Q: what is a quotient?
A: A quotient is the number of times a divisor goes into a dividend
Q: how to expand logarithms?
A: By using the properties of logs, you can expand logarithms in a number of ways. One common method is to use the power rule, which states that logarithms can be expanded by raising the power to the logarithm. For example, if you wanted to expand logarithm base two of eight, you would raise two to the power of three, since three is the logarithm base two of eight. This would give you the answer of two cubed, or eight.
Q: what is the mean of a data set?
A: the mean of a data set is the sum of all the data points divided by the number of data points
Q: suzanne can read 1 page in 3 minutes. how many pages can she read in 5 hours??
A: Suzanne could potentially read 800 pages in 5 hours.
Q: how to condense logarithms?
A: Logarithms can be condensed by using properties of logs. For example, if you have two logs that are multiplied, you can condense them by adding the exponents.
Q: how to do elimination?
A: There are a few steps involved in solving a system of linear equations using elimination.
Q: how to simplify exponents?
A: To simplify an exponent, you can use the properties of exponents. For example, if you have an exponent that is a sum, you can use the property that says that x^(a+b) = x^a * x^b.
Q: how to find interval of convergence?
A: This can be found by finding the radius of convergence, which is the largest value of $r$ such that the series converges when $|x|<r$. To find $r$, one can use the ratio test.
Q: what is a recursive formula?
A: A recursive formula is a formula in which each term is defined in terms of the previous term(s).
Q: how to find the foci of a hyperbola?
A: The foci of a hyperbola are the points on the major axis at which the perpendicular bisectors of the lines joining the apex to the vertices of the hyperbola intersect the major axis.
Q: how to find p(a and b)?
A: p(a and b) = p(a) * p(b)
Q: what is e equal to?
A: e is approximately equal to 2.71828
Q: how to find the y intercept of an equation?
A: 8=2(y-4)
Q: how to multiply rational expressions?
A: The first step is to identify the LCM (least common multiple) of the denominators. Once you have the LCM, you can multiply each fraction by the LCM, which is called cross-multiplying.
Q: how to determine end behavior?
A: One way to determine the end behavior of a polynomial is to look at the leading term. The leading term is the term with the highest degree. The end behavior of the polynomial will be determined by whether the leading term has a positive or negative exponent. If the exponent is positive, the graph will approach infinity as x goes to positive infinity. If the exponent is negative, the graph will approach negative infinity as x goes positive infinity.
Q: how to find relative extrema?
A: There is no definitive answer to this question since it depends on the particular function under consideration. However, one approach to finding relative extrema is to take the first derivative of the function and set it equal to zero. This will give you the points where the function is locally maximized or minimized.
Q: how to simplify a log?
A: One way to simplify a log is to use the properties of logs to rewrite it in a simpler form. For example, if you have the log of a product (xy), you can rewrite it as the sum of the logs of x and y (log x + log y).
Q: how to find vertex of a parabola?
A: There are two ways to find the vertex of a parabola. The first way is to use the equation for a parabola, which is y = ax^2 + bx + c. The second way is to find the Vertex Form of a parabola, which is y = a(x-h)^2 + k.
Q: how to find the end behavior of a function?
A: One way to find the end behavior of a function is to graph the function and see what happens as x approaches positive and negative infinity.
Q: how to find a tangent line?
A: There is no one definitive answer to this question. There are multiple ways to find a tangent line, depending on the context and the information given.
Q: how to differentiate a function?
A: By taking its derivative.
Q: what is ln 1?
A: The natural logarithm of 1 is 0.
Q: what does the exclamation point mean in math?
A: The exclamation point means factorial in mathematics.
Q: what is equivalent equation?
A: A equivalent equation is a mathematical statement that two things are exactly the same.
Q: what is the quotient of?
A: the quotient of a number is the result you get when you divide that number by another number.
Q: what is rounding to the nearest hundredth?
A: Rounding to the nearest hundredth means finding the nearest number with two decimal places.
Q: what does it mean to rationalize a denominator?
A: Rationalizing a denominator is when you multiply the numerator and denominator of a fraction by the same number (not 0) so that the denominator becomes a rational number.
Q: how to find complex zeros?
A: There are a few ways to find complex zeros of a function. One way is to use the quadratic formula. Another way is to use the graphing calculator to find the points where the function’s value is zero.
Q: how to determine if a function is continuous?
A: The definition of continuity is that given any small enough ε, there exists a small δ such that whenever x is within δ units of a, f(x) is within ε units of f(a).
Q: how to put an equation in slope intercept form?
A: The easiest way to put an equation in slope-intercept form is to solve for y. This can be done by using algebraic methods to isolate the y term on one side of the equation.
Q: how to use elimination method?
A: In order to use the elimination method, you must have a set of linear equations with the same variables. You then choose one variable to eliminate, and use the equations to eliminate that variable.
Q: how to convert to standard form?
A: Standard form refers to the “normal” form of an equation. In other words, it is an equation that is solved using the standard algebraic operations of addition, subtraction, multiplication, and division.
Q: what is slope intercept equation?
A: Slope-intercept equation is a linear equation of the form y = mx + b where m is the slope and b is the y-intercept.
Q: what does reject mean?
A: to refuse to consider or approve (something)
Q: how to find real zeros?
A: There are various ways to find real zeros. One way is to use the quadratic equation. Another way is to use the fact that if y = 0 then x must be a zero of the function.
Q: how to write an explicit formula?
A: y=n^2+3
Q: how to find marginal distribution?
A: By finding the derivative of the joint distribution with respect to one of the variables, we can find the marginal distribution of the other variable.
Q: how to find the equilibrium price?
A: By using the supply and demand curve
Q: how to write a slope intercept equation?
A: y=mx+c
Q: what is the antiderivative of ln x?
A: The antiderivative of ln x is xln x.
Q: what is ln of 1?
A: 0
Q: what is a radical number?
A: A radical number is a number that is the square root of another number.
Q: what is the variance?
A: The variance is a measure of how spread out the data is.
Q: how to find a rational number?
A: You can find a rational number by expressing it as a fraction p/q where p and q are integers and q is not equal to zero.
Q: how to know how many solutions an equation has?
A: The number of solutions an equation has can be determined by solving the equation.
Q: how to find the length of a curve?
A: There are many ways to find the length of a curve, but one common method is to use calculus. To find the length of a curve using calculus, you need to find the arc length function. This can be done by finding the derivative of the position vector of the curve.
Q: how to divide long division?
A: To divide using long division, you will need to divide, multiply, subtract, bring down, and repeat.
Q: what is the prime factorization of 45?
A: The prime factorization of 45 is 3×15.
Q: how to find mixed numbers?
A: You can find mixed numbers by adding a whole number and a fraction together. For example, to find the mixed number for 3 1/2, you would add 3 (the whole number) and 1/2 (the fraction) together to get 3 1/2.
Q: how to write a logarithmic equation?
A: A logarithmic equation is written as ln(x)=b, where x is the number and b is the base.
Q: how to find exponential growth?
A: To find exponential growth, you need to find the growth rate first. The growth rate is the rate at which the function is growing. To find the growth rate, you need to take the derivative of the function.
Q: how to find the holes of a rational function?
A: The holes of a rational function can be found by finding the roots of the numerator.
Q: what is ln(e)?
A: ln(e) is equal to 1.
Q: what is a set of numbers?
A: In mathematics, a set is a collection of well-defined objects, called elements or members. Sets are usually denoted by capital letters.
Q: how to solve difference quotient?
A: There is no one-size-fits-all answer to this question, as the best way to solve the difference quotient will vary depending on the function and interval in question. However, in general, the difference quotient can be found by dividing the difference between the function’s values at two points within the interval by the difference between those two points’ independent variables.
Q: how many is a set?
A: A set is a collection of objects.
Q: how to combine logarithms?
A: Logarithms can be added when they have the same base. This is because the logarithm of a product is the sum of the logarithms of the factors. For example, log base 2 (8) = 3 because 2^3 = 8. Therefore, log base 2 (8) + log base 2 (1/8) = 3 + (-3) = 0.
Q: how to find the parent function?
A: You can find the parent function by tracing the code back to the point where the function is called.
Q: how to find the y intercept of a parabola?
A: The y intercept can be found by solving for y when x = 0 in the equation of the parabola.
Q: what does a small standard deviation mean?
A: A small standard deviation means that the data are clustered closely around the mean.
Q: what is the index of a radical?
A: the index of a radical is the number that is written above the radical symbol
Q: what is 8 divided by 12?
A: 8 divided by 12 equals to 0.666666666666667.
Q: what is an identity equation?
A: In mathematics, an identity equation is an equation that is always true for any value of the variable.
Q: what is a rational zero?
A: A rational zero is a real or complex number x such that x is a zero of a rational function, that is, a function that can be written as the ratio of two polynomials.
Q: what is equal to 1/2?
A: 0.5
Q: what is the least common multiple of 4 and 8?
A: The least common multiple of 4 and 8 is 8.
Q: what is a multiple of 9?
A: There are many numbers that are multiples of 9. Examples include 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90.
Q: what is a associative property?
A: An operation is associative if the order of the operands does not affect the result.
Q: how to find if a function is continuous?
A: There is not a definitive answer to this question since it depends on the function in question. However, some methods to determine if a function is continuous include using the definition of continuity, examining the graph of the function, or using limit theorems.
Q: how to find the unit price?
A: To find the unit price of a commodity, divide the total cost by the number of units.
Q: how to find linear approximation?
A: Linear approximation is a mathematical procedure for finding a straight line that comes close to fitting a set of data points.
Q: how to find the width?
A: The width is w = l — h + 1.
Q: y=mx+b what is x?
A: x=(y-b)/m
Q: what is the domain of a rational function?
A: The domain of a rational function is all real numbers except those for which the denominator is equal to zero.
Q: what are subsets of real numbers?
A: There are three types of subsets of real numbers: whole numbers, integers, and rational numbers.
Q: what does ordered pair mean?
A: An ordered pair is a couple (or pair) of objects where the order of the objects is significant.
Q: what does exponential growth mean?
A: Exponential growth is defined as a growth rate that is proportional to the current value of the function. In other words, it is a growth rate in which each increment is proportional to the size of the previous one.
Q: what’s associative property?
A: The associative property is a property of some binary operations that states that the order of operation does not change the result.
Q: what is x on a graph?
A: x is usually the independent variable, while y is the dependent variable.
Q: what is the inverse of a graph?
A: The inverse of a graph is a graph where the vertices and edges are reversed.
Q: what is a term in math example?
A: In mathematics, a term is usually a single numerical value or variable, and it can be separated from other terms by a sign such as “+” or “-”.
Q: how to find tangent line at a point?
A: There are many ways to find a tangent line, but one common method is to use calculus. First, find the derivative of the function at the point where you want to find the tangent line. Then, use the derivative to find the equation of the tangent line.
Q: how many 3 digit positive integers are odd and do not contain the digit 5?
A: 72
Q: how to rewrite log in exponential form?
A: log(x) = e^x
Q: how to rewrite in vertex form?
A: y = 2x — 1
Q: how to tell a function?
A: A function is a relations where each element in the domain is “paired” with a unique element in the codomain.
Q: how to find cubed?
A: To find a number cubed, you raise the number to the power of 3. So, 8 cubed would be 8 to the power of 3, or 8*8*8.
Q: how to find slope on a line graph?
A: There are a few different ways to find the slope of a line graph. One way is to use the equation y=mx+b, where m is the slope and b is the y-intercept. Another way is to use the rise over run formula, which is the change in y divided by the change in x.
Q: how do you get range?
A: You can get range by using the .range() method on a list.
Q: how to solve long division?
A: long division is solved by dividing the dividend into smaller numbers until the desired answer is reached.
Q: how to identify a polynomial?
A: A polynomial is an equation that contains one or more terms.
Q: how to write a complex number in polar form?
A: To write a complex number in polar form, the first step is to find the magnitude. The magnitude is the distance from the origin to the point on the complex plane. The angle is the angle between the positive x-axis and the line connecting the origin to the point on the complex plane.
Q: how to find a point of inflection?
A: To find a point of inflection, you need to take the second derivative of the function that defines the curve. The point of inflection is the point where the second derivative changes from positive to negative, or vice versa.
Q: what is e lnx?
A: it is the inverse of the natural logarithm function
Q: what is the value of 4!?
A: 4! = 4 * 3 * 2 * 1 = 24
Q: what are two consecutive integers?
A: two numbers that come one after the other in order
Q: what is a rectangular array?
A: A rectangular array is a two-dimensional array.
Q: what is the radius of convergence?
A: The radius of convergence is the maximum distance from the center of a series that the series will continue to converge.
Q: what is the intersection of a line and a plane?
A: The intersection of a line and a plane is a point.
Q: what is a linear polynomial?
A: A polynomial with degree one.
Q: whats a factorial?
A: it is a mathematical operation in which a number is multiplied by each of the numbers below it until 1
Q: what is the solution to the inequality ??
A: The inequality is only true when x is less than or equal to −2.
Q: what is a term in a polynomial?
A: The terms in a polynomial are the parts of the polynomial that are being added (or subtracted) together. Each term has a coefficient, which is the number in front of the variable, and an exponent, which is the number of times the variable is being multiplied by itself.
Q: what is the volume of a cylinder formula?
A: The volume of a cylinder is V = πr^2h
Q: what is general form in math?
A: There is no single “general form” in mathematics. Depending on the context, the term “general form” might refer to a particular type of mathematical expression (e.g. a polynomial), a particular way of representing a mathematical object (e.g. a matrix), or a general method for solving a class of problems (e.g. the method of induction).
Q: what’s a rational function?
A: A rational function is a function that can be written as a ratio of two polynomials.
Q: what is a goodness of fit test?
A: A goodness of fit test is a statistical test that is used to determine how well a model fits a dataset.
Q: how many subsets with an odd number of elements does a set with 10 elements have??
A: There are 511 subsets with an odd number of elements in a set with 10 elements.
Q: how to graph x=4?
A: x = 4
Q: how to find closed form of summation?
A: One approach to finding a closed form expression for a summation is to use induction.
Q: how to find local min and max?
A: There is no definitive answer to this question as it depends on the function and the data being used. A common approach is to find the first derivatives of the function and set them equal to zero. This will give the locations of the local minima and maxima.
Q: how to find the difference quotient of a function?
A: To find the difference quotient of a function, first choose two points on the graph of the function. Then, divide the difference of the function values at those points by the difference of the independent variables.
Q: how to find percent frequency?
A: To find the percent frequency, divide the absolute frequency by the total number of items and multiply by 100.
Q: how to prove a rectangle?
A: a rectangle is a four-sided figure with four right angles.
Q: how to find leading coefficient of polynomial?
A: We can use the leading coefficient test for polynomials to find the leading coefficient.
Q: how to find the basis of a column space?
A: A vector space has a basis if and only if it is finite dimensional. So, if the column space is finite dimensional, then it has a basis.
Q: how to do translations on a graph?
A: You can do translations on a graph by shifting the graph horizontally or vertically.
Q: how to find column space?
A: Let $A \in \mathbb{R}^{m \times n}$. The column space of $A$, denoted by $\mathrm{col}(A)$, is the subspace of $\mathbb{R}^m$ generated by the columns of $A$.
Q: how to find cartesian equation?
A: To find a cartesian equation, you need to know the coordinates of at least two points that lie on the line or curve that you want to describe. Once you have these coordinates, you can use the cartesian equation to calculate the coordinates of any other points on the line or curve.
Q: how to do set builder notation?
A: One way to do set-builder notation is to list the element(s) of interest, separated by commas, within braces {}. Another way is to list the property(s) that members of the set must have, within braces {}.
Q: how to find complex conjugate?
A: to find the complex conjugate of a complex number, take the conjugate of each term.
Q: how to find the equation of a function?
A: To find the equation of a function, one must first identify the variables in the function and then establish a relationship between them. This can be done by solving a system of equations or by using a graphing calculator.
Q: how do you find the point of intersection?
A: The point of intersection is the point at which two lines or curves cross each other.
Q: how to solve for x in a log equation?
A: To solve for x in a log equation, use the properties of logarithms to rewrite the equation in exponential form, and then solve for x using the exponentiation property.
Q: how can you quickly determine the number of roots a polynomial?
A: Use the root formula: for a quadratic equation, there are two roots; for a cubic equation, there are three roots; and so on.
Q: what is the value of log 625 5?
A: The value of log 625 5 is 4.
Q: what is x^3/2?
A: x to the 3rd power divided by 2
Q: what are roots on a graph?
A: x^3/2 is the square root of x cubed.
Q: what is 240 degrees in radians?
A: 240 degrees is equal to 4.189 radians.
Q: what does a positive residual mean?
A: A positive residual means that the predicted value is higher than the actual value.
Q: what are terms in a polynomial?
A: The terms in a polynomial are the coefficients of the individual terms.
Q: what do rational numbers look like?
A: Rational numbers are any numbers that can be expressed as a fraction, such as 1/2, 3/4, or 5/8.
Q: what is a common difference in math?
A: A common difference is the difference between successive terms in a sequence. For a function, the common difference may be thought of as the slope of the function.
Q: what is the absolute value of zero?
A: Zero has no absolute value because it is not positive or negative.
Q: what is quadrant 3?
A: Quadrant 3 is negative.
Q: what is a 91 grade?
A: A 91 grade is an A-.
Q: how to calculate ln?
A: To calculate ln, you can use a calculator or use the equation ln(x)=log10(x)/log10(e).
Q: how to determine a polynomial function?
A: There is no definitive answer to this question since it depends on the specific situation and data set you are working with. However, some methods that could be used to determine a polynomial function include looking at the data set itself and using a graphing calculator or computer software to generate a graph of the data. By inspecting the graph, you may be able to identify what type of polynomial function (if any) would best fit the data. Additionally, you could fit a variety of different polynomial functions to the data and compare the results to see which function provides the best fit.
Q: how to graph y 3×4?
A: You would graph this equation the same way you would any other equation, by finding the points of intersection and plotting them on a graph.
Q: how to solve equations with exponents?
A: One way to solve equations with exponents is to use the laws of exponents. For example, if you have an equation that says “x^2 = 4,” you can take the square root of both sides to solve for x.
Q: how to graph parent functions?
A: There is no set algorithm for graphing parent functions. However, common methods for graphing parent functions include using the function’s domain and range to identify the graph, using the function’s symmetry to identify the graph, using the function’s asymptotes to identify the graph, and using the function’s intercepts to identify the graph.
Q: how to do log equations?
A: To solve log equations, one must use logarithm laws to move everything except for the variable(s) of interest to one side. Then, the variable(s) can be isolated and solved for.
Q: how do you solve logarithmic equations?
A: To solve a logarithmic equation, you need to use the properties of logs to rewrite the equation in a form that can be solved.
Q: how to determine a function from a table of values?
A: from a table of values, you can determine a function by finding a pattern in the data. for example, if there is a linear pattern, you can determine a linear function.