in the form ax²+bx+c, in which a, b, and c are constants, the value of given quadratic equation a+b+c is 0.
What is simplification?Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.
For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as [tex]2x^2 + 4x = 2x(x+2).[/tex]
Simplifying an equation might involve isolating a variable on one side of the equation, or solving for the value of an unknown.Simplifying a fraction might involve finding a common denominator and canceling out common factors in the numerator and denominator.Simplifying a square root might involve expressing it in simplest radical form.The goal of simplification is to make the expression or equation easier to understand, manipulate, or solve.
The expression given is already in the form ax^(2) + bx + c, so we can simply add the coefficients of the x^(2), x and constant terms to find the value of a+b+c:
[tex](2x^{(2)} -3x+1)-(-2x^{(2)}-3x+2) = 2x^{(2)} - (-2x^{(2)}) + (-3x) - (-3x) + 1 - 2[/tex]
a+b+c = 2 - (-2) + (-3) - (-3) + 1 - 2 = 2 + 2 - 3 - 3 + 1 - 2 = 0
Therefore, the value of a+b+c is 0.
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What is the common denominator of Y +( y 3 3 in the complex fraction y +( y 3 3 )/ 5 9 2 3y?
The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.
What makes it a denominator?The Latin word "nomen," which also appears in words like "nominate" and "nomenclature," is the root of the English word "denominator," which means "name." And that's essentially what a fraction's denominator does: it "names" or denotes the kind of fraction that is specified by the numerator (the top part).
How to calculate common denominator?step1
{y + [(y - 3)/3]}/(5/9 + 2/3y)
multiply and divide with ‘9y'
9y/9y.{y + [(y - 3)/3]}/(5/9 + 2/3y)
9y.y + 9y.y - 3/3 / 9y(5/9) + 9y(2/3y)
9y.y + 3y(y - 3) / 9y(5/9) + 9y(2/3y)
9y.y + 3y(y - 3) / y.5 + 9y.2/3y
9y2 +3y2 -9y / 5y +6
12y2 - 9y / 5y + 6
The denominator will be 5y + 6
step2
The common denominator of y + [(y - 3)/3] in the complex fraction {y + [(y - 3)/3]}/(5/9 + 2/3y) is 5y + 6.
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What are the 2 coordinate systems?
The two main types of coordinate systems used in mathematics and physics are Cartesian and Polar Coordinates.
What is coordinates system?A coordinate system is a system used to identify and locate a point in space. It is the basis for maps, navigation and surveying. Coordinate systems can be two-dimensional or three-dimensional, and can use a variety of units such as latitude, longitude, and feet. Coordinate systems are used in a variety of fields such as engineering, architecture, geology, and navigation. Coordinate systems help to identify and locate points in space and are essential for charting and mapping the physical world.
Cartesian Coordinates, named after the French mathematician and philosopher René Descartes, use a two-dimensional plane to represent points with an x-axis and a y-axis. These coordinates are expressed as ordered pairs (x,y) and represent points in relation to the origin (0,0). This can be used to plot graphs and equations, and is the most commonly used coordinate system.
Polar Coordinates are based on a two-dimensional plane centered on a pole. Points are expressed as ordered pairs (r,θ) where r is the distance from the pole and θ is the angle from the polar axis. This coordinate system is useful for finding distances and angles in a circle. It is used frequently in physics and astronomy.
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(3x-2)(-x^2-10x-7)
(3x−2)(−x
2
−10x−7)
Answer: -3x^3-28x^2-x+14
Step-by-step explanation:
(3x-2)(-x^2-10x-7)
1: We would usually use the FOIL method, but since we don't have binomials we are going to start with the first number in our problem.
3x x -x^2=-3x^3
3x x -10x= -30x^2
3x x -7= -21x
-2 x -x^2=2x^2
-2 x -10x= 20x
-2 x -7=14
2. Add like terms
-3x^3-28x^2-x+14
A reearcher etimate that a foil i 3200 year old. Uing carbon-14 dating, a procedure ued to determine the age of an object, the reearcher dicover that the foil i 3600 year old. A. Find the percent error. Repone
$11. \overline{1}\%$
11 point 1 repeating percent
$12. 5\%$
12 point 5 percent
$88. \overline{8}\%$
88 point 8 repeating percent
$112. 5\%$
112 point 5 percent
Quetion 2
b. What other etimate give the ame percent error?
year old
The percent error for the given actual and estimated age of the fossils discovered by the researcher is equal to 11.11%.
As given in the question,
Actual estimated age of the fossil =3200 year old
Expected age discovered by the researcher of the fossil = 3600 year old
Formula for percent error is given by :
Percent error = | ( Actual age - Expected age ) / (Expected age) | × 100
Substitute the values we get,
Percent error = | ( 3200 - 3600 )/ 3600 | × 100
⇒ Percent error = 0.111111 × 100
⇒ Percent error = 11.11 %
Therefore, the percent error of the fossil discovered by the researcher is given by 11.11%.
The above question is incomplete , the complete question is :
A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating, a procedure used to determine the age of an object, the researcher discovers that the fossil is 3600 years old.
Find the percent error?
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y varies directly as the square root of x
y=11 when x=4
Express y as a function of x.
What is the value of x when y=44?
What is StartFraction 4 Over 6 EndFraction divided by StartFraction 3 Over 12 EndFraction
The quotient is:__
PLS HELP ME IT'S A ASSIGNMENT!!!!!!
The quotient between the two fractions will give:
(4/6)÷(3/12) = 8/3
How to solve the quotient between two fractions?Here we want to find the quotient between the fractions 4/6 and 3/12.
The quotient between any two fractions a/b and c/d can be solved as:
(a/b)÷(c/d) = (a*d)/(b*c)
Then our quotient can be solved in the following way as:
(4/6)÷(3/12) = (4*12)/(3*6)
(4*12)/(3*6) = (48/18)
Now we can simplify that fraction, if we divide both numerator and denominator by 2, we will get:
24/9
Now we can divide both by 3, then we will get the simplified fraction:
8/3.
That is the correct answer.
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Answer: The answer is 2 2/3
Step-by-step explanation: I got it right on edge
What is the rectangle of CDEF rotation of 270° clockwise around the origin
The graph of the image of the rectangle DEFG after 270° rotation counterclockwise is created using Microsoft Word and included here in the exercise
What are the vertices' coordinates?A pair of numbers called coordinates can be used to determine the position of a point or shape in a two-dimensional plane. A point's position on a 2D plane is described using the phrases "x-coordinate" and "y-coordinate."
A specific point on a grid, also known as a coordinate plane, is identified by coordinates, a pair of numbers (also known as Cartesian coordinates), or sporadically a letter and a number. The two axes of a coordinate plane, which has four quadrants, are the x (horizontal) and y (vertical) axes (vertical).
To find a point's coordinates in a coordinate system, perform the opposite.
Starting at the point, slide up or down a vertical line until you reach the x-axis. It's where your x-coordinate is.
Repeat the preceding procedures while adhering to a horizontal line to obtain the y-coordinate. The x and y coordinates can be used to find a location on the coordinate axes. The x and y coordinates of two points can be used to determine their separation. Using the x and y coordinates for two points simplifies the process of determining a line's slope.
The coordinates of the vertices of the rectangle DEFG are;
D(7, 8), E(10, 8), F(10, 9), G(7, 9)
A rotation of 270° counterclockwise about the origin gives;
Point of preimage = (x, y), point of image after the rotation = (y, -x)
The preimage point D(7, 8) has the image point as D'(8, -7) after the 270° CCW rotation
Similarly, after the 270°CCW rotation, we have;
The preimage point E(10, 8) has an image at E'(8, -10)
The preimage point F(10, 9) has an image at F'(9, -10)
The preimage point G(7, 9) has an image at G'(9, -7)
The graph of the image of the rectangle DEFG after 270° rotation counterclockwise is created using Microsoft Word and included here in the exercise
The complete question is,
Graph the image of rectangle DEFG after a rotation 270° counterclockwise around the origin
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Hallie and Mattie donated blue jeans to the clothing drive. Hallie donated 2 pairs of blue jeans. Mattie donated 6 pairs of blue jeans. Write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans.
Answer: your answer is 2:6 or 1:3 simplified
The ratio to represent the relationship between hallies donation of jean and Mattie's donation of jeans is 2:6
2:6 simplified is 1:3
Step-by-step explanation: Hope this helps!! :)))
19 Nimra buys a 3 kg box of sweets for £17.60
She puts the sweets into bags to sell.
Each bag contains 150g of sweets.
Nimra fills as many bags as possible.
She will sell each bag for the same price.
Nimra wants to make a profit of at least 35%
Assuming she sells all the bags,
? what is the lowest price Nimra should charge for each bag?
£
(5)
The lowest price that would yield a profit of 35% is 1.18.
What is profit and loss?A product is sold at a profit if the price is higher than the cost price. When a product is sold for less than what it costs to produce, the seller suffers a loss.
Each bag contains 150g of sweets.
The total number of bags filled with a total of 3kg sweets can be calculated as follows:
3kg = 3000g
Number of bags = [tex]\frac{3000}{150}[/tex] = 20 bags
Profit is given by the following formula:
[tex]P= \frac{SP - CP }{CP} * 100[/tex]
The Cost price, CP = 17.60 and profit is 35%, substitute the value in the formula above:
[tex]35 = \frac{SP - 17.60}{17.60} *100\\ \\\frac{(35)(17.60)}{100} = SP - 17.60\\\\6.16 = SP -17.60\\\\6.16 + 17.60 = SP\\\\SP= 23.76[/tex]
Find the cost of each 30 bags as follows:
[tex]1 \text { bag} = \frac{23.76}{20}\\ \\1 \text { bag} = 1.18[/tex]
Hence the lowest price that would yield a profit of 35% is 1.18.
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Please solve this for me and show steps that would be a big help!
Answer:
bagel: $3OJ: $2Step-by-step explanation:
You want the price of a bagel and a can of OJ if 2 bagels and 1 can costs $8, and 3 bagels and 2 cans cost $13.
EquationsYou can write an equation for the value of each purchase. The cost of a bagel can be represented by 'b', and 'j' can be used for the cost of an orange juice.
2b +1j = 83b +2j = 13SolutionThe coefficients of j are related by a factor of 2, so we can make the sum of coefficients of j be zero if we subtract the second equation from 2 times the first:
2(2b +1j) -(3b +2j) = 2(8) -(13)
b = 3 . . . . . . . . . . . . . . simplify
Now, we can use this value in the first equation to find j:
2(3) +1j = 8
1j = 2 . . . . . . . . . subtract 6
A bagel costs $3, and a can of orange juice costs $2.
1. A restaurant sells large and small submarine
sandwiches. Rolls for the sandwiches are ordered
from a baker. The roll for a large sandwich costs
$0.25 and the roll for a small sandwich costs
$0.15. Melissa, the manager of the restaurant,
ordered 130 more large rolls than small rolls.
What was the greatest number of large rolls she
received if she spent less than $63 show your work
The greatest number of rolls that Melissa received if she spent less than $63 is 206.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Cost for a large sandwich roll = $0.25
Cost for a small sandwich roll = $0.15
Let x be the number of small rolls that Melissa ordered.
Then number of large rolls she ordered = x + 130
Total cost for the rolls = 0.25(x + 130) + 0.15x
Melissa spent less than $63.
0.25(x + 130) + 0.15x < 63
(0.25x) + (0.25 × 130) + 0.15x < 63
0.4x + 32.5 < 63
0.4x < 30.5
x < 76.25 ≈ 76
Number of small rolls she ordered maximum is 76.
Number of large rolls she ordered is 76 + 130 = 206
Hence Melissa ordered 206 large rolls at maximum.
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Why do we use horizontal line test?
The horizontal line test is used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value.
A function that is one-to-one can be inverted, meaning that it has an inverse function. Inverse functions are important in many areas of mathematics, such as solving equations, finding derivatives, and studying geometric transformations.
The horizontal line test is used because it provides a simple and easy way to determine if a function is one-to-one without having to solve for the inverse function. By drawing a horizontal line through the graph of a function and seeing if the line intersects the graph at most once, it is possible to determine if the function is one-to-one without the need for complex calculations or algebraic manipulations.
Another reason is that the horizontal line test can be applied to functions that are defined on a closed interval or on all real numbers and it is a visual way to understand if a function is one-to-one.
In conclusion, the horizontal line test is used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.
The test is simple and easy to apply, and it provides a visual way to understand if a function is one-to-one without the need for complex calculations or algebraic manipulations. It can be applied to functions that are defined on a closed interval or on all real numbers.
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If crytal room meaure 10. 5 ft long and 7 feet wide and 9 feet tall how much paint will be needed to paint her bedroom
Assuming that the walls of the room are 8 feet tall, and that you need one gallon of paint for every 400 square feet of wall space, then you would need 5.125 gallons of paint to paint the walls of the room.
1. Calculate the square footage of the walls:
10.5ft x 7ft x 2 (sides of walls) = 147 sq. ft
2. Divide the total wall square footage by the coverage area of the paint (400 sq. ft.):
147 sq. ft. ÷ 400 sq. ft. = 0.36 gallons
3. Add 10% extra paint for wastage:
0.36 gallons x 1.1 = 0.396 gallons
4. Round up to the nearest gallon:
0.396 gallons = 0.4 gallons
5. Multiply the gallon of paint by 4 (4 walls):
0.4 gallons x 4 = 1.6 gallons
6. Round up to the nearest gallon:
1.6 gallons = 2 gallons
Hence, you would need 5.125 gallons of paint to paint the walls of the room.
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What are the 4 steps in constructing perpendicular bisector?
The four steps in constructing a perpendicular bisector are follows.
Find the midpoint of the line segment: To find the midpoint of a line segment, take the average of the x coordinates and the average of the y coordinates. This can be written as a formula: M(x,y) = (x1 + x2/2, y1 + y2/2).
Find the slope of the line: To find the slope of the perpendicular bisector, take the negative reciprocal of the original line segment’s slope. This can be written as a formula: m = -1/m1, where m1 is the original line segment’s slope.
Find the equation of the line: To find the equation of the perpendicular bisector, plug in the slope and midpoint into the point-slope form of a line equation. This can be written as a formula: y – y1 = m(x – x1).
Construct the perpendicular bisector: To construct the perpendicular bisector, draw the line corresponding to the equation found in step 3. The line should be perpendicular to the original line segment, and should pass through the midpoint.
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ellie had a package of 15 candies. after opening it, she found there were 13 candies that were not green. If she opened three more packages of candies, how many green candies could expect in total?
there apples weigh about a pount about how much would one apple cost (round to the nearest cent)
Answer: $1.31
Step-by-step explanation:
if you use todays cast
d) Calculate the profit for each given value of x and y using the profit equation and record each
amount in the shaded cells of the table.
1000
900
yo
700
600
500
400
300
200
100
0
0
x
100
200
300
400
X=
500
600
700
800
900
XI
1000
As a result, the answer to the provided equation problem is 1.39500 profit and 2.400 loss.
What is equation?A mathematical equation is a formula that joins two statements by employing the equal symbol (=) to indicate equality. In algebra, a statement demonstrating the equality between two mathematical equations is known as an equation. For example, the equation 5x + 5 = 14 puts an equation between both the two numbers. Between the sentences along either side of a letter, a mathematical relationship is constructed. Typically, the symbol acts as both the sole variable and the lone determinant. As an illustration, 8x - 4 = 2.
Here,
A C number of vehicles
Monthly expenses are subtracted from total monthly income to determine profit.
=> (25-6)C - (23500-6000) (23500-6000) (23500-6000)
=> P = 19C-17500
3000 autos need to be maintained,
Earnings are 19(3000)-17500.
Gain: $39500
If 900 automobiles are received in a given month, a profit or loss will result.
Earnings are 19(900)-17500.
Gain: -400.
Yes, a loss.
The solution to the given equation's issue is thus 1.39500 profit and 2.400 loss.
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What are the 4 steps to solve an equation?
The 4 steps to solve an equation:
Identify the terms and coefficients in the equation.Use inverse operations to isolate the variable.Check your answer by substituting the value back into the original equation.Interpret the solution within the context of the problem.How to solve an equation?When solving an equation, the first step is to identify the terms and coefficients in the equation. This means looking for any constants, variables, and coefficients and understanding their relationship to one another. Once the terms have been identified, inverse operations such as addition, subtraction, multiplication, and division can be used to isolate the variable and solve for the unknown. After the equation has been solved, it is important to double check the answer by substituting the answer back into the original equation. If the equation is still true, then the answer is correct. Finally, the solution must be interpreted within the context of the problem. This means determining the meaning of the answer and how it can be used to solve the overall problem.Learn more about equations: https://brainly.com/question/22688504
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natalia orders 5 chocolate chip cookies for every 2 sugar cookies.She needs 42 cookies in all. Chocolate chip cookies cost $1.50 each and sugar cookies cost $0.75 each. How much will natalie spend in all on her cookies?
Therefore , the solution of the given problem of unitary method comes out to be $54.
A unitary method is defined.A single or distinct unit variable is referred to as being "unitary". Therefore, the goal of this technique is to define values in favor of a finite unit. For instance, the unitary method can be used to calculate how many kilometers a car will travel on one litre of gas if it goes 44 on two.
Here,
Given :
In place of every two sugar cookies, Natalie orders five chocolate chip cookies.
In total, she needs 42 cookies. Each sugar cookie costs $0.75, while each chocolate chip cookie costs $1.50.
thus ,
total cost is : 30 * 1.50 + 0.75*12
=> 54
Therefore , the solution of the given problem of unitary method comes out to be $54.
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Evaluate the expression for the given value of the variables.
0.5c−1.5d
c=17, d=3
HELP DUE IN 20 MIN
Answer:
4
Step-by-step explanation:
Step 1:
Substitute:
0.5(17)-1.5(3)
Step 2:
Multiply:
8.5-4.5
Step 3:
Subtract:
4
what is the missing term
Answer: - 15x
Step-by-step explanation:
Write two different equivalent forms of
the expression 2*x+3
On solving the question, The polynomial is 2x + 3 the equivalent forms are (4x- 2x + 3), (x + x +2 +1)
What is Equivalent Forms ?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.
When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
The polynomial is 2x + 3
The equivalent forms are (4x- 2x + 3), (x + x +2 +1)
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Please help as soon as possible!!!
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1.
Answer:One
Step-by-step explanation:
What type of function is f/x )= x 3?
The type of function which f(x)=x^3 is the cubic function.
What is a cubic function?
A cubic function is a function in mathematics where the variables x can take on real values and the coefficients a, b, c, and d are complex numbers. In other words, it is a real function as well as a polynomial function of degree three.
F(x) = x³ denotes the "basic" cubic function. It is depicted in the graph below. The greatest power over the x variable(s) in a cubic function is 3. The graph can be made "wider" or "skinnier" by the coefficient "a," or it can be reflected (if the value is negative): The graph's y-intercept serves as the constant "d" in the equation.
A cubic function equation is of the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants (or real numbers) and a ≠ 0.
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$39.20 = 0.49m divided by 0.49
1. The price of a car that was bought for $10,000 and has depreciated 10% yearly. Find the price of the car
8 years later.
2. The equation for the price of a baseball card that was bought for 5 dollars and has appreciated 5% yearly. Find the value of the card 25 years later.
1 . Price of car 8 years later is $4305.
The price of a car that was bought for $10,000 and has depreciated 10% yearly can be calculated by multiplying the original price of the car ($10,000) by (1 - 0.10) raised to the power of the number of years (8). It means the car will lose 10% of its value each year for 8 years. Therefore, the price of the car 8 years later would be $4304.67. This is the final amount after 8 years of deprecation on the original price of the car.
2. The yearly value of the card 25 years later is $16.93 and equation of price is given by 5 * (1 + 0.05)^t where t is time.
The formula used to calculate the future value of an item that appreciates at a certain annual rate is called compounding. In this case, the baseball card was bought for $5 and has appreciated at a rate of 5% per year. The formula used to find the value of the card 25 years later is "Price = initial value * (1 + interest rate)^number of years". Plugging in the given values, we get: "Price = 5 * (1 + 0.05)^25"
Price=5(1+0.05)^25
Price=5(1.05)^25
Price=16.93
so the final price of baseball is $16.93
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Even pound of fertilizer can cover 1400 quare feet how many quare feet can be covered by 2 pound of fetilizer
If seven pound of fertilizer can cover 1400 square feet, 2 pounds of fertilizer can cover 400 square feet.
Therefore the answer is 400 square feet.
If seven pounds of fertilizer can cover 1400 square feet, we can set up the following proportion:
7 pounds / 1400 square feet = x pounds / y square feet
So y square feet = ( x pounds × 1400 square feet) / 7 pounds
To find out how many square feet can be covered by 2 pounds of fertilizer, we can solve for y by substituting in 2 for x:
y square feet = ( 2 pounds × 1400 square feet) / 7 pounds
y square feet = 2 × 1400 / 7
y square feet = 2800 / 7
y square feet = 400
So 2 pounds of fertilizer can cover 400 square feet.
--The question is incomplete, complete question is given below--
"Seven pound of fertilizer can cover 1400 square feet. How many square feet can be covered by 2 pound of fertilizer?"
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What is aspect ratio formula?
The aspect ratio is the proportional connection between the width of a video image compared to its height. It is usually expressed as width: height (separated by a colon), such as 16:9 or 4:3. The aspect ratio sets how wide a video is formatted and acts on how it will fit on your viewing screen.
When it comes to shooting video, the aspect ratio is tied to what resolution the camera records the image size in, with most DSLRs recording in a 16:9 aspect ratio.
The most popular aspect ratios for videos on the web are:
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Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
An= (4+3n^2)/(n+5n^2)
Lim n-> An =
To determine whether the sequence converges or diverges, we can use the Squeeze Theorem.
We can see that
[tex]4/(n + 5n^2) < = An < = (4 + 3n^2)/(n + 5n^2)[/tex]
As n tends to infinity, [tex]4/(n + 5n^2)[/tex] tends to 0 and[tex](4 + 3n^2)/(n + 5n^2)[/tex] tends to[tex]4/(5n^2)[/tex] which also tends to 0.
So by the Squeeze Theorem, we can say that An tends to 0 as n tends to infinity. Hence the limit of the sequence is Lim n-> An = 0
We can also see that the numerator of An is a constant and the denominator is a polynomial with degree 2. Since the denominator's degree is greater than the numerator, the limit will be zero as n -> infinity.
Therefore, the sequence converges to 0.
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The library has 65400 art books and 9600 science books. What part of all the books are art. The fraction in the answer must be irreducible
Answer:
6.8125
Step-by-step explanation:
i goggled itttttt
Answer:
9,600/75,000, 16/125
Step-by-step explanation:
art+science=75000
9600
75000 =16/125