Yes, a function can have no holes when it has no common factor at both numerator and denominator.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
What is a hole?In Mathematics, a hole can be defined as a point on the graph wherein the input value of a given function is undefined or not defined. This ultimately implies that, a hole is a point on the graph of a rational function where the input value causes both its numerator and denominator to be equal to zero (0).
In conclusion, we can reasonably infer and logically deduce that it is very possible for a function to have no holes.
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The table represents a quadratic function. Write an equation of the function in standard form.
The function's standard form equation is equivalent to [tex]\frac{-x^2}{4}+1=0[/tex].
A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.
The standard form of a quadratic equation in mathematics is given by;
[tex]ax^2+bx+c=0\\y=f(x)=ax^2+bx+c[/tex]
Next, using the information in the previous table, we would create the following system of equations:
[tex]-3=a(-4)^2+b(-4)+c\\-3=16a-4b+c[/tex].......equation (i)
[tex]0=a(-2)^2+b(-2)+c\\0= 4a-2b+c[/tex]........equation(ii)
[tex]1=a(0)^2+b(0)+c\\1=c[/tex].........equation (iii)
Inputting the value of c into equations 1 and 2 results in:
[tex]-4=16a-4b[/tex]......ewuation(iv)
[tex]-1=4a-2b[/tex]......equation(v)
Equation 5 is multiplied by two and solved concurrently to yield:
[tex]-2=8a\\a=\frac{-2}{8} \\a=\frac{-1}{4}[/tex]
What we have for b's value is:
[tex]-1=4a-2b\\-1=4(\frac{-1}{4})-2b\\ -1=-1-2b\\2b=0\\b=0[/tex]
Inputting the values of a, b, and c into a quadratic equation in standard form:
[tex]ax^2+bx+c=0\\\frac{-1}{4}x^2+(0)x+1=0\\ \frac{-x^2}{4} +1=0[/tex]
When x equals 2, we get:
[tex]\frac{-x^2}{4} +1=0\\\frac{-2^2}{4}+1=0\\ \frac{-4}{4}+1=0\\ -1+1=0[/tex]
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How can you determine if the two angles are congruent by AAS A?
By using the the application of ASA we can determine the two angles are congruent by AAS.
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
AAS congruence can be proved in easy steps.
Suppose we have two triangles ABC and DEF, where,
Diagram attaches at the end of the solution.
∠B = ∠E [Corresponding angles]
∠C = ∠F [Corresponding angles]
AC = DF [Adjacent sides]
By angle sum property of triangle, we know that;
∠A + ∠B + ∠C = 180 ………(1)
∠D + ∠E + ∠F = 180 ……….(2)
From equation 1 and 2 we can say;
∠A + ∠B + ∠C = ∠D + ∠E + ∠F
∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D
Hence, in triangle ABC and DEF,
∠A = ∠D
AC = DF
∠C = ∠F
Hence, by ASA congruency, (AAS: the application of ASA)
Δ ABC ≅ Δ DEF
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What is the y-intercept of y =- 5x?
Y- intercept for the line y = 5x is 0. This can be get from the standard equation for a line.
For the The standard equation for a line is,
y = ax + b
y is called the dependent variable because its value depends on the value of x
a is the slope of the line
x is called the independent variable because it can be any value
b is the y-intercept
Here y is a function of x. You could simply write it as y = 5x. Thus if we compare to the standard form equation y = ax + b, a=5 and b=0. Thus the y-intercept is zero. The reason that this is the case is that when you set x=0 the value is plotted on the y axis because the equation for the y axis is the line defined by x=0. Any value in the x, y plane where x is equal to zero plots on the vertical line going through (0,0) or in other words the y axis.
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The equation P = 0.00892t^2 + 1.1149t + 78.4491 models the
United States population, P, in millions since 1900. If t
represents the number of years after 1900, then what is
the estimated population in 2025 to the nearest tenth of a
million?
343.9
219.0
356.9
217.8
The estimated population in 2025 is 356.9
What is estimation ?
In math, estimating can be used to roughly calculate an answer (getting a "rough response") or to verify its accuracy (getting the "proper answer"). Even when estimating large numbers or decimal numbers, you shouldn't need to utilize a calculator or other documented techniques.
Estimation is frequently performed by sampling, which involves counting a small sample of a given thing and extrapolating that number to a wider population. Calculating the number of sweets of a particular size that are contained in a glass jar serves as an illustration of estimation.
There are 125 years from after 1900 to 2025
P = 0.00892t^2 + 1.1149t + 78.4491
P= (0.0089x125x125)+(1.1149x125)+78.4491
=139.0625+139.3625+78.4491
=356.87
=356.9
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5(?+3)+?(6 + 3)=108.
Answer:?=93/14
Step-by-step explanation:
the ? is the variable in this equation so we have to solve for it
1. distributive property ->
5(?+3) = 5?+15
?(6+3) = 9?
so 5?+15+9?=108 -> 14?+15=108
2. then solve,
14? -15 = 108 -15
14?=93
?=93/14
because the population distribution is skewed, the principal is considering using the median number of absences last month instead of the mean number of absences to summarize the distribution. describe how the principal could use a simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50
The simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50 is given as follows:
A for loop with 50 iterations.For each iteration, a sample is selected, then the median is computed and stored in an array.After the 50 iterations, the mean of these medians is computed.After computing the mean, the standard deviation is computed.What is sampling?Sampling is a technique for when a group of elements from a population is taken to represent the entire population.
Hence, for this problem, multiple samples of 50 students are taken, and for each sample, the median is computed and then stored in a list, according to the procedure described at the beginning of the answer.
Then, after the entire procedure runs, we will have a sample of 50 values, which represent the median for each sample. Then the standard deviation is calculated as the square root of the sum of the difference squared between each of these observations and the mean of all these observations, divided by 50, which is the cardinality of the data-set.
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What is an example of an inverse variation equation?
y = 3/x equation is an example of inverse variation between the variables x and y .
Now, According to the question:
The equation with the inverse variation between the variables 'x' and 'y' .
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
y = 3/x is an example of inverse variation.
Hence, y = 3/x equation is an example of inverse variation between the variables x and y .
Let's know:
What is an Inverse variation equation?
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.
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help me pleaseee! asap would be lovely :)
Answer:
x = - 28/101
Step-by-step explanation:
Answer:
x=-42
Step-by-step explanation:
[tex]-3x-28=98\\(-3x-28)+28=(98)+28\\-3x=126\\\frac{-3x}{-3}=\frac{126}{-3}\\x=-42[/tex]
PLEASE HELP! Thank you
Answer:
1. 7
2. 5/3
3. 2.6
Step-by-step explanation:
The "+" or "-" sign of a number is disregarded in this operation since distance in mathematics is never negative. You can tell what a number's absolute value is by putting it between two vertical bars known as absolute value brackets.
Answer:
1. 7
2. 5/3
3. 2.6
Step-by-step explanation:
The absolute value is the distance between a number and zero
1. We see the distance is 7, so the answer is 7
2. We see the distance as 5/3, so the answer is 5/3
3. We see the distance is 2.6, so the answer is 2.6
What is the formula for calculating the slope m of a line?
The formula or equation used to determine the slope of a straight line is as follows:
m = (Y₂-Y₁)/(X₂-X₁)
What is an equation?An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.
Equations can be graphed, they are used to model many problems and theories.
The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:
m = (Y₂-Y₁)/(X₂-X₁)
Where the points are:
P₁ = (X₁,Y₁)P₂ = (X₂,Y₂)Learn more about equations at:
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What type of function is f/x )= sinx?
f(x) = sinx is an trigonometric function.
A trigonometric function is a type of mathematical function that is defined in terms of the angles of a right triangle. The most common trigonometric functions are sine, cosine, and tangent. The function f(x) = sinx is a sine function, which is defined as the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. The sine function can be used to calculate the angles of a triangle when the lengths of two sides are known. It is also useful for modeling many real-world phenomena such as the motion of waves and the oscillations of pendulums.
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in this 10 digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3 what is the value of A + B + C
helppppppp
The value of A + B + C based on the information is A. 5.
How to illustrate the information?From the information, we have digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3.
It should be noted that all multiple of 8 have it's digits add up to a multiple of 9. This can be illustrated as:
4 + A + B + C + 2 + 3 + 9 + 0 + 4 + 0
= 22 + A + B + C
This will be equated to 27 which is the nearest multiple of 9
22 + A + B + C = 27
A + B + C = 27 - 22
A + B + C = 5
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Complete question
In this 10 digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3 what is the value of A + B + C?
A 5
B 6
C 7
D 8
Is 8 a multiple yes or no?
Therefore , the solution to this problem is yes 8 has multiple which are 16,24,32 etc.
What is multiple?A multiple in mathematics refers to the product produced by multiplying two numbers or variable. In this instance, the number 7 is multiple by 56.
The expression is termed as multiple .Fun Facts is an additional example of multiples. 0 is a multiple of all numbers since it produces zero when multiplied by any other number.
Here,
There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.
There are two consecutive results in this sequence, and there is an 8-digit gap between each subsequent number and the one before it.
The results of multiplying any integer by other natural numbers are known as multiples.
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Can a 4 year old count to 100?
Yes, a 4 year old can typically count to 100.
What is counting?Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.
Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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Graph the image of the triangle using the transformation given.
Amadou misses 2% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 32?
The total free throws Amadou attempts, if Amadou misses 2% of the free throws he attempts in a season, he missed 32, is 1600.
What is the percentage?As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
Amadou misses 2% of the free throws he attempts in a season, he missed 32,
Calculate the total number of throws as shown below,
2% of x = 32
Here, x is the total number of throws,
0.02 × x = 32
x = 32 / 0.02
x = 1600
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The following chart shows the number of days a book is overdue and the fines for that book. Find an equation that defines the fines with respect to the number of days overdue. EXPLAIN your steps.Explain what the values in your final equation mean.
The equation that defines the fines with respect to the number of days overdue is written as: y = 0.1x + 1.
How to Write a Linear Equation?The equation that defines the fines with respect to the number of days overdue can be written as a linear equation that is expressed in slope-intercept form as y = mx + b, where the slope or unit rate is m, while the y-intercept or initial value is b.
Using two points from the chart, (2, 1.20) and (5, 1.50), find the slope or unit rate:
Slope / unit rate (m) = change in y / change in x = (1.50 - 1.20) / (5 - 2)
m = 0.3 / 3
m = 0.1
Find the y-intercept by substituting m = 0.1 and (x, y) = (2, 1.20) into y = mx + b:
1.20 = 0.1(2) + b
1.20 = 0.2 + b
1.20 - 0.2 = b
1 = b
To write the equation, substitute m = 0.1 and b = 1 into y = mx + b:
y = 0.1x + 1
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How do you know if an equation is consistent and independent consistent and dependent or inconsistent?
Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent. otherwise inconsistent
The classification which best describes the system of equations is; Consistent and dependent
A linear or nonlinear system of equations as the case may be is termed consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In essence, when substituted into each of the equations, they make each equation hold true.
Additionally, the system of equations is dependent because the value of each variable is dependent on the others.
Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.
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How do you find the length of a rectangle when given the area?
we will find the length of rectangle when area is divided by the breadth of rectangle.
what are the properties of rectangle?Some properties are rectangle are stated below:
1. rectangle has four right angles
2. rectangles has four sides and equal opposite sides which are parallel to each other.
3.rectangle has two diagonals which are similar in length.
which is the formula for finding the length?The bigger side lengths are called length and the smaller sides are called breadth of rectangle.
if area of rectangle is given, we can find length when area is divided by its breadth.
length = area/breadth
hence, length of rectangle is determined from the value of area and breadth.
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whats 78,563 divided by 98
Ty for whoever helps me <3
Answer:
801.66
Step-by-step explanation:
calculator
Answer:
801.6632653061
Step-by-step explanation:
.......
What number makes the expressions equivalent? −1.1 −1.4m + 0.4 = ? − 1.4m
Answer: -0.7
Step-by-step explanation:
-1.1 - 1.4m + 0.4 = ? - 1.4m
-1.1 + 0.4 = -0.7
-0.7 - 1.4m = -0.7 - 1.4m
A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
The average change in water volume is (answer here)iter(s) per day.
The average change in the volume of water per day is obtained as 0.625 litres.
What is the rate change of volume?The rate change of volume is the change of volume with respect to time.
For instantaneous change the derivative of the expression of volume can be taken.
The average change in the volume of water can be obtained as follows,
Average change = Volume of water ÷ Number of days
= 2.5 ÷ 4 = 0.625
Hence, the average change in water volume is given as 0.625 liters per day.
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Someone help meeeee. I do not understand this work
Answer:
Step-by-step explanation:
i belive it would be 500 divided by 20m
What is 25x+1 = 125x-1?
Answer:
x= 1/50 or 0.02, or x=50^-1
Answer:
[tex]x=\frac{1}{50}[/tex]
Step-by-step explanation:
If you would like to see the steps here they are.
what is the biggest number to mankind?
Answer:
googolplex
Step-by-step explanation:
it just is
Answer:
A Googolplex
Step-by-step explanation:
It is written as 10^googol and 10^10^100
If a₁ = 4 and an = -4an-1 +5 then find the value of a5
If a₁ = 4 and an = -4an-1 +5 then the value of a5 is 72, in the given sequence.
What is sequence?A group of enumerated objects where repetitions are allowed and order is crucial is referred to as a sequence in mathematics. Similar to a set, it has members. The sequence's length is expressed in terms of its number of elements.
Given that, sequence
[tex]a_1=4, a_n=4 a_{n-1}+5[/tex]
Now
[tex]a_2=4 a_1+5[/tex]
[tex]a_2=4 \times 4+5[/tex]
[tex]a_2=21[/tex]
[tex]a_2=4 \times 4+5[/tex]
[tex]a_2=21[/tex]
And the common difference d = 21 - 4 = 17
Therefore [tex]a_5=a_1+4 d[/tex]
[tex]a_5=4+4 \times 17[/tex]
[tex]a_5=4+68[/tex]
[tex]a_5=72[/tex]
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What is the formula for calculating half-life?
The formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]
What is Half-life?The half-life is the amount of time required for a quantity (of substance) to reduce to half of its initial value.
The expression is commonly used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.
Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay).
For instance, the medical sciences may refer to the biological half-life of drugs and other substances in the human body.
Time doubles in proportion to life's exponential expansion.
The formula to calculate half-life: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]
Where N(t) is the quantity of the substance remaining, N₀ is the initial quantity of the substance, t is the time elapsed and t₁₎₂ is the half-life of the substance.
Therefore, the formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]
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What is an example of an inverse relationship in math?
An inverse relationship in math is a relationship between two quantities where one quantity increases as the other decreases and vice versa.
An example of an inverse relationship is the relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.
The relationship between temperature in degrees Celsius (C) and temperature in degrees Fahrenheit (F) is defined by the following equation:
F = (9/5)C + 32
This equation shows that as the temperature in degrees Celsius increases, the temperature in degrees Fahrenheit decreases. For example, if the temperature in degrees Celsius is 20, the temperature in degrees Fahrenheit is 68. If the temperature in degrees Celsius is 40, the temperature in degrees Fahrenheit is 104.
Therefore, the relationship between temperature in degrees Celsius and temperature in degrees Fahrenheit is an inverse relationship.
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ROLLER COASTERS The height of a roller coaster is 157.5 feet. If the roller
coaster's shadow is 60 feet long, how long will a person's shadow be if the
person is 5 feet 3 inches tall?
Answer:
2 feet
Step-by-step explanation:
(60 / 157.5) * 63 inches = 24 inches = 2 feet
Calculate. Then, write a situation to match this expression and explain what 48.78 ÷ 0.9 the quotient means in your situation.
Answer:
Calculate: 48.78/0.9 = 54.2
Write a situation: Richard has 48.78 ounces of grape juice that he wants to ration out for his friends at his birthday party. Each cup the friends get can hold 0.9 ounces of grape juice.
What does the quotient mean: The quotient, 54.2, means that Richard had given 54.2 ounces of grape juice to all of his friends combined.