Solve Equations with Fractions
7K views · Oct 4, 2022 analyzemath.com
This video first explains the steps to solve an equation with brackets. Then equations with fractions are solved following the steps: 1 - find the lowest common multiple of the denominators 2 - multiply all terms of the equations by the lowest common multiple of the denominators found in step 1. 3 - expand the brackets 4 - group like terms on each side of the equation 5 - isolate the terms with x on one side and the terms with number on the other side of the equation 6 - find the solution. More at https://www.analyzemath.com/middle_school_math/grade_9/grade-9-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Use the Rational Root Theorem to Find the Zeros, Factor and ...
34K views · Oct 3, 2022 analyzemath.com
The objectives covered in this video are: 1 - Use the rational root theorem to find the zeros of given polynomials 2 - Use division to factor the given polynomial 3 - Complete the factoring of the polynomial 4 - Find all zeros and their multiplicities. 4- Find the behavior when the variable x increases in absolute value and sketch the graphs of the polynomial. The polynomials studied are Example 1: P(x) = 2 x^3 + 7 x^2 + 4x + 4 Example 2: P(x) = - 3 x^5 - 14 x^4 -22 x^3 -12 x62 + 2 + 2 More math problems with solutions at https://www.analyzemath.com More at https://www.analyzemath.com/linear-algebra.html More at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html
Find the Equation of a Polynomial Given its Graph - Grade 12
1K views · Oct 3, 2022 analyzemath.com
The x-intercepts are obtained from the graph and used as zeros to write the polynomial in factored form. The multiplicity of the zeros is determined by the shape of the graph around the x-intercept, whether the graph cuts or touches the x-axis. The y-intercepts are used to find the leading coefficient of the polynomial. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Factor and Sketch the Polynomial - x^4 - 5x^3 - 3x^2 + ...
26K views · Oct 3, 2022 analyzemath.com
In this video, the rational root theorem is first used to find possible rational zeros. Then the synthetic division of the polynomial is used to completely factor the polynomial and hence its zeros and their multiplicities. The behavior of the polynomial, as the absolute value of x increases, is determined. All the above information is put together and the polynomial is sketched. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Find a Polynomial Given two Remainders and a Factor - Grade ...
29K views · Oct 3, 2022 analyzemath.com
Given two remainders and their corresponding divisors as well as a factor of a polynomial, the solution to find the polynomial is presented. The polynomial is first written as P(x) = x^3 + b x^2 + cx + d since it is a polynomial of degree 3 and its leading coefficient is equal to 1. The coefficients b, c, and d are found by writing 2 equations using the remainder theorem which states that the remainder of the division P(x) / (x - k) is equal to P(k). Also since (x - 1) is a factor, P(1) = 0. We, therefore, end up with a system of three linear equations in three variables b, c, and d which is solved, and hence the polynomial is completely determined once a, b and c are found. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html
Sketch the trigonometric function y = -0.5 sin(4(x+pi/3)) +...
11K views · Oct 3, 2022 analyzemath.com
A method based on substitution is used to find the 5 key points of the graph of the trigonometric function y = - 0.5 sin ( 4(x+pi/3) ) + 2.5 and sketch over two periods. The substitution PHI = 4 (x+pi/3) is made and the function is written as y = - 0.5 sin ( PHI ) + 2.5 PHI is a new variable and takes 5 values in the range [ 0 , 2 PI ]. A table of values is made including the values of y as a function of PHI. The last step is to calculate the x values using the values of PHI. From the substitution PHI = 4 (x+pi/3) , we can write x = PHI / 4 - pi/3 We, therefore, end with up with a table including the PHI values, the y values, and the x values but of course, the PHI values are not needed in the graph, they were used for calculation purposes. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html
Find the Equation of a Trigonometric Function Given Its Grap...
107K views · Oct 3, 2022 analyzemath.com
In this video, it is shown, through an example, how to find the equation of a trigonometric function, given by its graph. The function suggested is of the form: V(t) = A cos (Bt + C) + D where t is the variable. Formulas to find the parameters A (chosen to be positive) and D describing the amplitude and vertical shift of the trigonometric function are deduced: A = (Vmax - Vmin) / 2 , gives A greater than zero. D = A = (Vmax +Vmin) / 2 The period of the function is determined from its graph and the formula: Period = 2 pi / B , B greater than zero. is used to find B. The parameter C is related to the phase shift and is determined by locating a maximum (or a minimum) of the function using the graph. Assume the maximum is at t = T, and write the equation V(T) = A cos (B T + C) + D = A + D and knowing A, B, D, and T, solve a trigonometric equation for C which gives an infinite number of solutions. More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html
Sketch the graph of the rational function y = (2x - 4)/(x + ...
14K views · Oct 3, 2022 analyzemath.com
The domain, vertical and horizontal asymptotes, x and y intercepts as well as the table of signs of the function y = (2x - 4)/(x + 2) are first discussed, then they are used to sketch its graph. More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve Rational Inequalities (x+1)/(x+2) - 1 ≥ 1/...
4K views · Oct 3, 2022 analyzemath.com
In this video, the rational inequality : (x+1)/(x+2) - 1 ≥ 1/(x-1) is solved including detailed steps using the table of signs. The main objectives of the video are 1 - Group all terms and write the inequality in standard form with one side equal to zero. 2 - Factor both numerator and denominator of the rational expression 3 - Create a table of signs 4 - Read the solution set of the inequality. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve Trigonometric Equation cos(2x) - 2/sec (x) = 2 - ...
14K views · Oct 3, 2022 analyzemath.com
A trigonometric equation involving multiple angles and a reciprocal trigonometric function is solved showing all steps with details. Trigonometric identities are used to rewrite cos(2x) = 2 cos^2(x) - 1 and 2/sec (x) = 2 cos (x) . The substitution u = cos(x) is made which helps in writing the given equation as a quadratic equation which is solved for u and then u is solved for x. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve the Logarithmic Equations : ln(x^2+-2) - ln(x-1) = 2 ...
19K views · Oct 3, 2022 analyzemath.com
In this video, the equation (ln(x^2+-2) - ln(x-1) = 2) including logarithmic functions is solved including all detailed steps and the logarithmic rules used to transform the equation. First, the two logarithms on the left side are grouped using the formula: ln (A) - ln(B) = ln (A/B), and 2 on the right side is written as ln(e^2). With these, we have the form ln(W) = ln(V) hence W = V which is an algebraic equation. When the algebraic equation is solved, the solutions are checked because the domain of the function ln(x) requires that x must be positive. More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve the Exponential Equation 3 * 4^x + 2^x = 30 - Grade ...
131K views · Oct 3, 2022 analyzemath.com
In this video, an equation with exponential functions of different bases is solved with all detailed steps and rules of exponents used to transform the equation. The expression 4^x is first transformed as (2^2)^x = 2^(2x) = (2^x)^2, hence the exponents are written with the same base. Then the substitution u = 2^x is made and the equation is written as a quadratic equation then solved for u then u solved for x. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Verify Trigonometric Identities - Grade 12
63K views · Oct 3, 2022 analyzemath.com
A trigonometric identity with single and multiple angles is transformed and verified using other basic trigonometric identities. Using basic identities, the left side of the identity is rewritten so that it is exactly written in the same form as the right side. tan(2x) is written as : tan(2x) = sin(2x) / cos(2x), then sin(2x) is written as : sin(2x) = 2 sin(x) cos(x) and cos(2x) = cos^2x - sin^2x, then simplifications follow. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Find the Exact Value of a Trigonometric Function - Grade 12
4K views · Oct 3, 2022 analyzemath.com
Find the exact value of tan(13 pi / 12) by first expressing the angle in terms of special angles and then using trigonometric formulas. 13 pi / 12 is expressed as 13 pi / 12 = pi + pi/12 and therefore tan(13 pi / 12 ) = tan( pi / 12) pi/12 = pi/3 - pi/4 then the formula of the tangent of difference: tan(pi/3 - pi/4) is used More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
System of a 2 by 2 Linear Equations with Parameter - Grade 1...
27K views · Oct 3, 2022 analyzemath.com
Discuss the solutions of a system of 2 by 2 linear equations 2 x + 6 y = -2 -3 x + a y = 4 including parameter "a" in the second equation. The question is to find the values of parameter "a" for which the system has no solution. Three ways to answer the question, including a graphical method, are presented. More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
long division of polynomials
211K views · Oct 3, 2022 analyzemath.com
The algorithm for the division of polynomials is presented along with the relationship between the dividend D, the divisor d, the quotient Q, and the remainder R. The result of the division is written as D/d = Q + R/d or D = Q d + R The result of the division is checked by expanding D = Q d + R. More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve Polynomial Inequalities Using Table of Signs
7K views · Oct 3, 2022 analyzemath.com
Several examples of polynomial inequalities are solved and the solution set is written using inequality symbols, intervals, and graphically on the number line. The inequality is written in standard form with the right side equal to zero and the polynomial on the left side is factored, Then a table of signs is produced from which the sign and hence the solution of the polynomial is deduced. More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve Rational Inequalities Using Table of Signs
6K views · Oct 3, 2022 analyzemath.com
Several examples of inequalities with rational expressions are solved and the solution set is written using inequality symbols, intervals, and graphically on the number line. The inequality is written in standard form with the right side equal to zero and the polynomials in the numerator and denominator of the rational expression on the left are factored. A table of signs is then produced and the sign and hence solution set of the rational expression is deduced. More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html
Quadratic functions at http://www.analyzemath.com
5K views · Feb 20, 2022 analyzemath.com
A video-applet that explains the effects of the parameters a, b and c on the graph of a quadratic function of the form f(x) = ax^2 + bx + c. More applets at http://www.analyzemath.com
Rational Functions from www.analyzemath.com
5K views · Feb 20, 2022 analyzemath.com
A video-applet to investigate the properties of rational functions. More applets may be found at http://www.analyzemath.com
Maximum Area of Rectangle form www.analyzemath.com
5K views · Feb 20, 2022 analyzemath.com
A video-applet that uses dynamic pictures to explain the problem of maximizing the area of a rectangle given that the perimeter in constant. More applets may be found at http://www.analyzemath.com
Find the Inverse of a Function - Part I
5K views · Feb 20, 2022 analyzemath.com
A tutorial on to find the inverse of a function given by a formula. From www.analyzemath.com see also http://www.analyzemath.com/stepbystep_mathworksheets/functions/inverse_square_root.html http://analyzemath.com/stepbystep_mathworksheets/functions/inverse_linear.html http://analyzemath.com/stepbystep_mathworksheets/functions/inverse_cubic.html
Graphical interpretation of First Derivative
958 views · Feb 20, 2022 analyzemath.com
Graphical interpretation of the first derivative using local tangent http://www.analyzemath.com
interactive unit circle with sin(x), cos(x) and tan(x)
2K views · Feb 20, 2022 analyzemath.com
Online Interactive unit circle to show the relationship between sin(x), cos(x) and tan(x) on the unit circle and rectangular system of axes at http://www.analyzemath.com/unitcircle/unit_circle_applet.html
Smallest distance from point to a circle
27K views · Feb 20, 2022 analyzemath.com
Calculate the smallest distance from a point to a circle. More math exploration, tutorials and problems at www.analyzemath.com
Find Compositions of functions
6K views · Feb 20, 2022 analyzemath.com
Find the composition of two functions with full explanations. More on composition of functions at : www.analyzemath.com/CompositionFunction/CompositionTutorials.html
Absolute Value in Mathematics
32K views · Oct 25, 2022 analyzemath.com
This video discusses the definition of absolute value in mathematics with examples on how to simplify and write expressions including absolute expressions without absolute value. The relationship between the square root and the absolute value is also discussed. More on the absolute value at https://www.analyzemath.com/Absolute_Value_Function/simplify-absolute-value-expressions.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Slope Intercept Form of a Line
7K views · Oct 27, 2022 analyzemath.com
The slope-intercept form of a line in the first example is determined from the graph of a line and in the second example from the general form of a line. More on the intercept form of a line at https://www.analyzemath.com/Slope_Intercept_Line/Slope_Intercept_Line.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve Absolute Value Equation with Unknown on Both Sides
9K views · Oct 27, 2022 analyzemath.com
This video discusses the ideas and steps behind solving equations with absolute value and the unknown on both sides of the equation. More on equations with absolute value at https://www.analyzemath.com/Equations/solve-equations-with-absolute-value.html More advanced examples on equations with absolute value at https://www.analyzemath.com/absolute-value-equations-inequalities/absolute-value-equations-inequalities.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve Simple Absolute Value Equations
6K views · Oct 27, 2022 analyzemath.com
This video discusses the ideas and the steps behind solving equations with absolute value on one side and a real number on the other side. Three examples are solved including an example with no solutions. More on equations with absolute value at https://www.analyzemath.com/Equations/solve-equations-with-absolute-value.html More advanced examples on equations with absolute value at https://www.analyzemath.com/absolute-value-equations-inequalities/absolute-value-equations-inequalities.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve Right Triangle
13K views · Oct 27, 2022 analyzemath.com
This video shows how to use trigonometric ratios and the Pythagorean theorem to solve three right triangle problems. In the first example, the hypotenuse and one angle are given. In the second example, the two sides that make the right angle are given and in the third example only the hypotenuse is given but the right triangle is an isosceles triangle. More advanced examples on right triangle problems at https://www.analyzemath.com/Trigonometry_problems/solve-right-triangle-problems.html More right triangles questions at https://www.analyzemath.com/trigonometry_questions/right_triangle.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Factor a Polynomial with two Variables
5K views · Dec 27, 2022 analyzemath.com
Factor the polynomial 2 x^2 - 4 x + 3 x y - 6 y by first grouping and then use the commo factor.
Find the Inverse of a Square Root Function
12K views · Dec 29, 2022 analyzemath.com
Find the inverse of a square root function showing all the steps.
Find the Inverse of a Rational Function
1K views · Dec 29, 2022 analyzemath.com
The video explains the step needed to find the inverse of a rational function.
Find the Inverse of a Quadratic Function with Limited Domain
2K views · Dec 29, 2022 analyzemath.com
The video explains the steps to find the inverse of a quadratic function with limited domain given explicitly.
Find Points of Intersection of a Parabola and a Line
21K views · Dec 27, 2022 analyzemath.com
This problem is about finding the points on intersection of a parabola and a line given by their equations.
Review the Graphs, Domains and Ranges of some of the Basic F...
9K views · Dec 29, 2022 analyzemath.com
This video is about the graphs, domains and ranges of some of the most basic functions, namely: y = x, y =absolute(x), y = x^2, y = square-root (x), y = 1/x and y = x^3.
Find the Equation of a Quadratic Function Given its Graph
11K views · Dec 29, 2022 analyzemath.com
In this video the steps to find the equation of quadratic function given its graph are explained in details.
Calculate the Determinant of a 3 by 3 Matrix
8K views · Dec 30, 2022 analyzemath.com
This video presents the steps needed to find the determinant of a 3 by 3 matrix using determinants of 2 by 2 matrices.
Calculate Integral of Polynomials
7K views · Dec 30, 2022 analyzemath.com
This videos gives detailed steps on how to calculate the integral of a polynomial.
Find the Point of Intersection of a Circle with a Line
10K views · Jan 1, 2023 analyzemath.com
This vides shows all the steps needed to find the point of intersection of a circle with a line.
Find the Equation of a Line Through two Points in 3D
10K views · Jan 2, 2023 analyzemath.com
Find the parametric and symmetric equations of the line through the two points P(1 , 2 , 3) and Q(0 , - 2 , 1).
Find Point of Intersection of Two Lines in 3 D
5K views · Jan 1, 2023 analyzemath.com
This video explains the steps to find the point of intersection of two 3D lines with one given in parametric form and the second given in symmetric form.
Calculate the Derivative of f(x) = sin (2x^2 + x - 2) Using ...
10K views · Dec 31, 2022 analyzemath.com
This video explains how to use the chain rule of differentiation to calculate the derivative of a composite function of the form sin(u) where u is a function of x.