Answers
Answer:
[tex]-\frac{1}{64}[/tex]
Step-by-step explanation:
Evaluate the following limit.
[tex]\lim_{x \to 0} \frac{\frac{1}{x+8} -\frac{1}{8} }{x}[/tex]
(1) - Simplify the limit
[tex]\lim_{x \to 0} \frac{\frac{1}{x+8} -\frac{1}{8} }{x}\\\\\Longrightarrow \lim_{x \to 0} \frac{\frac{1(8)}{(x+8)(8)} -\frac{1(x+8)}{8(x+8)} }{x}\\\\\Longrightarrow \lim_{x \to 0} \frac{\frac{8-x-8}{8(x+8)} }{x} \\\\\Longrightarrow \lim_{x \to 0} \frac{\frac{ -x}{8(x+8)} }{x} \\\\\Longrightarrow \lim_{x \to 0} \frac{-x}{8x(x+8)} \\\\\Longrightarrow \boxed{\lim_{x \to 0} \frac{-1}{8(x+8)} }[/tex]
(2) - Plug in the limit
[tex]\lim_{x \to 0} \frac{-1}{8(x+8)}\\\\\Longrightarrow \lim_{x \to 0} \frac{-1}{8((0)+8)}\\\\\Longrightarrow \lim_{x \to 0} \frac{-1}{8(8)} \\\\\therefore \boxed{\boxed{\lim_{x \to 0} \frac{\frac{1}{x+8} -\frac{1}{8} }{x}=-\frac{1}{64} }}[/tex]
Related Questions
What is the importance of roots of polynomial equation?
Answers
So on solving the provided question we can say that the importance of roots of polynomial equation because as the roots are the core of it. it helps in forming of that polynomial
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
here,
the importance of roots of polynomial equation because as the roots are the core of it. it helps in forming of that polynomial
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What is dilated by a factor of 3?
Answers
Factor of scale (Dilation) Factor of scale (Dilation) How much larger or smaller the image will be depends on the scale factor in the dilation of a mathematical entity (compared to the original object).
What does it mean to be "dilated by a factor"?Factor of scale (Dilation) Factor of scale (Dilation) How much larger or smaller the image will be depends on the scale factor in the dilation of a mathematical entity (compared to the original object). An expansion takes place when the scale factor's absolute value is higher than one.The most important thing to remember is that the dilation value influences the distance between two places.A is initially one unit below P and two units to P's left, just like in the first example (dilation by a factor of three). Since 1 + 3 = 3, the dilated point, A', should be three units below P. Since 2*3 = 6, A' ought to be six units to the left of P.To learn more about dilation refer to:
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Xin has $126 to purchase balloons for her friend's birthday. Each balloon costs $6. The function p= 126-6m represents the amount of
money Xin has after purchasing n balloons. What is the zero of the function?
Answers
So, on solving the question we can say that equation p= 126-6m ; p = 2 = -124 = -6m => m = 20.6666666667
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the equation is p= 126-6m
p = 2
-124 = -6m
m = 20.6666666667
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Daniel and Elizabeth had to choose between making a 600-mile round trip by car or plane. Round-trip airfare was $260 for each of them and would take 2 hours. Round-trip cab fare to the airport would add $15. Driving their car would take 2 days each way and would add the cost of gas, food, and lodging. Elizabeth estimated that the whole trip would need $60 for gas, their combined food bill of $25 per day (4 days) , and that a room to share would be $48 for each night of the 4 total nights they would stay in a motel. Find the average cost per passenger-mile of driving.
Answers
The average cost per passenger - mile of driving is $0.503 per mile.
What is Average Cost?Average cost is calculated by dividing the total cost by the total output quantity.
There are two options for Daniel and Elizabeth, either by driving car or by plane.
We have to calculate the average cost per passenger - mile of driving in car.
Cost of gas = $60
Food bill for a day for two of them = $25
Food bill for a day for one = 25 / 2 = $12.5
Food bill for one passenger for 4 days = $12.5 × 4 = $50
Cost of room for 1 night = $48
Cost of room for 4 nights = $192
Total cost for 1 passenger = $60 + $50 + $192 = $302
Average cost per passenger - mile of driving = 302 / 600 = $0.503 per mile.
Hence the average cost per mile per passenger is $0.503 per mile.
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I don’t know how to do this (geometry)
Answers
Answer: The value of x = 7
Step-by-step explanation:
In the figure consider the parallelogram is a ABCD parallelogram
A parallelogram is a two-dimensional shape.
It has four sides, in which two pairs of sides are parallel.
Also, the parallel sides are equal in length.
If the length of the parallel sides is not equal in measurement, then the shape is not a parallelogram.
Similarly, the opposite interior angles of a parallelogram should always be equal. Otherwise, it is not a parallelogram.
AB = 3x+5
CD = 5x-9
where AB || CD and AD || BC
Also, AB = CD and AD = BC
then 3x+5 = 5x-9
when simplify the equation,
5x = 3x+5+9
5x = 3x+14
then
5x-3x = 14
2x = 14
x = 14÷2
x = 7
then the value of x = 7
when substituting value of x in equations
AB = 3x+5 = 21+5 = 26
CD = 5x-9 = 35-9 = 26
AB = CD
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Anya is 3 years older than her brother,Cole. In 11 years,Cole will be twice Anya’s current age. Find their current age
Answers
By solving these equations, Cole is currently 27 years old, and Anya is 30 years old.
How does math work out age?A person's date of birth is compared to the date on which their age needs to be calculated as part of the age calculation process. The person's age is determined by deducting the person's birthdate from the given date. Age equals Given Date - Birthdate
Let x stand in for Anya's current age and y for Cole's present age.
Cole's older brother, Anya, is three years older. Hence:
x = y + 3
x - y = 3 (1) (1)
The total of their ages will be 79 in 11 years. Hence:
(x + 11) + (y + 11) = 79
x + y = 57 (2) (2)
Equations 1 and 2 are simultaneously solved to produce:
x = 30, y = 27
Cole is currently 27 years old, and Anya is 30 years old.
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Which of the following is an equation(a) 2x +3 + 5(b) 2x + 3< 5(c) 2x + 3 35(d) 2x + 3 = 5
Answers
Answer:
2x+3=5
Step-by-step explanation:
2x+3=5 us the only one with an equals to sign
an equation always have an equals to
Evaluate the expression 9x for x = 2
Answers
The value of expression 9x for x= 2 is 18.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression = 9x
For x=2
Value of expression=9*2
=18
Hence,
After evaluating 9x for x=2 value will be 18.
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How to find gradient
Answers
The difference between the y coordinates and the difference between the x coordinates then divide them
What is a gradient in math?Gradient is a differential operator used in mathematics to transform a three-dimensional vector-valued function into a vector whose three elements are the partial derivatives of the function with respect to its three variables. The gradient sign is ∇
As a result, f = ifx + jfy + kfz, where fx, fy, and fz are the first partial derivatives of f and I j, and k are the unit vectors of the vector space, is the gradient of a function, also known as grad f or f. f is the direction of the heat-flow vector in a temperature field, where f is a temperature field in physics that indicates the temperature at every point in a space.
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Does 5 5 and 7 make a right triangle?
Answers
The base of the triangle 7 can be divided in half by a line of symmetry of the isosceles triangle, which will bisect the vertex angle. This creates two right triangles: Each with a base of 3.5 and a hypotenuse of 5.
What is meant by isosceles triangle?
A triangle with two equal sides is known as an isosceles triangle in geometry. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception.The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.Isosceles triangles have been studied mathematically since the Babylonian and Egyptian periods.Isosceles triangles have been utilized as ornamentation since the dawn of time and are widely seen in architecture and design, such as in building pediments and gables.To learn more about isosceles triangle refer to
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The base of triangle 7 can be bisected by the line of symmetry of the isosceles triangle that bisects the apex angle. This creates two right triangles.
Each has a base of 3.5 and a hypotenuse of 5.
What does isosceles triangle mean?A triangle with two equal sides is called an isosceles triangle in geometry.
Both exactly 2 equal sides and at least 2 equal sides are permissible specifications, with the exception of equilateral triangles in the latter version. The bipyramid, the golden triangle, the isosceles right triangle, and the face of the Catalan solid are examples of isosceles triangles.
Isosceles triangles have been studied mathematically since Babylonian and Egyptian times.
Used as an ornament since the dawn of time, isosceles triangles are widely used in architecture and design, including in the construction of pediments and pediments.
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Jean’s highest bowling score last season was 237 out of 300. What percent is Jean’s high score?
Answers
Answer:
79%
Step-by-step explanation:
imma human calculator and no one can stop me
( 237*100):300 =
23700:300 = 79
*79% is the answer*
Given MO=NP PROVE MN=OP
Answers
1. MO = NP (Given)
2. MO = MN + NO (Segment Add)
NP = NO + OP (Segment Add)
3. MN + NO = NO + OP (Transitive / Substitution)
4. MN = OP (Subtraction POE)
Write the letter of each answer
Answers
T. Yes
P. Yes
if you have any questions on how I got It I would be more than happy to explain!! Have a great day! :))
How do you graph 2 3 on a number line?
Answers
We have plotted the point (2/3) on a number line and attached and explained it below.
A number line is one of the methods of visually representing any point that is a real number on a graduated straight line. This is made by marking graduations on a simple normal line and then marking whatever point we need on it.
The point (2/3) has been given in the problem which we need o plot on the number line. Since this point is a fraction, we need to divide/solve it first and then see where it will fit. On dividing the fraction, we find that the point is 0.66. Now, we find the graduations 0 and 1 since it lies between them. The image for this has been attached below.
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Every month, the library holds a book sale. All books are $1.50. Choose the statement below that is true. A The price of a book depends on what kind of books you buy. B The kind of book you buy depends on the price. C The total cost of your books depends on how many books you buy. D The number of books you buy depends on the total cost.
Answers
The only true statement among the options given is C, The total cost of your books depends on how many books you buy.
What is the direct proportion?
Direct proportion, also known as direct variation, is a relationship between two variables in which the ratio of the variables is always constant. This means that if one variable increases, the other variable will also increase, and if one variable decreases, the other variable will also decrease.
According to the information given, all books are $1.50 each, so the price does not depend on what kind of book you buy. The statement A is false.
Also, the kind of book you buy does not depend on the price, so statement B is false.
The number of books you buy does depend on the total cost, so statement C is true.
Therefore, the only true statement among the options given is C, The total cost of your books depends on how many books you buy.
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]What is the first step in solving the quadratic equation -5x2+8=133?
taking the square root of both sides of the equation
subtracting 8 from both sides of the equation
squaring both sides of the equation
adding 8 to both sides of the equation
Answers
The first step in solving the quadratic equation is subtracting 8 from both sides.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
5x² + 8 = 133
Subtract 8 into both sides.
5x² = 133 - 8
5x² = 125
Divide both sides by 5.
x² = 125/5
x² = 25
x = √25
x = 5
Thus,
The root of the equation is 5.
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HELP PLS WHATS THE VALUE
Answers
Applying the triangle sum theorem, the value of x in the triangle is: C. 36.
What is the Triangle Sum Theorem?The Triangle Sum Theorem states that the sum of the measures of the interior angles of a triangle is 180 degrees. This theorem applies to all triangles, regardless of their shape or size.
The theorem can be proven using the fact that the sum of the measures of the interior angles of any polygon with n sides is (n-2)x180. Since a triangle has three sides, the sum of its interior angles is 180 degrees.
Therefore:
2x + 2x + x = 180
Combine like terms
5x = 180
Divide both sides by 5
5x/5 = 180/5
x = 36
The value of x is: C. 36.
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What is called a complex number?
Answers
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, which satisfies the equation i2 = -1.
What is complex number?
The number a is the real part of the complex number and b is the imaginary part. A complex number is said to be a sum of a real number and an imaginary number. Complex numbers are used in many branches of mathematics, including calculus, linear algebra, quantum mechanics, and electrical engineering.
They are also used in engineering, physics, chemistry, and other scientific fields. Complex numbers are useful in many real-world applications, such as finding the roots of a polynomial equation or solving systems of linear equations. Complex numbers can also be used to represent points in the plane and can be used to model phenomena in the physical world, such as electrical circuits and waveforms.
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Pls the area of the figure.
Answers
Answer:
36
Step-by-step explanation:
4 x 4 = 16
2 x 10 = 20
You would have to separate the square and the rectangle.
The way you do this is by cut of the number and subtracting them, like 6 and 2 to get the square.
How many rules are there in algebra?
Answers
Answer: There is only 5 rules in algebra.
Step-by-step explanation:
How do I dilate a shape on a grid using a scale factor of 1 2?
Answers
Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.
How do you dilate by scale factor?We locate the dilation's center point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.Keep in mind that each coordinate must be multiplied by the scale factor in order to enlarge an object in the coordinate plane. The mapping will be (x, y) (1.5 x, 1.5 y) with this dilation. The original is represented by the blue quadrilateral in the graph above, while the dilatation is shown by the red picture. Connect the image's vertices to the centre of dilation by drawing straight lines.To learn more about multiply refer to:
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Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.
How do you dilate by scale factor?We locate the dilation's center point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.
Keep in mind that each coordinate must be multiplied by the scale factor in order to enlarge an object in the coordinate plane. The mapping will be (x, y) (1.5 x, 1.5 y) with this dilation. The original is represented by the blue quadrilateral in the graph above, while the dilatation is shown by the red picture. Connect the image's vertices to the center of dilation by drawing straight lines.
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ken added 5/8 cups more walnuts to the trail mix how many cups of Tremors does he have
Answers
Answer:
Please provide more information. Since you don't provide the original amount of walnuts used, we can't solve the problem.
Rhind Rhind Papyrus Problem 27
A quantity ,and its ⅕ added together becomes 21. What is the quantity
which means : x + x ⅕ = 21
Answers
Answer:x=35/2 or 17.5
Step-by-step explanation:
x + .2x = 21
1.2x = 21
1.2x/1.2 = 21/1.2
x = 17.5
answer a i just did it
Step-by-step explanation:
Classifying Right triangles
Answers
Therefore , the solution of the given problem of triangle comes out to be √3 ,√4,√5 advance to acute triangle category as they have small angle less than 90 degree.
What is the triangle?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
Here:
Given :
=> 4 ,4√3,8
=> 0.5 , 1.3 , 1.2
=> 1.8 ,√6 ,0.8
=> √3 ,√4,√5
These can be advance to acute triangle category as they have small angle less than 90 degree.
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For which data set below would the median be the best representation of the typical value or behavior of the data set.
Group of answer choices
Religious affiliation
Ages of college students
Weights
Sale prices for homes
Answers
The median would be the best representation of the typical value or behavior of the data set for "Ages of college students".
What is median?The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The statistical median is the number in the midpoint of a series of numbers. To get the median, sort the numbers by size; the number in the center is the median. The term median is derived from the Latin word medius, which also meaning middle. A number in the center of a list is known as the median in mathematics.
Here,
The median would be the best depiction of the data set's usual value or behavior for "Ages of college students".
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In January, Jamie pays $2.00 for a tube of toothpaste. When she buys the same brand and size of toothpaste in February, she pays $2.25. What is the percent of increase in the price of the toothpaste from January to February? Round to the nearest tenth of a percent.
Answers
Answer:
12.5%
Step-by-step explanation:
0.125 * 2 = .25
2+.25 =2.25
It is a 7th grade question btw easy
Answers
The value of q, based on the equation given, can be found to be - 1 / 6
How to find q?To find q, you need to collect like terms on the correct side of the equation to be able to solve for q.
When given the equation,
1 / 2 = q + 2 / 3
You collect like terms to be:
q = 1 / 2 - 2 / 3
q = ( 3 - 4 ) / 6
q = - 1 / 6
In conclusion, the value of q is - 1 / 6.
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Question 3 1Points Hector paid $2.70 for a package of cheddar cheese slices. There are 18 slices in the package. What is the unit price of the cheddar cheese?
Answers
the unit price of the cheddar cheese is $0.15.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, we have,
Hector paid $2.70 for a package of cheddar cheese slices.
There are 18 slices in the package.
i.e. the unit price of the cheddar cheese = $2.70/18
=$0.15
hence, the unit price of the cheddar cheese is $0.15.
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The upfront cost of a Porsche is 64K. At the end of 12 Years, the car is worth only $4000, Write a linear equation to represent the value of the car in terms of the year.
Answers
The linear equation to represent the value of the car in terms of the year will be c = 64000 - 5000y
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this situation, the upfront cost of a Porsche is 64K and at the end of 12 Years, the car is worth only $4000.
The difference in amount will be:
= $64000 - $4000
= $60000
Number of years = 12
Amount in depreciation per year = $60000 / 12
= $5000 per year
The linear equation to represent the value of the car in terms of the year will be:
c = 64000 - 5000y
where c = value
y = number of years
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ABDE is a cyclic quadrilateral.
ABC and EDC are straight lines.
Angle DBC = 60°.........................................................
Answers
The measurement of angle BCD is 30°
What is a cyclic quadrilateral?A cyclic quadrilateral is a four sided shape that can be inscribed into a circle. Each vertex of the quadrilateral lies on the circumference of the circle and is connected by four chords. The opposite angles of a cyclic quadrilateral have a total of 180°.
Given that, ABDE is a cyclic quadrilateral. ABC and EDC are straight lines. Angle DBC = 60°
According to the figure, BD║ AE
Therefore,
∠ DBC ≅ ∠ EAB (definition of corresponding angles)
∠ EAB = 60°
Since, ∠ EAB : ∠ BCD = 2:1
Therefore, ∠ BCD = 60 × 1/2 = 30°
Hence, the measurement of angle BCD is 30°
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