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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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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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).
What is a intercept theorem?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 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.
What is Java long answer?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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What is the standard deviation of 25?
Variance's square root is always the standard deviation. √25 thus equals 5.
Describe the term standard deviation?Both the standard deviation and the variance are indicators of how far data deviates from the mean. Because the results are all in data form or units, S.D. provides accurate results. Variance produces squared data findings, making it challenging to compare to actual data. Therefore, it makes sense to compare findings using S.D. rather than variance.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.
Variance produces squared findings that make it impossible to compare to actual data without. You can only understand differences from getting S.D.Thus,
√25 = 5.
Variance's square root is always the standard deviation.
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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
What is y =- 4 on a graph?
Answer:
I think it's a vertical line.
what is the slope if all y's are 5 in a table of data
Answer: 0 slope; horizontal line
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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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
What is the nature of the roots of x² − 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√(b^2 - 4ac)]/2a
In this equation, a = 1, b = -3, and c = 4
x = [-(-3) ± Â√((-3)^2 - 4(1)(4))]/2(1)
x = [(3) ± Â√(9 - 16)]/2
x = (3 ± Â√(-7))/2
x = (3 ± 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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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 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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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)
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
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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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
How to write an equation in slope intercept form?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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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.
What is reflection?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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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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Thank you to whoever replies<33
Answer:
between 1 and 10 percent
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 pointsPoints earned for signing up = 60 pointsPoints earned for each visit to the movies = 5.5 pointsNumber of visits Joshua needs to earn his first free movie ticket = v5.5v + 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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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
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.
What is function?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.
What is equation of a straight line ?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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What are the 3 methods used to calculate volume?
3 methods used to calculate volume are-
Volume by Space SolverCalculate Volume Using Density and MassVolume by Displacement SolverDefine the three method to find volume?Volume by Space SolverEvery 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 Using Density and MassThe 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 by Displacement SolverYou 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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How do you know when a graph is inequality?
When plotting an inequality on a graph, treat the <, ≤, >, or ≥sign as an equals sign.
What is a graph of inequality?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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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]
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.
How would you rate the probability?The likelihood of getting a four when a specific die is thrown is 1/3. Scores of 1, 2, 3, and 6 each have a 1/6 probability.The ranked probability score (RPS) is a metric used to assess how well predicted events match probability distributions. When determining how near the forecast distribution is to the observed value, both the position and spread of the distribution are considered.If you look at the table, you will see that a "Z" score of 0.0 indicates a probability of 0.50, or 50%, and a "Z" value of 1, which indicates one standard deviation above the mean, indicates a probability of 0.8413, or 84%.According to the probability formula, the likelihood that an event will occur is equal to the proportion of favorable outcomes to all outcomes. Number of favorable outcomes/Total Number of outcomes determines the probability that an event will occur, P(E).To learn more about the probability refer to:
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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:
The two equations are 1.5x+1.25y = 30 and x+y = 22 and values of x and y are 10 and 12 respectively.
What is an equation?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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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°.
What is a vector?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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