The teacher is handing out note cards to her students. She gave 48 note cards to the first student, 54 note cards to the second student, 60 note cards to the third student, 66 note cards to the fourth student, and 72 note cards to the fifth student. If this pattern continues, how many note cards will the teacher give to the sixth student?

Functions are expressed by writing a variable in terms of other variables known as the independent. The derivative of the given function is -3/(x-2)².

Given the function below;

f(x) = 3/x-2

Since it is a quotient, we can use the quotient rule to express the equation as shown:

let u = 3 and v = x -2

du/dx = 0 and dv/dx = 1

According to the rule;

dy/dx = (x-2)(0) - 3(1)/(x-2)²

dy/dx = 0-3/(x-2)²

dy/dx = -3/(x-2)²

Hence the derivative of the given function is -3/(x-2)²

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Answer:

14,987

Step-by-step explanation:

Answer:

1.93233498E244

Step-by-step explanation:

Answer:

3.14159265

Step-by-step explanation:

The equation for the lines whose graph is depicted below is y = x/2.

In order to write the equations for these straight lines, we would have to determine the slope of the straight lines.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

From the graph (see attachment), we have the following data:

Points on x-axis = (0, 2).

Points on y-axis = (0, 1).

Substituting the given points into the formula, we have;

Slope, m = (1 - 0)/2 - 0)

Slope, m = 1/2.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (2, 1), we have:

y - 1 = 1/2(x - 2)

y - 1 = x/2 - 1

y = x/2 - 1 + 1

y = x/2.

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685.8 feet

Sea level is a reference to elevation of the ocean or land interface called the shoreline.

Land that is above this elevation is higher than sea level and lower is below sea level.

The bottom of the canon is at 51 3/10 below the sea level which is also written as -51 3/10 ……(1)

The nest is at 737 1/10 feet above the sea level so it is expressed as

737 1/10  ….(2)

To find the distance between the bottom of the canyon and the bird’s nest we subtract (2) from (1)

737.1 – 51.3

= 685.8 feet

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Answer:

y = 2x + 11

Step-by-step explanation:

To find the slope, use the equation (y2 - y1)/ (x2 - x1). You get (15 - 5)/(2 - (-3), or 2. Then, use the slope you just found in the equation y - y1 = slope (x - x1), or y - 15 = 2 (x - 2). Simplifying down you get y = 2x -4 + 15, or y = 2x + 11, which is your final answer.

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According to the circle graph, doing well in school is a problem that affects B. 1,400,000 high school teenagers.

The circle graph shows that 12% of high school students have the problem of doing well in school.

In actual numbers, this is:

= 12% x number of high school teenagers

Solving gives:
= 12%  x 14,054,077

=  1,686,489 students

= 1,400,000 approximate

In conclusion, option B is correct.

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Answer:

Step-by-step explanation:

Expression given:

Find its value when g = 10:

Answer:translation

Step-by-step explanation:

The names of 0 employees are written on 0 cards. the cards are placed in a​ bag, and three names are picked from the bag - here simple random sampling technique was used.

Basic irregular testing can provide you with an extremely precise image of how your motto performs with the typical individual, yet it won't give you nitty gritty data about unambiguous gatherings. Utilizing straightforward irregular testing permits scientists to make speculations about a particular populace and leave out any inclination. This can assist with deciding how to settle on future choices. It has been expressed that "the rationale behind straightforward arbitrary examining is that it eliminates predisposition from the choice method and ought to bring about delegate tests".

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The picnic area is 20 inches wide in the drawing in her scale of 1 inch : 4 yards.

Unitary method is a technique for first solving the value of a single digit unit and from there we can find the value of any given unit.

According to the given question lillian drew a scale drawing of a county park. the scale she used was 1 inch : 4 yards.

The picnic area is 80 yards wide in real life.

∴ The width of the picnic area in here drawing in inches will be

= 80/4 inches.

= 20 inches.

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The correct option is A. x = 1(1/3) and y = 2(1/3) in the mixed fractions.

A system of equations is a collection of equations that all have the same variables.

Now, the given equation in the question are-

7x - y = 7      ........(equation 1)

and x + 2y = 6     ........(equation 2)

Multiplying both side of equation 1 with 2, we get

14x - 2y = 14         ........(equation 3)

Add equation 2 and 3.

x + 2y + 14x - 2y = 6 + 14

15x = 20

x = 4/3

x = 1(1/3)

Substitute the value of x in equation 1.

4/3 + 2y = 6

2y = 6 - 4/3

2y = 14/3

y = 7/3

or y = 2(1/3)

Therefore, the values for variables x and y are calculated as:

x = 1(1/3) and y = 2(1/3).

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Answer:

r=7cm

Step-by-step explanation:

the diameter (distance from one side of the circle to the opposite side) is given in the picture. the radius is 1/2 the diameter, so r=7cm

*i'm assuming the 14cm given is referring to the straight line in the circle and not the circumference

The simplified expression for the area of the given rectangle is 12x + 40

As per the given figure:

The length of the rectangle given in the question: 3/5x + 2

The breadth of the rectangle given in the question: 20

The formula for the area of a rectangle is given by:

Area of rectangle  = Length of the rectangle * Breadth of the rectangle

Area of rectangle  = (3/5x +2)*20

=(3x + 10)/5 * 20

= (3x + 10) * 4

= 12x + 40

Area of rectangle  = 12x + 40

So, the simplified expression for the area of the rectangle with the given length and breadth is 12x + 40

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Answer:

$39.30

Step-by-step explanation:

First find out 70% which is $91.70

And then do 131-91.70=39.30

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If Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10, and 12 seconds respectively and toll together at 11:00, then they will toll together again at 11:02.

Least common multiple abbreviated as LCM is used to determine the time at which the six bells will toll together again.

The least common multiple of two or more numbers is the smallest number that is a multiple of those numbers.

The least common multiple of 2, 4, 6, 8, 10, and 12 can be found by prime factorization.

Prime factorization of :

2 = 2^1

4 = 2 x 2 = 2^2

6 = 2 x 3

8 =  2^3

10 = 2 x 5

12 = 2 x 2 x 3 = 2^2 x 3

The least common multiple can be calculated by the multiplication of the prime factors raised to their highest power.

Therefore,

LCM = (2^3) (3) (5) = 120

Hence the bells will toll together again after 120 seconds

As 120 seconds = 2 minutes

Therefore, the time at which they will toll together again is calculated to be 11:02.

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Answer:

See the table below
For n, the answer is 2n+1

Step-by-step explanation:

The number of trees in each figure represents an arithmetic sequence where the difference between subsequent figures is 2  (caled the common difference)

So the sequence is

Figure(n)    Number of Trees

1                  3
2                 5  
3                 7
4                 9  (7+2)
5                11   (9+2)

n                 2n + 1

In general, for any arithmetic sequence we can write an equation for the nth term as [tex]a_n = a_0 + d(n-1)[/tex] where [tex]a_0[/tex] is the first term and d is the common difference

So for this example, we have [tex]a_0 = 3[/tex] and d=2 giving
[tex]a_n = 3 + 2(n-1) = 3 + 2n -2 = 2n + 1[/tex]

This is

Answer:

It's C/ Option 3

Step-by-step explanation:

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The range of the function f(x) = |x|+3 is [3,∞)

Given,

The function f(x) =|x|+3

Consider

f(0)=|0|+3= 3

f(1)=|1|+3= 4

f(2)=|2|+3= 5

We know

|x|≥0

So even if we take negative value for x, the |x| will be positive

So,

f(-1)=|-1|+3=1+3=4

f(-2)=|-2|+3= 2+3=5

We know, range is the set of all possible outcomes.

The range of the function f(x)= |x|+3 = [3,∞)

Hence, the range of the function f(x) = |x|+3 is [3,∞).

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Answer:

 {y | 3 ≤ y < ∞}

Step-by-step explanation:

Felicia will practice for a total of 496 hours

Felicia will practice for 112 hours on Monday

She will practice for 134 hours on Tuesday

She will practice for 2 hours on Wednesday

Total number of hours spent in week 1= 112 + 134 + 2

= 248 hours

She did the same routine the following week

= 248 × 2

= 496

Hence Felicia will practice for a total of 496 hours for the 6 days

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Answer:

Step-by-step explanation:

Answer:

evaluating a function means finding the value of f(x) or f(y).......

Answer:

replace all the x variables with whatever x has been assigned

Step-by-step explanation:

evaluating a function means finding the value of f (x) = or y equals that corresponds to a given value of x to do this simply replace all the x variables with whatever x has been assigned for example if we are asked to evaluate f (4) then x has been assigned the value of 4

The quadrilateral is a parallelogram.

Properties of parallelogram,

a>The opposite sides of the parallelogram are equal and parallel.

b>parallel lines have an equal slope.

Let now find the length of the opposite side of the parallelogram

To find the length we have ,

            [tex]\sqrt{(x_{2} ^{2} -x_{1} ^{2} ) +(y_{2} ^{2}-y_{1} ^{2} )}[/tex]

(-2, 3) , (-2, 6)

Slope = 6-3/ -2+2 = infinity

Length L1 = [tex]\sqrt{(-2 + 2)^{2} + (6 - 3)^{2} }[/tex]

                = 9

(-6, -1), (-6, 2)

Slope = 2+1/ -6 + 6 = infinity

Length L2 = [tex]\sqrt{(-6 + 6)^{2} + ( 2 + 1)^{2} }[/tex]

                = 9

Therefore the given vertices are of a parallelogram, as the  length and slope are equal.

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The 12.5  tablespoons of the spray will he need to use for 5 gallons of water.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

For mixing a spray to kill weeds, Howard is to use 2 1/2 tablespoons for each gallon of water.

We have to find How many tablespoons of the spray will he need to use for 5 gallons of water..

According to given question we have

2 1/2 =5/2 tablespoons for each gallon of water.

5/2 tablespoons =1 gallon of water.

1 gallon of water=5/2 tablespoons

5 gallons of water=5/2*5 tablespoons

5 gallons of water=25/2 tablespoons=12.5  tablespoons

Therefore, the 12.5  tablespoons of the spray will he need to use for 5 gallons of water.

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If the median of 6 consecutive integers is 9, the largest number is equal to 8.5.

Given the following data:

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

For the largest number, we have:

Since consecutive integers must follow each other sequentially with a difference of 1, so the largest number is given by:

Largest number = Median + (n - 1)/2

Substituting the given parameters into the formula, we have;

Largest number = 6 + (6 - 1)/2

Largest number = 6 + (5)/2

Largest number = 6 + 2.5

Largest number = 8.5.

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a) Both the length and the width of the rectangle are square roots of integers.

b) The length and the width of the rectangle are 6√5 units and 3√5 units, respectively.

Irrational numbers are numbers that not rational, that is, numbers that not of the form m / n, where m and n are integers and n is different of zero. Rational numbers may be integers or not.

Now, the statement indicates that the length and the width of rectangle have measures of 2 · x and x, respectively, and that the area of the rectangle is equal to 90 square units. The area formula is presented below:

90 = (2 · x) · x

90 = 2 · x²

x² = 45

x = √45

x = √(9 × 5)

x = √9 × √5

x = 3√5

a) Both the length and the width of the rectangle are square roots of integers.

b) The length and the width of the rectangle are 6√5 units (approx. 13.416 units) and 3√5 units (approx. 6.708 units), respectively.

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Answer:

B

Ab + bc =ac

3x-4 + 4x+2 =26

7x=28

x=4

Answer:

Step-by-step explanation: We can plug 2 into the equation for x:

3 - 2(4 + 2)

3 - 8 - 4

3 - 8 = -5

-5 - 4 = -9