It is impossible to create an equation for a circle given exactly two points.
Let's consider the two basic equations of circle, i.e, the standard equation and general equation.
Now, Standard equation of circle with center (h, k) and radius r is represented as
(x−h)² +(y−k)² =r²
Note here we need values of three unknowns, h, k, r to get equation of a certain circle.
The other general equation of circle is of the form
x² + y² + 2gx + 2fy + c = 0
Again, values of three unknowns (g, f and c) are necessary for obtaining equation of a certain circle. So in both cases, values of three unknowns are required to have an equation of a distinct circle. In order to calculate, the values of these three unknowns, we must first require three conditions that would be produced by three equations. Solving those equations, allows us to construct the equation of circle. So if only two points are given, then these gives two equations with three unknowns. It would be impossible to get three distinct values from two equations. So, there is no possible distinct circle for two points.
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HELP ME PLEASE : Math is a bit different at the North Pole. Can you solve this math with Christmas symbols problem?
The sum of the two Santa models is 24.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is math is a bit different at the north pole and a problem is shown in the image.
We can assume the three variables as : [x], [y] and [z]. So, we can write the equations as -
3x = 21 ........ Eq[1]
y + z = 16 ........ Eq[2]
x + y - z = - 1 ........ Eq[3]
Now, it is given that -
3x = 21
x = 21/3
x = 7
and
y + z = 16
y = 16 - z
So, we can write the equation as -
x + y - z = - 1
7 + 16 - z - z = - 1
23 - 2z = - 1
2z = 24
z = 12
So, we can write -
[z] + [z] = 12 + 12 = 24
Therefore, the sum of the two Santa models is 24.
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What is the y-intercept of the exponential function?
Answer:
y- intercept = - 1
Step-by-step explanation:
to find the y- intercept, let x = 0 in f(x) and evaluate
using rule of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
f(x) =- 32[tex](2)^{x-3}[/tex] + 3 , then
f(0) = - 32 [tex](2)^{0-3}[/tex] + 3
= - 32 [tex](2)^{-3}[/tex] + 3
= - 32 × [tex]\frac{1}{2^3}[/tex] + 3
= - 32 × [tex]\frac{1}{8}[/tex] + 3
= - 4 + 3
= - 1 ← y- intercept
What number is one more than 39?
The answer is 40, by using 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.
Here, what we can do is use addition to find the number one more than 39.
= 39 + 1
= 40
Hence, the number one more than 39 is 40.
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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").
Here, what we can do is use addition to find the number one more than 39.
= 39 + 1
= 40
Does anyone know how to solve this?
solve for x
3(x-2)^2-10=4-11x
Answer:
x=3.25
Step-by-step explanation:
To solve this you would have to distribute the 3 to both numbers in the parenthesis and then you'd combine like terms. Once you combine like terms it'll be a bit easier to solve. When I distributed and combined like terms I got 3x-12-10=4-11x and then I solved and got x=3.25
Not sure if this is how your supposed to solve this problem for your assignment but for us it's usually like this...if it happens to be wrong then I'm sorry.
At a supermarket, shopping trolleys are 1 meter long. Your friend works by collecting them and stacking them into an area. Each shopping trolley in the stack adds on 0.25 m. How many trolleys could be stacked in a single line of 10 metres?
Answer:
If each shopping trolley is 1 meter long, and each trolley in the stack adds 0.25 meters, then the total length of the stack will be equal to the length of each trolley plus the length added by each additional trolley in the stack. This means that the total length of the stack will be equal to 1 + 0.25 = 1.25 meters per trolley.
If the stack has a total length of 10 meters, and each trolley adds 1.25 meters to the stack, we can divide the total length by the length added by each trolley to find the number of trolleys that can be stacked in a single line of 10 meters:
10 / 1.25 = <<10/1.25=8>>8 trolleys
Therefore, if each shopping trolley is 1 meter long and each trolley in the stack adds 0.25 meters, a single line of 10 meters could hold a stack of 8 trolleys.
Step-by-step explanation:
What age can you skip count?
Therefore , the 6 year old children can able to skip count to 1 to 100 counting by making them learn.
What do you mean by counting?Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.
Here,
Around age 6, kids start to learn how to skip count. Skip counting teaches your youngster to count swiftly and gets them ready to grasp the fundamentals of multiplication.
The simplest way to count is in skip increments of 10, which are essentially identical to regular increments of 10 with the exception of an extra '0': 10, 20, 30,... 80, 90, 100.
Therefore , the 6 year old children can able to skip count to 1 to 100 counting by making them learn.
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Enter the correct answer in the box.
This graph represents a transformation of the parent cube root function.
Graph shows a radical function plotted on a coordinate plane. A curve enters quadrant 3 at (minus 10, minus 3.2), goes through (minus 4, minus 3), (0, minus 2.5), data point (3, minus 1), (5, 0), and exits quadrant 1.
Replace the values of h and k to create the equation of the transformed function.
Replacing the values of h and k to create the equation of the transformed function gives us; y = [∛(x - 4)] - k
What function does the graph represent?The graph represents a transformation of the parent cube root function.
The parent cube root function is; y = ∛x
In this parent function, we see that the value of h and k are equal to 0. Where;
h = 0, k = 0 in parent function
Then the graph changes direction at the coordinate (0,0) in parent function.
From the given graph, we can see that it changes direction at the coordinate (4,-1)
This tells us that the graph is shifted by 4 units to the right and then by 1 unit downwards.
Thus, it means that the value of h = 4 and the value of k = 1.
Thus, the equation of the transformed function will be written as;
y = [∛(x - 4)] - k
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What number is ten more than 21?
The number that is 10 more than 21 is 31, 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.
Here, what we can do is use addition to find the number 10 more than 21.
= 21 + 10
= 31
Hence, the number 10 more than 21 is 31.
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A tailor cuts 234 yards from a roll of fabric to make one curtain. She has 1812 yards of fabric available to make curtains. Use the drop-down menus to answer each question.
The symbol that should be used is the division symbol. On the other hand, in the result the whole number represents the number of curtains, while the fraction represents a fraction of the next curtain.
Given :
The numerator: Number above.
The denominator: Number below.
A whole number: Optional element.
The number of curtains the tailor can make is equal to the total fabric divided by the fabric required for one curtain. Based on this, the symbol should be ÷.
= 18 1/2 ÷ 2 3/4
The whole number represents the number of curtains. The division of the total fabric and the total fabric required for one curtain will include a whole number and a fraction. In this situation, the whole number represents the number of curtains that can be made from the total fabric.
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What is the median of 25 and 29?
The median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 25 and 29. When we order this set from least to greatest, we get 25, 29. There are two numbers in this set, so the median is the average of the two middle numbers, which is the only number in the set. The only number in this set is 27, so the median is 27.
To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are two numbers in the set, so the median is the average of the two middle numbers.
In summary, the median of the set of numbers 25 and 29 is 27. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
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Please help !!!!!!!!
Answer: 64.5 hours
Step-by-step explanation:
2580 divided by 40
Due tomorrow
I need help with #2
Please and thank you!
I need help with this
The value of function (f + g)(x) is 7x² + x - 4.
What is the function?A function is an expression, rule, or law in mathematics that defines a relationship between a single variable (the independent variable) and then another variable (the dependent variable).Here the functions provided are,
f(x) = 4x² - 5x
g(x) = 3x² + 6x - 4
The p addition property of functions (f + g)(x) allows them to be written as,
(f + g)(x) = f(x) + g(x)
In the above equation, we can substitute the values of each function.
(f + g)(x) = 4x² - 5x + 3x² + 6x - 4
We have to combine the similar terms,
(f + g)(x) = 4x² - 5x + 3x² + 6x - 4
= 7x² + x - 4
So (f + g)(x) = 7x² + x - 4
Therefore the correct answer is option B.
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Jonas knows the following information about the
19
1919 members in his travel group:
5
55 members have been to both the United States and Australia.
11
1111 members in total have been to the United States.
12
1212 members in total have been to Australia.
Can you help Jonas organize the results into a two-way frequency table?
Have been to the United States Have not been to the United States
Have been to Australia
Have not been to Australia
The complete two-way frequency table is shown below.
what is frequency table?
a table that displays the distribution of a characteristic's occurrence frequency in accordance with a specific set of class intervals.
explanation:
Denote the events as follows:
U = a member have been to the United States
NU = a member have not been to the United States
A = a member have been to Australia
NA = a member have not been to Australia
The information provided is:
A NA Total
U 5 __ 11
NU __ __ __
Total 12 __ 19
Complete the table as follows:
n (U ∩ NA) = n (U) - n (U ∩ A)
= 11 - 5
= 6
n (NU) = N - n (U)
= 19 - 11
= 8
n (NU ∩ A) = n (A) - n (U ∩ A)
= 12 - 5
= 7
n (NA) = N - n (A)
= 19 - 12
= 7
n (NU ∩ NA) = n (NA) + n (U ∩ NA)
= 7 - 6
= 1
Therefore, the complete 2-way Frequency table is:
A NA Total
U 5 6 11
NU 7 1 8
Total 12 7 19
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What are the steps to solving 5x 3 13?
Linear expressions or equations are expressions in which the highest power of the variable is one 5x+3= 13 in four steps
steps 5 x + 3 = 13. 5x+3=13. Subtract 3 from both sides. Subtract 3 from both sides.
5x=13-3. 5x=13−3. Subtract 3 from 13 to get 10. Subtract 3 from 13 to get 10.
5x=10. 5x=10. Divide both sides by 5. Divide both sides by 5.
x=\frac{10}{5} x=510 Divide 10 by 5 to get 2. Divide 10 by 5 to get 2.
Linear expressions or equations are expressions in which the highest power of the variable is one.
Quadratic expressions or equations are expressions in which the highest power of the variable is two.
Cubic expressions or equations are expressions in which the highest power of the variable is three.
Quartic expressions or equations are expressions in which the highest power of the variable is four.
From the expression, 5x + 2 given,
the highest power of x is one. So it is a linear expression.
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How do you explain what a function is?
A function is a mathematical relationship between the domain and the range, two sets of values. The range is the set of output values that the function produces, and the domain is the set of input values for which it is defined.
What is a function, exactly?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
Consider the function f(x) = x^2 as an illustration. This function generates the value f from the supplied value x. (x). This function will return the value 9 if the given value is 3, since 3^2 = 9.
Generally speaking, a function describes the relationship between two sets of values (the domain) (the range). For instance, the relationship between the input value x and the output value f(x) is described by the function f(x) = x^2.
A formula, which is a guide that explains how to calculate the output value for a specific input value, is typically used to express a function. For instance, the function f(x) = x^2 has the formula f(x) = x^2. We just enter the input value into the formula and simplify to determine the output value for a particular input value.
A fundamental idea in mathematics, functions are used to model and describe a wide variety of real-world occurrences. For instance, the quadratic function f(x) = x^2 + 2x + 1 can be used to simulate how an item would move in the presence of gravity. A population's expansion over time can be predicted using the exponential function f(x) = 3^x.
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a) Change 12 out of 43 to a percentage
b) Change 43 out of 57 to a percentage
Answer:
a) 27.9069767442
b} 75.439%
Step-by-step explanation:
The equation y=−x4+5 describes line 1. The equation x+4y=−40 describes line 2.
Which statement is true?
Responses
Line 1 is neither parallel nor perpendicular to line 2.
Line 1 is parallel to line 2.
Line 1 is perpendicular to line 2.
The lines y = - 4x + 5 and y = x + 4y = - 40 is neither parallel nor perpendicular.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, Are two lines y = - 4x + 5 and y = x + 4y = - 40.
Now,
x + 4y = 40
4y = - x + 40.
y = - (1/4)x + 10.
We know lines parallel to each other have the same slope and lines perpendicular to each other have a slope that is negative reciprocal of each other.
So, Line 1 is neither parallel nor perpendicular to line 2.
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Two brothers, Leo and William, are racing their bikes around
a 9.5-mile loop. Since Leo is younger, he is given a 1.5-mile
head start. The graph to the right shows Leo's progress.
The expression 19x can be used to determine y, the distance
in miles that William has traveled after x hours have passed.
Which statement about this situation is not true?
A. William is traveling at a faster speed than Leo.
B. The difference between their speeds is exactly
1.5 miles per hour.
C. Leo traveled only 8 miles during the race.
D. Both brothers will finish the race in 1/2 hour.
The incorrect answer is b) The difference between their speeds is exactly 1.5 miles per hour.
What is distance?
The distance between two sites is the length of the route. The metre is the SI unit for distance.
What is speed?
The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.
What is time?
The amount of time that something happens, goes through a process, or remains the same.
Let distance be Y and time be X.
Distance (Y) travelled by William after X hours;
Y= 19X
Speed of Leo = [tex]\frac{distance}{time}[/tex]
= [tex]\frac{8}{0.5}[/tex]= 16 m/hr
Difference in speed= 19-16= 3m/hr
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suppose that 62 percent of the graduates from your high school go on to four-year colleges, 15 percent go on to two-year colleges, 18 percent find employment, and the remaining graduates search for a job. if a randomly selected student is not going on to a four-year college, what is the probability he or she will find employment?
Using the AND rule of probability and percentage calculations, The answer is 0.0684.
What do you mean by probability?Probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
What do you mean by percentage?Percentages are fractions with a 100 as the denominator. The percent symbol (%) is used next to the number to denote that it is a percentage.
62% goes to college.
% not going to college = 100%-62%
=38%
on that 38%, 18% gets employment,
probability = 0.38 * 0.18
=0.0684
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a team of researchers gets a list of all 500 members of an organization they want to include in the study. they only have funding and time to survey 50 members. they take the list of members, randomly select a starting point, and select every 10th name from the list for the sample. what is the sampling interval?
The required sample interval in the given situation is 10.
What is the sampling interval?The sampling interval is the space or period of time in which measurements or data collection occur.
This is known as the "nth selection" in research and occurs when we choose the nth participant (or sample unit) from the list; this sampling interval results in a random selection from the entire population.
Calculating the sampling interval involves dividing the population size by the desired sample size to arrive at the predetermined periodic interval.
So, have a population size of 500 people.
The number of members to be selected is only 50.
We already know that to find the sample interval, we should divide the population size bu the required sample size.
Now, calculate the sample interval as follows:
= 500/50
= 50/5
= 10
Therefore, the required sample interval in the given situation is 10.
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The value of 12004+ 32004+52004+72004+ 92004 is calculated using a powerful
computer. What is the units digit of the correct answer?
Units digit - 6
Step-by-step explanation:
A. 12004+ 32004 = 44008
B. 52004+72004 = 124008
Total - 44008+124008+ 92004 = 208016
Units digit - 6
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How do you solve for mean and SD?
We determine the mean and standard deviation for a statistical observation by considering the available data set and size of data.
What is mean and standard deviation?In the statistics, the mean value is the average value of all available data set.
The standard deviation is an estimation that implies how far each data is apart from the mean value.
How do we solve for mean and standard deviation?Suppose we have a list of data. The data list is denoted by X and the total number of data is N. Now we will add all the data set and the result is denoted by ∑X
Mean value formula = the sum of data / number of data = ∑X/N
In the next, we will determine the square value of all data and the list is denoted by X². Finally, we add all the X² and the result is ∑X²
now, standard deviation is calculated by the formula,
standard deviation = √[∑X²/N - (∑X/N)²]
hence, we can solve for mean and SD
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Is the square root of an integer always irrational Why or why not?
No, the Square root of an integer is not always irrational because the square root of perfect squares is not irrational.
What is an irrational number?Any real number that cannot be written as p/q, where p and q are both integers, the quotient of two integers.
If a number is not a perfect square, the square root of that number is not rational.
For example, the square root is 4 is 2.
The square root of 9 is 3.
But whereas the square root of 5 is 2.23606797755555...... which is irrational
The square root of 8 is 2.8284271247555..... which is irrational.
So, therefore square root of a number is not irrational always it can be rational also.
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What is the function of rational root theorem?
A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.
A polynomial expression is given and after solving them we get the two values known as the roots of the function.
These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .
We should use the rational root theorem only when the value of coefficients are small.
The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,
p is an integer factor of the constant term a0, and
q is an integer factor of the leading coefficient an.
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How to solve pls. I need help really bad I don’t understand
Answer:
The answer for the question is 3.7
What is the formula of rational function?
The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.
What is rational function ?
A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. Example 1. f(x) = [tex]\frac{x}{x - 2}[/tex].
Rational functions are typically identified by the degrees of the numerator and denominator. For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. A rational function model is a generalization of the polynomial model.
The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.
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The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days. How do the functions in the table compare? since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria b than bacteria a at the start. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria b than bacteria a at the start. Since the maximum value in the table for bacteria a is greater than the maximum value in the table for bacteria b, bacteria a has a faster growth rate than bacteria b. Since the minimum value in the table for bacteria a is less than the minimum value in the table for bacteria b, bacteria a has a slower growth rate than bacteria b.
False , the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
Given :
A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
False, it is the y-intercept of the function that indicates the amount at the start of the experiment.
B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
True, the y-intercept is given when x = 0, indicating the initial value of the function.
C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.
False, because the maximum value of each table is given in different times, and also the initial value of each table is different.
D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.
False, the growth rate is not given by the inicial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.
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Full question :
is in the image uploaded.
What is equidistant from the angles of a triangle?
The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.
Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.
A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.
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how to cross multiply fractions with whole numbers
If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.
What are fractions and whole numbers?A number that is not negative and doesn't have any fractional or decimal components. Anything that isn't a whole number is a fraction. most often expressed with a numerator (top) and denominator (bottom). All fractions should ideally be "correct" fractions, that is, less than 1.
You can multiply a fraction by a whole number by only multiplying the numerator which is the top number on the bar. for example:
E = 2 x 3/4
E = 6/4
E = 1²/₄
Hence, If you simply multiply the numerator, which is the top number on the bar, you can multiply a fraction by a full number.
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