What is the formula to find the nature of the roots of a quadratic equation?.

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?

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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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 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

Answer:

Step-by-step explanation: potatoes

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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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:

D is the answer

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.

When the magnitude level of an earthquake is between 3. 0 3. 9 then the category is known as minor category.

The scale goes from "minor" for earthquakes with a magnitude between 3.0 and 3.9, when people typically start to feel them, to "great" for earthquakes with a magnitude more than 8.0, when major damage is anticipated.

A single earthquake frequently has many somewhat different magnitudes published for it. This occurs because there is a complex relationship between seismic readings and magnitude, and several methods frequently produce slightly different magnitudes for the same earthquake.

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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

The actual height of the Statue of Liberty in meter is 93 m

It is a constant relationship between different measurable quantities.

Data of the problem:

We calculate the proportion of the model scale:

1/1000 = 9.3/x

We clear the variable, noticing the rules of clearing:

Clearing the variable we have:

1/1000 = 9.3/x

x* (1/1000) = 9.3

x = (9.3*1000) / 1

x = 9300 cm

Converting the centimeter to meters we have:

9300 cm * (1 m /100 cm) = 93 m

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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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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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So, the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

To find the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use elimination method.

The first step of elimination method is to eliminate one of the variables by adding or subtracting the equations. In this case, we will multiply the first equation by 4 and the second equation by -3 and add them:

4(3x + 5y) = 4(17)

12x + 20y = 68

-3(4x + 4y) = -3(-13)

-12x - 12y = 39

then we can add these two equations:

12x + 20y = 68

-12x - 12y = 39

0 = 29

This is an impossible equation, which means that the system has no solution.

Therefore, the y value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

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The graph of the system of equations can be seen in the image at the end, and the solution is (0.5, 1.5)

Here we want to show which graph shows the system of equations below:

y = 3x

y = x + 1

So the graph will have two linear equations, the first one:

y = 3x

Passes through the points (0, 0) and (1, 3) (check that by evaluating)

And the equation:

y = x + 1

Passes through (0, 1) and (1, 2)

Then the correct option is the first one, and the graph of the gis the one below.

There we can see that the solution is (0.5, 1.5)

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The money spent on a phone plan can be represented by the inequality:

50 + 25x > 100 and the total money spent on the phone service exceeds the amount of the gift card after the 2nd month.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The inequality represents the total cost of the phone plan, where x represents the number of months for which the service is used.

The first part of the inequality, 50$, represents the initial cost of the phone.

The second part, 25x, represents the monthly cost of the service, 25$ per month.

So, the inequality represents the total cost of the phone plan as the sum of the initial cost of the phone and the monthly cost of the service for x number of months.

50 + 25x > 100

It states that the total cost (50 + 25x) of the phone plan is greater than 100$.

It's the total cost you have to pay for the phone and the service.

It's used to know when the total cost exceeds 100$, which is the gift card's value.

To find out when the total spent on the phone service exceeds the amount of the gift card, we can substitute in the inequality with the given values and solve for x.

50 + 25x > 100

x > (100-50)/25

x > 2

So, the total spent on the phone service exceeds the amount of the gift card after the 2nd month.

Therefore, The money spent on a phone plan can be represented by the inequality : 50 + 25x > 100 and the total money spent on the phone service exceeds the amount of the gift card after the 2nd month.

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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 equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a circle have a diameter of 12 units and a center that lies on the y-axis, we need to find its equation,

We know that, the standard form of the equation of a circle is expressed as;

(x-a)² + (y-b)² = b=r²

where;

(a, b) is the center of the circle

r is the radius of the circle

We have,

diameter = 12 units

radius = 12/2 = 6 units

If the center lies on the y-axis, the center will be at (0, 3)

Substituting into the formula, we will have (x-0)² + (y-3)² = 6²

x²+ (y-3)² = 36

Hence, the equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

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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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Answer:

The First food will save the most money

Step-by-step explanation:

150lb- $53

75lb- $336.75

The first one saves them quite a bit of money.

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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The internal angle of a regular polygon is equal to 108°. A 5-sided polygon is a pentagon.

An -sided polygon with regular sides that are all the same length and symmetrically arranged around a common center is known as a regular polygon (i.e., the polygon is both equiangular and equilateral).

Only a few regular polygons are "constructible" with the compass and straightedge of classical Greece.

A regular polygon's interior angle measures 108°.

The pentagon is a 5-sided polygon.

A two-dimensional closed figure with three or more straight sides is called a polygon.

A polygon is any shape with straight edges, such as a triangle or rectangle.

Figures with open sides or any curved sides are not considered to be polygons.

Therefore, the internal angle of a regular polygon is equal to 108°. A 5-sided polygon is a pentagon.

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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

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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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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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 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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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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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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