When P x )= x³ 3x² 4x 32 is divided by x 2 The remainder is?.

An exponential function F(y)=g^y (g power y).

The log function is one of the functions and  We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y. If the base is e and we are dealing with the natural log, then the inverse of f(x) = ln(x) is f^-1(y) = e^y.Rewriting these relationships substituting f(x) with y and f^-1(y) with x, we see that the inverse of y = log subb(x) is x = b^y and the inverse of y = ln(x) is x = e^y. Both the inverse and the original function state the same relationship,

so now,

f(x)=log base g x.

g^f(x)=x

g^y=f(y).

f(y)=g^y.

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The zeros of polynomial function f(x) = x³ + 2x² -x - 2 are x = -2, x = 1 and x = -1

Here, we have been given polynomial function  f(x) = x³ + 2x² -x - 2

The definition of zeros of function states that zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.

To find the zeros of function f(x), we need to equate f(x) to zero then solve it for x.

⇒ f(x) = 0

⇒  x³ + 2x² -x - 2 = 0

⇒ x²(x + 2) -1(x + 2) = 0             ............(Seperate out like terms)

⇒ (x + 2)(x² - 1) = 0                     .............(factor out like terms)

⇒ (x + 2)(x + 1)(x - 1) = 0  

⇒ (x + 2) = 0   OR  (x + 1) = 0  OR  (x - 1) = 0  

Thus x = -2, x = 1 and x = -1 are zeros.              

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The complete question is:

What are the zeros of the polynomial function  f(x)= x³ + 2x² -x - 2?

Tan 30 degrees has a value of 1/√3. 30° is represented by the radian symbol tan /6.

Trigonometric functions are crucial for much research, including those involving wave motion, light motion, the velocity of harmonic oscillators, and other topics.

Tan 30° has a value of 1/√3 in fractional form and 0.577 in decimal form.

Using trigonometric functions, the value of tan 30° is represented as follows:

Tan 30° is equal to (sec 2 30°-1)

Tan = 1/cot = 30°

=1/√3

There are several ways to calculate tan 30 degrees, including using the trigonometric ratio formula since we already know that tan x = Perpendicular / Base.

ABC with angle A being 30° in a right-angled triangle.

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The total cost of the items that Jacob bought will be 58.94.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, Jacob goes to the storeto buy items for the week. At walmart hebuy bread for 2.99 milk for 4.50 a bushel of cilantro for .50 detergant for 13.99 nori for 2.99 a wrench for 5.99 toilet paper for 21.99 and sandwhich meat for 5.99.

The total cost will be:

= 2.99 + 4.50 + 0.50 + 13.99 + 2.99 + 5.99 + 21.99 + 5.99

= 58.94

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Complete question

Jacob goes to the storeto buy items for the week. At walmart hebuy bread for 2.99 milk for 4.50 a bushel of cilantro for .50 detergant for 13.99 nori for 2.99 a wrench for 5.99 toilet paper for 21.99 and sandwhich meat for 5.99. Calculate the total cost

Yes, 1 is a square number.

Now, According to the question:

Square numbers are those numbers that are produced by multiplying an integer to itself. If n is an integer, then [tex]n^2[/tex] is the square of n.

What are the examples of square numbers?

The examples for square numbers are:

[tex]6^2[/tex] = 36

[tex]10^2[/tex] = 10 x 10 = 100

[tex]15^2[/tex] = 15 x 15 = 225

[tex]12^2[/tex] = 12 x 12 = 144

When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.

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The easiest way to find a specific term in a binomial expansion is to use the binomial theorem.

The binomial theorem is a fundamental theorem in mathematics that is used to expand expressions which involve two terms, known as binomials, raised to a power.

The binomial theorem states that for any non-negative integer n, the expansion of (x+y)ⁿ is given by the sum of all terms of the form (xⁿ-k)(y^k)/k! where k ranges from 0 to n. This theorem can be used to calculate any term of a binomial expansion.

For example, to calculate the third term of (x+y)⁵, set k = 2 and substitute the appropriate values into the expression (x⁵-2)(y²)/2! which gives 5x³y². This is the third term of (x+y)⁵. The binomial theorem is a powerful tool that can be used to simplify, expand and simplify expressions involving binomials.

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The measurements of a cylinder if its volume is 500cm3 is

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given;

Volume of cylinder= 500cm3

Now, the volume of cylinder= [tex]\pi r^{2} h[/tex]

500=3.14*r^2*h

500/3.14=r^2*h

r^2*h=159.23

h=159.23/r^2

r^2=159.23/h

Therefore, the answer by the given volume will be h=159.23/r^2 and r^2=159.23/h

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The equation of the line containing midsegment XZ in the standard form is:

y = 2x +0

What is the Equation of line?

The equation of a line is a mathematical representation of the relationship between the variables x and y on a coordinate plane. It is typically written in the form "y = mx + b", where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The equation of the line containing the midsegment of a triangle can be found by taking the average of the coordinates of the midpoints of the two line segments that make up the midsegment.

First, we need to find the midpoint of AB:

Midpoint of AB = ((-4+8)/2, (1+-1)/2) = (2,0)

Then, we need to find the midpoint of BC:

Midpoint of BC = ((8+-2)/2, (-1+9)/2) = (3,4)

The equation of line XZ can be found by taking the average of the coordinates of X and Z, and solving for y:

y = (0+4)/2 = 2

x = (2+3)/2 = 2.5

Hence, the equation of the line containing midsegment XZ in the standard form is:

y = 2x +0

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Answer:

7+3

Step-by-step explanation:

6+4 = 10 and 7+3 = 10

The total time Karen spent riding her bike and swimming in the race is 135 minutes.

What is algebra ?

Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics.

To find the total time Karen spent riding her bike and swimming in the race, you need to add the time she spent riding her bike and the time she spent swimming.

Karen rode her bike for 1 1/2 hours, which is equivalent to 1.5 * 60 = 90 minutes.

She also swam for 45 minutes.

90 + 45 = 135,

The total time Karen spent riding her bike and swimming in the race is 135 minutes.

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Karen spent 135 minutes riding her bike and swimming in the race.

Algebra is a common thread that runs through practically all of mathematics. It involves the study of variables and the rules for manipulating them in formulas.

You must add the time Karen spent swimming and riding her bike to get the total amount of time she spent doing both during the race.

First, we need to convert Karen's bike riding time to minutes:

1 1/2 hours = 1 1/2 * 60 minutes = 90 minutes

Now we can add up Karen's bike riding time and swimming time:

90 minutes + 45 minutes = 135 minutes

So Karen spent 135 minutes riding her bike and swimming in the race.

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The mass of the brass ornament as described in the task content in terms of its volume and density is; 208.8.

Recall that the formula for the density of an object is given as;

Density = Mass / Volume.

Hence, given that the density of the ornament is; 8.7 and the volume of the ornament is; 24, it follows that the mass of the ornament can be evaluated as follows;

8.7 = Mass / 24

Mass = 24 × 8.7

Mass = 208.8.

Ultimately, the mass of the brass ornament is; 208.8.

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No, it is not possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(4cm + 5cm) =10cm

9cm = 10cm

LHS<RHS

A triangle is not possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The linear equation 3x + 11y = 10 has one solution.

The given linear equation is 3x + 11y = 10. To find the number of solutions for this equation, we can use the following method:

1. Rewrite the equation in the form of y = mx + c, where m is the coefficient of x and c is the constant term.

   3x + 11y = 10

   -3x/11 = y -10/11

   y = -3/11x +10/11

2. Check the slope and the y-intercept, if the slope is infinite, it means the equation is a vertical line and it has no solutions, if the y-intercept is infinite, it means the equation is a horizontal line and it has infinitely many solutions.

In this case, the slope is -3/11 which is a finite value, also the y-intercept is (0,10/11) which is a finite value, so the equation is not a vertical or horizontal line, it is a standard form of a linear equation, and it has a unique solution.

Therefore, the linear equation 3x + 11y = 10 has one solution.

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Answer:

Step-by-step explanation: potatoes

The square root of 17 is 4.123. Therefore, 1 √17 = 1 × 4.123 = 4.123.

What is square root ?

square root of quite a number is a price, which on multiplication through itself, gives the authentic number. The square root is an inverse approach of squaring a number. consequently, squares and rectangular roots are associated principles.

suppose x is the square root of y, then it is represented as x=√y, or we can specific the same equation as x2 = y. right here, ‘√’ is the unconventional image used to symbolize the foundation of numbers. The fine quantity, whilst extended by way of itself, represents the rectangular of the number.

The square root of the square of a positive range offers the unique quantity.

Now, 17^2 · 17^-5 = 17^2 - 5 = 17^-3 = 1 / 17^3

Solve 17²⁰¹⁷ - 17  is?

17²⁰¹⁷-17

= 17²⁰¹⁷×1

= 17²⁰¹⁷

Therefore, The square root of 17 is 4.123. Therefore, 1 √17 = 1 × 4.123 = 4.123.

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Answer:

a T-shirt = $31

a sweatshirt = $44

Step-by-step explanation:

Let T represent T-shirts and S represent sweatshirts.

Jayden sells 9 T-shirts and 3 sweatshirts for $420:

9T + 3S = 420

Carson sells 1 T-shirt and 6 sweatshirts for $296:

T + 6S = 296

-9T - 54S = -2,664

9T - 9T + 3S - 54S = 420 - 2,664

-51S = -2,244

S = 44 is the price for a sweatshirt, for the price of a T-shirt:

T + 6S = 296

T + 6×44 = 296

T + 264 = 296

T = 31

240 tiles are required to cover a wall of size 4m by 3m

Let l be the length of the wall and b be the breadth of the wall

Then, l = 4m and b = 3m

Area of the wall is given by,

Area = length × breadth

= 4 m x 3 m

= 12 m^{2}

Also given that area of one marble tile = 25 cm x 20 cm

= 500 cm^{2}

Converting the measure of area of one marble tile in metres

= 0.05 m2

[Since 1 m^{2} = 10000 cm^{2}]

Now,

Area of one marble tile is 0.05 m^{2}

Number of tiles required to cover the wall

= Area of wall/ Area of one marble tile

= 12/0.05

= 240 tiles

Therefore, 240 tiles are required to cover a wall of size 4m by 3m or area of 12 m²

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The median of the following set of data (39.8, 39.6, 39.2, 39.6 and 39.5) is 39.6.

Median is a number separating the higher half from the lower half of a data sample, population, or probability distribution.

The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one (e.g., the median of {3, 3, 5, 9, 11} is 5.

The following set of data was given this question;

39.8, 39.6, 39.2, 39.6 and 39.5

We arrange these data as follows:

39.2, 39.5, 39.6, 39.6, 39.8

The middle number or median is 39.6

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Answer:

The updated mean after adding 43 to the data set is 41.

Step-by-step explanation:

In statistics, the median is a measure of central tendency that represents the middle value of a data set when it is arranged in ascending or descending order.

We know that the general formula for finding median,

If the total number of data points (n) is odd, the median is the value at the  [tex]\frac{n+1}{2}[/tex] th position.

If the total number of data points (n) is even, the median is the average of the values at the [tex]\frac{n}{2}[/tex] th and [tex]\frac{n}{2} +1[/tex] th  positions.

Given data set: 31, 41, 50, 28, 52, 38, 56, 27

Case 1: Calculate the current median

Arrange the data set in ascending order:

27, 28, 31, 38, 41, 50, 52, 56

Determine the total number of data points (n):

In this case, there are 8 data points.

Calculate the median using the general formula

In Case 1, since n = 8, it is an even number. Thus, the median is the average of the values at the 8/2 = 4th and (8/2 + 1) = 5th positions, which are 38 and 41, respectively.

Calculate the median: [tex]\frac{38 + 41}{2}[/tex] = [tex]\frac{79}{2}[/tex] = 39.5

Hence it is verified

Case 2: Calculate the updated mean

Add the new number to the data set

Add 43 to the data set:
27, 28, 31, 38, 41, 50, 52, 56, 43

Arrange the updated data set in ascending order:
27, 28, 31, 38, 41, 43, 50, 52, 56

Determine the new total number of data points (n):
In this case, there are 9 data points.

Calculate the new median using the general formula:

In case 2, since n = 9, it is an odd number. Thus, the median is the value at the (9+1)/2 = 5th position, which is 41.

Therefore, after adding 43 to the data set, the new median becomes 41.

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Answer:

$6750.50

Step-by-step explanation:

F = Pe^(rt)

8327.94 = P × e^(0.0175 × 12)

P = 8327.94/e^0.21

P = 8327.94/1.23376806

P = 6750.5

Paula will use 20 oz of sauce and 80 oz of cheese to make 5 pizzas.

We can use the rate of use of pizza sauce and cheese to determine how much of each ingredient Paula will use to make 5 pizzas.

From the information provided, we can see that for every 4 oz of sauce, Paula uses 16 oz of cheese. We can use this ratio to determine the amount of sauce and cheese used for any number of pizzas.

To make 5 pizzas, Paula will use 4 x 5 = 20 oz of sauce and 16 x 5 = 80 oz of cheese.

So, Paula will use 20 oz of sauce and 80 oz of cheese to make 5 pizzas.

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Answer:

See pictures:

A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.

In Mathematics, the y-intercept is also known as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

From the information provided above, the slope and data points on this line include the following:

In Mathematics and Geometry, the slope of any straight line can be calculated by using this this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope (m) = (0 - 3)/(2 - 0)

Slope (m) = -3/2

Therefore, the required equation based on a y-intercept of 3 is y = -3x/2 + 3.

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Answer:

each bag of trail mix costs $2 and each loaf of pumpkin bread costs $9.

Step-by-step explanation:

To find the cost of each item, we need to solve the system of equations.

We can use substitution method:

3x + 2y = 24

x + y = 11

Solving for x in the second equation:

x = 11 - y

Substituting this into the first equation:

3(11 - y) + 2y = 24

Solving for y:

33 - 3y + 2y = 24

-y = -9

y = 9

Then we can use y = 9 in the equation x = 11 - y to find x:

x = 11 - 9 = 2

So each bag of trail mix costs $2 and each loaf of pumpkin bread costs $9.

The total number of people at the stadium is 11000.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

At a football stadium, 2% of the fans in attendance were teenagers.

If there were 220 teenagers at the football stadium.

the total number of people at the stadium= 220*100/2

                                                                     =1100

Hence, the total number of people at the stadium is 11000.

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Exact numbers have an unlimited number of significant figures and is therefore denoted as option D.

These are the numbers which are used in counting and defining other quantities which are assumed to be exact and usually have no remainders and they have an infinite number of significant figures.

An example is number “3” is exact as well and could be expressed as 3.0000000000000. This means that the number of significant figures can be unlimited because any amount of figures can be placed after the number which is therefore the reason why it was chosen as the correct choice.

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Answer:

96/x

Step-by-step explanation:

When two variables x and y vary inversely, their product is a constant. Therefore, the function that models the inverse variation between x and y is:

x*y = k

where k is the constant of proportionality.

We can use the given information to find the value of k:

x = 12 when y = 8

so, k = xy = 128 = 96

Now we can use this value of k to write the function that models the inverse variation:

x*y = 96

To find the inverse variation, we divide both sides by y,

x = 96/y

Alternatively, we can write y = 96/x

So, the function that models the inverse variation between x and y is either x = 96/y or y = 96/x

The number that belongs in the green box is 14.7. The solution has been obtained using law of sines.

What is law of sines?

According to the law of sines, all of the angles in the problem must have an equal ratio between the sine of each angle and the length of the side opposite to that angle.

As per law of sines,

sin A/a =  sin B/b = sin C/c

In the figure, we are given two angles and we know that in a triangle sum of all angles is 180°.

Therefore,

125° + 32° + x = 180°

x= 23°

Let the side be 'a'

Using law of sines,

⇒sin 125°/a = sin 23°/7

⇒a sin 23° = 7sin 125°

⇒a = 7sin 125°/sin 23°    (Dividing both sides by sin 23°)

⇒a = 14.7

Hence, the number that belongs in the green box is 14.7.

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Estimating the width and mass of objects necessitates meticulous attention to detail, a thorough understanding of the measurement tools and techniques employed, and an awareness of any potential difficulties.

Estimating the width and mass of objects can be difficult in general for several reasons:

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A unique type of right triangle known as a Pythagorean triple has lengths on all three sides that are whole numbers.

The 3-4-5 triangle, with a hypotenuse of 5 and sides 3 and 4, is the most well-known and smallest of the Pythagorean triples.

The 3 : 4 : In arithmetic progression, the only right triangles with edges are the five triangles. Pythagorean triple-based triangles are Heronian, with an integer area and integer sides.

A right triangle with side lengths that are 3:4:5 is called a 3-4-5 right triangle. To put it another way, Pythagorean Triples are the sides-to-side ratios of a 3-4-5 triangle. This ratio can be stated as follows: Side 1: Side 2: 3n = hypotenuse: 4n: 5n = 3: 4: 5.

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The functions for the total cost per month for data use are linear in each of the given options.

Correct responses;

1. A(1) = 60,   B(1) = 35

2. A(7.5) = 60,   B(7.5) = 100

3. The monthly charge for Option A fixed. The monthly charge for Option B includes a fixed monthly fee and $10 per gigabyte used.

4. Please find attached the combined graph of Option A and Option B. Option B is more affordable when the (extra) data usage is less than 3.5 gigabytes each month.

The amount of gigabytes of data the student would have for $50 is 2.5 gigabytes.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given parameters are;

Both plans data allowance per month = 2 gigabytes

The monthly cost for each option is;

Option A: A(x) = 60 = Constant

Option B: B(x) = 10·x + 25

Solution:

1. The values of A(1) and B(1) are;

A(1) = 60

B(1) = 10 × 1 + 25 = 35

Therefore;

A(1) = $60

B(1) = $35

2. The values of A(7.5), and B(7.5) are;

A(7.5) = 60

B(7.5) = 10 × 7.5 + 25 = 100

A(7.5) = $60

B(7.5) = $100

3. The description of each data plan are;

Option A

The data plan of option A has a fixed charge of $60

Option B

The charges on the data plan on option B consist of a fixed monthly charge of $25, and $10 per gigabyte of data used.

4. Please find attached the graph of the functions of Option A and Option B. From the graph, the most affordable plan to use based on the data usage is;

Option B; If the data used a month, x < 3.5 gigabytes

Option A; If the data used a month, x > 3.5 gigabytes

Either Option A or Option B if the data usage per month is exactly 3.5 gigabytes

The amount the student budgets per month = is $50

By using Option B, we have;

B(x) = 10·x + 25 = 50

10·x = 50 - 25 = 25

x = 25 / 10 = 2.5

At $50, the amount of gigabytes the student can get is x = 2.5 gigabytes

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