-by-step explanation:

we can round 1.252 to 1.25

to find how much 2 euros is, we first have to make 1.25 into 2.

to do that, we will use the same equation to get the answer for £

1.25/5*8=0.25*8=2. now we repeat for £1

1/5*8=0.20*8=1.6

hope it helps

11 > x is the possible values for the number.

In algebraic formulations, numbers are represented by letters or alphabets without their numerical values being specified. The fundamentals of algebra taught us how to represent an unknown value using letters like x, y, and z. Here, these letters are referred to as variables. A mathematical expression may have both variables and constants. A coefficient is any value that is introduced before and increased by a variable.

Given that :The sum of a number x and 33 is greater than the product of 4 and that number.

x + 33 > 4x

33 > 3x

11 > x

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The solution to the system of the equations h = (1/2)t + 4 and h = (1/4)t + 5.5 will be 7 cm and 6 weeks.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Half a centimeter grows on a 4 cm bean plant per week. One-fourth of a centimeter is added to a 5.5 cm bloom per week.

Let h be the height of the plant and t be the number of weeks. Then the equations will be

h = (1/2)t + 4

h = (1/4)t + 5.5

The solution to the equations will be

(1/2)t + 4 = (1/4)t + 5.5

(1/2 - 1/4)t = 5.5 - 4

t / 4 = 1.5

t = 6

Then the height of the plant will be

y = (1/2)6 + 4

y = 3 + 4

y = 7

The solution to the system will be 7 cm and 6 weeks.

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Answer:

35/20 yards

Step-by-step explanation:

We know the keyword “cut” means to divide, so we now know we have to use division.

7 3/4÷5/1

First, make 7 3/4 an improper fraction.

7 x 4 = 28

28+7= 35

Remember to keep the denominator.

35/4 ÷ 5/1

Then, use the method Keep, Change, & Flip.

(35/4)(1/5) = 35/20

Therefore…

Each piece will be 35/20 yards long.

Answer:

     the value of h(4) is 36 from given equation.

Step-by-step explanation:

Given that

        h(x) = x³ - 2x² + x

To find

So, according the question

We have,

        h(x) = x³ - 2x² + x

For finding the value of h(4) from the given polynomial equation, we have to replace x from 4 or in other word we have to put x = 4 in given polynomial equation.

So, let's put x = 4 in that equation.

We get,

        h(4) = (4)³ - 2(4)² + 4

               = 64 - 2×16 + 4

               = 68 - 32

        h(4) = 36  

Answer: Hance the value of h(4) is 36 from given equation.

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Answer:

the father is 45 and the son is 15

Answer: The answers are (-8,8) and (2,-12)

Step-by-step explanation: I substituted the coordinates into the equations and on both sides they matched!

Hope this helps! :3

The values of the two unknowns x and y are 8 and 32 respectively.

Here, we are given the following set of ratios-

21x, 1/4, y/8

These ratios are all equivalent, this implies-

2/x = 1/4 = y/8

Let us take the first two ratios-

2/x = 1/4

cross multiplying the two we get

2 x 4 = x

8 = x

x = 8

We've found the value of x

Now, let us take the other two ratios-

1/4 = y/8

again, cross multiplying the two we get

y = 4 x 8 y = 32

Thus, the values of the two unknowns x and y are 8 and 32 respectively.

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Your question was incomplete. Check for full content below-

21x, 1/4, 7/8

If the given set of ratios is equivalent, find the unknowns.

The solutions of the linear equations are below:

(1/3)*x + 7 = 3 + (2/3)*x  is true if x = 12

5r−8=9r−12   is true if r = 1

(5/9)t− 27 = (1/9)t + 21   is true if t = 108

−(1/2)(−5y+4) = 2 + 1/2y  is true if y = 2.

a) The first linear equation we have is:

(1/3)*x + 7 = 3 + (2/3)*x

To solve this, move all the like terms together (I will move the ones with x to the left side and the ones without x to the right side).

(1/3)*x - (2/3)*x = 3 - 7

Now we just simplify:

-1/3*x = -4

Now we isolate x:

x = -3*-4 = 12

x = 12

That is the solution of the linear equation, so remember, you just need to isolate the variable.

Let's do the same for the other ones:

2) 5r−8=9r−12

5r - 9r = -12 + 8

-4r = -4

r = -4/-4 = 1

r = 1

3)  (5/9)t− 27 = (1/9)t + 21

(5/9)*t - (1/9)*t = 21 + 27

(4/9)*t = 48

t = (9/4)*48 = 108

4) −(1/2)(−5y+4) = 2 + 1/2y

Here we start by expanding the product in the left side, we will get:

(5/2)*y - 2 = 2 + (1/2)*y

(5/2)*y - (1/2)*y = 2 + 2

(4/2)*y = 4

2*y = 4

y = 4/2 = 2

y = 2

And so on, that is the general method to solve linear equations, just isolate the variable in one side of the equation and simplify the other side.

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Answer:

Above sea level (positive)

Below sea level (negative)

Temperature (can be both)

Money loans (can be both)

science (protons have both negative and positive charge)

Step-by-step explanation:

Answer:

C(x) = 20x + 120

Step-by-step explanation:

(a). If x=5 (you replace x with 5)

C(5) = 20(5) + 120

= 100+120=$220

Cost of producing five items is $220

(b). if x=16

C(16) = 20(16) + 120

= 320 + 120 = $440

Cost of producing sixteen items is $440

(c). C(35) = 820

This means that the cost of producing 35 items is $820

Hope this helps :⁠-⁠) xoxo

The possible cubes of an integer whose square is 100 can be 1000 and (-1000).

If the square of an integer is 100, then to find the value of integer we need to know the square root of 100

There exist two square roots of any number  one with negative sign and another with positive sign

The square roots of the given integer  that is 100  are 10 and -10

Now, we need to find out the value of [tex]10^{3}[/tex] and [tex]-10^{3}[/tex]

First cube  [tex]10^{3}[/tex] which can also be written as 10×10×10 = 1000

Second cube [tex]-10^{3}[/tex] which can also be written as( -10)×(-10)×(-10) = (-1000)

So, the possible cubes of an integer whose square is 100 can be 1000 and (-1000).

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The area of the remaining part of a large rectangle is 8m².

It should be noted that the original rectangle had sides of 8m by 6m.

In this case, it was stated that 4m was cut out from each side. The value of the remaining sides will be:

Area = Length × Width

Area = (8 - 4) × (6 - 4)

Area = 4 × 2

Area = 8m²

Therefore, the area of the remaining part of a large rectangle is 8m².

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Answer:

10

Step-by-step explanation:

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]

In linear equation ,the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.

What is linear equation?

Using the concept of proportional relationship, the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.

Using the concept of proportional relationship :

For Evian :

1.5 miles = 15 minutes

1 mile = x

1.5x = 15

x = 15 / 1.5

x = 10 minutes

For Toby :

2/3 miles = 6 minutes

1 mile = x

2/3x = 6

x = 6 ÷ 2/3

x = 9 minutes

For J :

0.75 miles = 9 minutes

1 mile = x

0.75x = 9

x = 9 / 0.75

x = 12 minutes

Therefore, the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.

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The complete question is -

Students at Polk Middle School are given a fitness test. The results of their tests are shown in the table. Use the table to answer questions d-c. a. Find the time it takes each student to run 1 mile. FITNESS TEST RESULT Evian 1 1/2 miles in 15 minutes Toby: 2/3 miles in 6 minutes Jillian 3/4 miles in 9 minutes.​

Based on the population of Brazil in 1855 and 1860, the estimated population in 1870 is C. 19.15 million

The increase in the population between 1855 and 1860 was:

= 12.51 - 10.112

= 2.398 million

The increase is:

= 2.398/10.112

= 24%

With an increase of 24% every 5 years, the population in 1870 is:

= 10.112 x (1 + 24%)³

= 19.27 million

In conclusion, we can estimate that the population of Brazil in 1870 was 19.15 million.

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According to the given statement

Money is spent on food =8640

on rent is = 3240

Savings refers to the money that is left over after consumer expenditure is deducted from disposable income during a specific time period. Savings, then, is the net amount of money that a person or household has left over after all bills and commitments have been paid.

Savings are retained as cash or cash equivalents (such as bank deposits), which carry negligible risk of loss but also negligibly low returns. Savings can increase through investing , but doing so necessitates risking some of the money.

According to the given value;

saving = 36000 x 2/5

= 7200 x 2

=14400

=36000- 14400

=21600. left

food = 40/100 x 21600

=40 x 216

=8640

rent = 15/100 x 21600

=15 x 216

=3240

Money is spent on food =8640

and on rent is = 3240

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Answer:

Option 3

Step-by-step explanation:

See attached image.

Answer:

x=45+5b

Step-by-step explanation:

x is  the total

The function, after the transformations is y'' = 1/4(x +84)

The function equation is given as:

y = |x|

1) Reflect the function about the y-axis.

This is represented as

(x, y) = (-x, y)

So, we have:

y' = |-x|

This gives

y' = |x|

This is represented as

(x, y) = (x, 1/4y)

So, we have:

y'' = 1/4y'

This gives

y'' = 1/4|x|

This is represented as

(x, y) = (x + 84, y)

So, we have:

y'' = 1/4(x +84)

Hence, the function, after the transformations is y'' = 1/4(x +84)

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Answer:

Step-by-step explanation:

1. m1=50 so m5= 50 (corresponding)

2. m4=45, then m6=123 (given in 4. but also... angles 6+8 = 180)

3. m2= 130, so m7 = 130 (alt interior)

4. m6 = 123, so m3 = (alt interior)

Value of the manuscript is as follows

A. The value of the manuscript 5 years ago is $250.

B. The value of the manuscript now is $10,000.

Appreciation is an increase in the value of an asset over time. This is unlike depreciation, which lowers an asset's value over its useful life. The appreciation rate is the rate at which an asset grows in value.

% increase=(new price - original price) / original price

8.0= 2000/original price

8*original price = 2000

original price = $250

So the value of the manuscript 5 years ago is $250.

Increase is 2000 , 5 times that.

new price is $10,000

The value of the manuscript now is $10,000.

Hence , the manuscript has the following value:

A. The manuscript was worth $250 five years ago.

B. The manuscript is currently worth $10,000.

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Answer:

AM= 2x+4

MB= 5x-8

AB= ?

So to get AB, you would need to find the total measurements of AM and MB.

AM=MB

2x+4=5x-8

2x=5x-12

-3x=-12

x=4

So now to find the measurement of AB, you need to plug it into AM and MB.

2(4)+4+5(4)-8= 24!!!

So the measure of AB would be 24.

Step-by-step explanation:

7.25 is the right response as a change figure.

According to the query, Joyce purchased 2.2 pounds of apples for a total of $1.25 per apple.

As a result, Joyce has paid a total of 2.2 x 1.25 = 2.75.

She then paid the $10 bill:

Amount left over: 10 - 2.75 = 7.25

Therefore, 7.25 is the right response as the remaining sum.

Cost price is the sum of money that is paid to the maker or the buyer for the good. They'll alter the sum and set a selling price later.

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The variable terms of the expression 5 - 8n - 3n² are: n, n²

(5 - 8n - 3n²)

In this question, we have been given an expression 5-8n-3n^2

We need to name the variable terms of the expression.

Also, we need to underline the variable part of each term.

We know that,  variable is a term which represents an unknown value or quantity.

We have been given an quadratic expression.

5 - 8n - 3n²

We can observe that, 5, -8, -3 are fixed numbers i.e., constants.

And the alphabet n can take any real value.

Consider the first term,

5 => it is a constant

Consider the second term,

- 8n => here, the variable is n

Consider the third term,

- 3n² =>  here, the variable is n²

Now, we underline the variable part of each term.

5 - 8n - 3n²

Therefore, the variable terms of the expression 5 - 8n - 3n² are: n, n²

(5 - 8n - 3n²)

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Answer:

Hope this helps :)

412 × 77 = 31,724

Which is estimated about 30,000 something.

The nearest whole number (ones place).

$14.59+ $5.83 + $0.89 =21 rounding off

Given,

$14.59+ $5.83 + $0.89

Whole no. is 0,1,2..

If we add these number we get 21.31 is 21

When rounding numbers, there are several basic guidelines that must be observed.

We must first determine our rounding digit. This is the digit that will be affected in the end.

Following that, we must examine the digit to the right of this location, which will determine the fate of the rounding digit.

We do not modify the rounding digit if the digit to the right is less than 5. All digits to the right of the rounding digit, however, are altered to 0.

If the digit to the right is 5 or greater, the rounding digit is increased by one, and all digits to the right of the rounding digit are converted to 0.

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The linear equation that passes through (10, 6) and (30, 12) is:

y = (3/10)*x + 3

Remember that the general line equation (in the slope-intercept form) is:

y = a*x + b

Where a is the slope and b is the y-axis intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

Then in this case the slope is:

a  = (12 - 6)/(30 - 10) = 6/20 = 3/10

Replacing that in our line we get:

y = (3/10)*x + b

To find the value of b we replace the values of one of the points, i will use (10, 6), it gives:

6 = (3/10)*10 + b

6 = 3 + b

6 - 3 = b = 3

Then we conclude that the linear equation is:

y = (3/10)*x + 3

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Answer:9874

Step-by-step explanation: