The possible **rational** zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

What is mean of rational zero ?

A rational zero is a rational number, which is a number that can be written as a **fraction** of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.

By Rational Zero Theorem,

If P(x) is a polynomial with integer coefficients and if is a zero of P(x) i.e.,(P( ) = 0),

then p is a factor of the constant term of P(x)

q is a factor of the leading coefficient of P(x)

Possible value of rational zero is p/q

Have given, f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex]

Here, constant term, p = +20

Leading coefficient, q = +1

The factors of the constant term +20 are ±1, ±2, ±4, ±5, ±10, ±20.

The factor of the leading coefficient is ±1.

Therefore , The possible **rational** zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.

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What is the nature of the roots of xÂ² âˆ’ 3x 4 0?

The** roots **of the **equation** are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.

The equation x^2 - 3x + 4 = 0 can be **factored** as (x - 4)(x - 1) = 0.

Therefore, the roots of the equation are x = 4 and x = 1.

To calculate this, we can use the **Quadratic Formula:**

x = [-b Â± Â√(b^2 - 4ac)]/2a

In this **equation**, a = 1, b = -3, and c = 4

x = [-(-3) Â± Â√((-3)^2 - 4(1)(4))]/2(1)

x = [(3) Â± Â√(9 - 16)]/2

x = (3 Â± Â√(-7))/2

x = (3 Â± iÂ√7)/2

**Therefore**, the roots of the equation are x = (3 + iÂ√7)/2 and x = (3 - iÂ√7)/2.

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the graph at right shows the situation after the u.s. removes a tariff on imports of canned tuna.

The **supply-demand** curve after US removed tariff on imports is provided. The customer surplus is denoted by area A+B+C+D, loss in producer surplus by A and government loss in revenue by C.

When supply is equal to the demand we get the equilibrium quantity produced and **equilibrium** price.

The** initial price** P0 is less than the equilibrium price and thus there is excess demand of the product and thus there is import. When tariff is removed price again drops increasing the excess demand and thus more product is imported.

**Consumer** surplus is the amount the customer saves as price set by the supplier is less than the amount the consumer is ready to pay. As the customer is ready to pay at P0, the customer surplus when price drop to P1 is given by area A+B+C+D.

The loss in **producer surplus** is denoted by the area A. As the tariff is removed, the loss in revenue for government is denoted by the area C.

--The question is incomplete, answering to the question below--

"The graph at right shows the situation after the U.S. removes a tariff on imports of canned tuna.

Which areas show the gain in consumer surplus?

A. C

B. A+B+C+D

C. A

D. B+C+D

Which area shows the loss in producer surplus?

A. B+C+D

B. A + B

C. A

D. A+B+C+D

Which area shows the loss in government tariff revenue?

A. A

B. C

C. A+B+C+D

D. B+C+D"

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What is the standard deviation of 25?

Variance's square root is always the **standard deviation.** √25 thus equals 5.

Saying that the median is 7, the mode is 2, and the variance is squared does not make much sense.

However, it makes sense to state that the **data's median,** mode, and standard deviation are 7, 2, and 4, respectively.

Thus,

√25 = 5.

**Variance's **square root is always the standard deviation.

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What are the 3 methods used to calculate volume?

3 methods used to calculate** volume **are-

Every physical object takes up space, and you may determine the volume of some of these by counting their individual parts. The volume of objects with straightforward shapes, such as cones, rectangular prisms, sphere, and cylinders, can be determined using this method most easily.

Calculate Volume UsingThe definition of density is the mass of an object per unit of volume. Therefore, using the equation: If you understand the object's density and can weigh it, you can calculate its volume.

volume = weight / density

Volume byYou might not be able to precisely gauge an object's physical dimensions if it has an unusual shape.

The volume that is displaced when an object is submerged in a liquid and perhaps a gas can be measured as a substitute. This approach to measuring volume is widely popular and, when used properly, very precise.To know more about the** volume of cube**, here

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Mrs. Ortega paid $188 for some jeans and T-shirts. A pair of jeans cost $26, and a T-shirt was $16 cheaper than a pair of jeans. If Mr. Ortega bought 3 pairs of jeans, how many T-shirts did she buy?

**Answer:**

A pair jeans=26$

:. 3 pair jeans=78$

1 t-shirt=10$

No of t-shirt=188$-78$/10$=11

What is the slope of 3x 5y =- 9?

**3x - 5y=-9** has a [tex]\frac{-3}{5}[/tex] **slope**.

A **line's steepness** can be determined by looking at its **slope**. To find the slope of a line, you need to have the **equation **of the line in the form y = mx + b, where m is the slope and b is the **y-intercept** (the point at which the line crosses the y-axis).

To put the equation 3x - 5y = -9 in this form, you can start by isolating the y term on one side of the equation:

3x - 5y = -9

-5y = -3x - 9

y = (-3/5)x - (9/5)

The slope of the line is therefore -3/5.

The complete question is:-

What is the slope of 3x - 5y =- 9?

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Sienna has 534 pounds of grapes. She eats 18 pound and gives 212 pounds to her brother.

How many pounds of grapes does Sienna have left?

**Answer: 304 Pound of Grapes**

**Step-by-step explanation:**

Sienna has 534 grapes. She eats 18 pounds of grapes.

[tex]534-18[/tex]

[tex]=516[/tex]

She gives 212 pounds of grapes to her brother.

[tex]516-212[/tex]

[tex]=\fbox{304 grapes left}[/tex]

Joshua has a points card for a movie theater. He receives 60 rewards points just for signing up. He earns 5.5 points for each visit to the movie theater. He needs at least 245 points for a free movie ticket. Which inequality can be used to determine vv, the minimum number of visits Joshua needs to earn his first free movie ticket?

The **inequality** that can be used to determine v, the minimum number of visits Joshua needs to earn his first free movie **ticket** is 5.5v + 60 ≥ 245

The minimum number of visits Joshua needs is approximately 34 visits.

How to write and solve inequality?Points needed for a free movie ticket = at least 245 pointsPoints5.5v + 60 ≥ 245

Subtract 60 from both sides

5.5v ≥ 245 - 60

5.5v ≥ 185

divide both sides by 5.5

v ≥ 185 / 5.5

v ≥ 33.63636363636363

Approximately,

v ≥ 34

Therefore, the **minimum** number of visits Joshua needs to earn his first free movie ticket is approximately 34 visits

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What is y =- 4 on a graph?

**Answer:**

I think it's a vertical line.

solve please solve my problems of math

**Answer:**

A = πx² cm²

**Step-by-step explanation:**

the area (A) of a circle is calculated as

A = πr² ( r is the radius)

Given circumference C = 2πx , and C is calculated as

C = 2πr , then equating gives

2πr = 2πx ( divide both sides by 2π )

r = x

Then

A = πr² = πx² cm²

Winter Wonderland charges children $0.50 per ride down the sledding hill plus an entrance fee. Todd sled down the hill 16 times and paid $18 for his time at winter wonderland.

What is the equation in y=mx+b form?

The **equation** of the amount to be paid by anyone using the ride in **slope intercept form** is; y = 0.5x + 10

The general form of the **equation **of a **Line** in slope intercept form is;

y = mx + b

where;

m is **slope**

b is **y-intercept**

Now, we are told that;

Amount charge by Winter Wonderland per child = $0.50

We are told that there is a separate entrance fee.

Amount of times todd sled down the hill = 16 times

Amount paid by todd = $18

Thus, using the** slope intercept form,** we have;

18 = 0.5(16) + b

18 = 8 + b

b = 10

Thus, the **equation** of this amount to be paid in **slope intercept form** is;

y = 0.5x + 10

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Thank you to whoever replies<33

**Answer:**

between 1 and 10 percent

Zalika spins a coin and throws a dice with eight faces numbered from 1 to 8. a Draw a sample space diagram. b Find the probability of scoring: i a head and an even number ii a tail and a prime number iii a head but not an 8.

The ranked probability score (RPS) is a metric used to assess how well predicted events match **probability **distributions.

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What is the f/x function called?

The domain and scope of the identity function are the same. Equation for the identity** function **is f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent** variable **(the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the** input value **leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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Write an equation or expression for the following. The quotient of twelve and a number is four times the number increased by one

**Answer: quotient deals with addition and times deal with multiplication**

**12/(n*4+1)**

What is the equation of a line of slope 1 by 3 and y-intercept 5?

The equation of line with** slope **1/3 and intercept 5 is y = 1/3 x + 5.

The general equation of a **straight line** is y = mx + c, where m is the gradient or **slope**, and y = c is the value where the line cuts the y-axis. This number c is called as intercept.

According to the questions,

**slope **= m = 1/3

and

**y-intercept** = c= 5

We know that,

The general equation of a **straight line** is y = mx + c

y = 1/3 x+ 5

The required equation of a line is y = 1/3 x+ 5

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(a)

Davin is raising money for a school trip by selling candy bars and packs of cookies. The price of each candy bar is $1.50 and the price of each pack of cookies is $1.25. Yesterday, Davin made $30 from selling a total of 22 candy bars and packs of cookies.

Create a system of equations to represent the number of candy bars sold, xx , and the number of pack of cookies sold, yy .

Equation 1:

Equation 2:

x=1.5x y=1.25x or like y=1.25/1.5x

The two **equations **are 1.5x+1.25y = 30 and x+y = 22 and values of x and y are 10 and 12 respectively.

An **equation **is a formula that expresses the equality of two **expressions**, by connecting them with the equals sign =.

Given that, Davin is raising money for a school trip by selling **candy bars **and packs of **cookies**. The price of each **candy bar** is $1.50 and the price of each pack of **cookies **is $1.25. Yesterday, Davin made $30 from selling a total of 22 **candy bars** and **packs of cookies.**

Let x represent the number of **candy bars** sold, and y be the number of pack of **cookies **sold,

Establishing the **equations**,

1.5x+1.25y = 30

x+y = 22

Solving the **equations**, we get.

x = 10 and y = 12

Hence, the number of **candy bars** sold 10 and the number of pack of **cookies **sold is 12

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The stationary section is on isle 14, one row over from the scents and perfumes.

The correct spelling are of the following words is Caucion :**caution ,**Isle :aisle and Cents :sents

The scent of her perfume is the signifier, and the feminine and romantic association she makes with the scent is the signified.

In linguistics, the concepts of signifier and signified are seen in **Saussure's **theory of the sign. A sign is formed by the pair signifier/signified. Signifier is a word, an image, anything that has a material form. Signified is the meaning attributed to the signifier by an individual. That means the same signifier can have different signifieds according to the each person. For Mary, the signifier "floral perfume" presents as its signified the "**feminine **and romantic" feeling. To a different person - myself, for instance -, a floral perfume does not have the same meaning. I do not see it as romantic or feminine. Instead, because the sweet smell gives me a headache, that has become my **signified **for it.

The stationary **section **is on isle 14, one row over from the perfumes and cents.

Hence Caucion :caution

**Isle **:aisle

Cents :sents

**the complete question is **

Correct the misspellings in these sentences.

Please use caucion when entering this area as the floor can be slippary.

The stationary **section **is on isle 14, one row over from the perfumes and cents.

Hence Caucion :caution

**Isle **:aisle

Cents :sents

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what’s the surface area? & B and c

**Answer:**

Surface area: 502 ft^2

B) Volume

C) Surface area

**Step-by-step explanation:**

Surface area Formula: 2(lw + wh + lh) = 2(13*15+15*2+13*2)= 502 ft^2

B) Volume because it's asking how much it can hold

C) Surface area because it's asking like how much paint should Cover the thing, not how much it can hold

hm someone help me pls

**Answer:**

A' = (1, -1)

B' = (2, 1)

C' = (4, 0)

D' = (3, -4)

**Step-by-step explanation:**

don't speak this language. however, I assume it says translate the quadrilateral by the column vector.

A = (-4, 3) ∴ A' = (1, -1)

B = (-8, 5) ∴ B' = (2, 1)

C = (-1, 4) ∴ C' = (4, 0)

D = (-2, 0) ∴ D' = (3, -4)

A cannonball is shot with a velocity of 90 m/s. If its vertical velocity at the top of its arc is 0 m/s and the horizontal velocity at the top of its arc is 45 m/s, at what angle was it shot?

The measure of the **angle **when a cannonball is shot will be 60°.

The quantity which has magnitude, and direction, and follows the **law **of **vector addition **is called a vector.

A **cannonball **is shot with a speed of 90 m/s. Assuming its **upward **speed at the highest point of its curve is 0 m/s and the flat **speed **at the highest point of its **bend **is 45 m/s.

We know that in projectile motion, the horizontal **velocity **does **not **change.

Let 'x' be the **angle **it shot. Then the cosine of the angle x is the **ratio **of horizontal velocity to the **resultant velocity **when it is shot. Then we have

cos x = 45 / 90

cos x = 1/2

cos x = cos 60°

x = 60°

The **proportion **of the point when a **cannonball **is shot will be 60°.

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Which outcome did the Battle of San Antonio de Béxar have?

A. Mexican troops forced the Texans to retreat.

B. Both sides withdrew from the town.

C. Texans captured San Antonio.

D. Mexican soldiers demolished the Alamo.

**Answer:**

b

**Step-by-step explanation:**

both sides withdrew

How do you find the second largest number in an array in Java?

The** idea **is to sort the array in **descending order** and then return the **second element** which is not equal to the **largest element** from the **sorted array.**

In order to have as** few implementation **dependencies as feasible, **Java **is a high-level, class-based, object-oriented **programming language.**

// **Java program** to find second** largest element **in an array

import java.util.*;

class GFG{

// Function to print the

// second** largest elements**

static void print2largest(int arr,int arr_size)

{

int i, first, second;

// There should be

// atleast two elements

if (arr_size < 2)

{

System.out.printf(" Invalid Input ");

return;

}

** // Sort the array**

Arrays.sort(arr);

// Start from second** last element**

// as the **largest element** is at last

for (i = arr_size - 2; i >= 0; i--)

{

// If the element is not

// equal to** largest element**

if (arr[i] != arr[arr_size - 1])

{

System.out.printf("The second largest " +

"element is %d\n", arr[i]);

return;

}

}

System.out.printf("There is no second " +

"largest element\n");

}

//** Driver code**

public static void main(String[] args)

{

int arr[] = {12, 35, 1, 10, 34, 1};

int n = arr.length;

print2largest(arr, n);

}

}

The idea is to sort the **array** in descending order and then return the second element which is not equal to the **largest element **from the **sorted array.**

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How do you know when a graph is inequality?

When plotting an **inequality **on a graph, treat the <, ≤, >, or ≥sign as an equals sign.

Treat the <, ≤, >, or ≥ sign as a = sign when putting an inequality on a **graph**.

Graph the equation as a dotted line if the inequality is either < or >.

Graph the equation as a solid line if the inequality is either ≤ or ≥.

How to Graph Linear Inequalities: Steps

(A) Always begin by separating the variable y from the inequality's left side.

(B) Symbolizing equality instead of inequality is step two.

(C) In the X, Y, XY, XY plane, graph the boundary line from step 2.

(D) The final step is to shade a portion or one side of the borderline.

Therefore, when plotting an inequality on a graph, treat the <, ≤, >, or ≥sign as an equals sign.

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what is the slope if all y's are 5 in a table of data

**Answer: 0 slope; horizontal line**

Is reflection and rotation the same?

**Reflection **is the act of flipping a figure over a line. The act of rotating involves turning a figure a predetermined distance around a point. And hence, reflection and rotation is not the same.

In mathematics, a reflection is an isometric mapping from a Euclidean space to itself with a set of fixed points called the hyperplane, also referred to as the axis or plane of reflection.

The image created by a reflection is the figure's mirror image in the axis or plane of reflection.

**Rotation:**

The concept of rotation in mathematics has its roots in geometry.

Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.

So, we can say that flipping a figure over a line is called reflection. Rotation is the process of turning a figure a specific amount around a point.

Therefore, reflection is the act of flipping a figure over a line. The act of rotating involves turning a figure a predetermined distance around a point. And hence, reflection and rotation are not the same.

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Is mean and SD the same?

**Answer:**

No, they are not the same

**Step-by-step explanation:**

Mean is simply the average sum of data. When Standard deviation is obtained from the average of the square of data

How do you find the inverse of x and y intercepts?

When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the **inverse**, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).

The **intercept theorem**, also referred to as Thales' theorem, the basic proportionality theorem, or the side splitter theorem, is a crucial concept in basic geometry that discusses the ratios of different line segments that are produced when two intersecting lines are intercepted by a pair of parallels.

It is equivalent to the ratios in similar triangles theorem. It is typically credited to the Greek mathematician Thales. Despite the fact that its first known demonstration may be found in Euclid's Elements, it was known to the ancient Babylonians and Egyptians.

Similarity and the intercept theorem go hand in hand. It is equivalent to the idea of **similar triangles** in that it may be used to demonstrate both the qualities of similar triangles and the intercept theorem.

Hence, When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the **inverse**, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).

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How to solve systems of equations by substitution with 3 variables?

To solve the **system of equations** using **substitution method **for three variables minimum three equations are required using following steps:

1. Get the value third variable in form of other two and substitute in other two equations.

2. Now get the value of second variable in first variable and get the **value **of all three variables.

Let us consider three** system of equations** in three **variable **are :

x + y + z = 0 __(1)

2x + 3y + z = 2 __(2)

3x + 2y + 2z = 1 ____(3)

Get the value of z in form of x and y from (1) and substitute in (2) and (3)

z = -(x + y)

2x + 3y -(x + y) = 2

⇒x +2y = 2 __(4)

3x + 2y +2(-(x +y)) = 1

⇒3x + 2y -2x -2y =1

⇒x = 1

Now substitute in (4)

1 + 2y = 2

⇒ y = 1/2

Now substitute the value of x and y in (1)

z = - ( 1 + 1/2)

⇒z = -3/2

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What does 5 more than mean?

'5 more than' means that a number is **5 units greater** than the original number, using the concept of **addition**.

**Addition** (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on **abstract objects** such as vectors, matrices, subspaces and subgroups.

Now, let us understand the meaning.

Let the original number be** x.**

'5 more than a number' implies **x + 5**.

This means that the new number, x + 5, is greater than the original number, x, by **5 units**. We also have to keep in mind, [tex]x + 5 > x[/tex].

Hence, the final meaning is** 5 units greater than the original number.**

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How the story ends after the climax and the falling actions?
XYZ Corp. has to change their online ordering system to compete with ABC Corp. They are changing their business process with a O A. change in business fundamentals B. request to improve process quality C. change in product line D. change in technology E. company reorganization
What are left leaning political parties?
Approximately _______ percent of men are color blind (and thus improper use of color can impair their ability to read information)
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What are the five main points of NAFTA?
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