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Assignment: Advanced Algebra Module Problem Set
1.) Given the following two points, write the equation of the line that goes through the two points. Show all your work.
(-3, 3) and (2, -7)
2.) Given the two systems of equations shown below, determine which system would be easiest solved using elimination and which using substitution.
Explain why.
System ASystem B
3x - 2y = 7 y = - 2/3 x + 8-4x - 6y = -5 2x - 3y = 12
3.) Solve the two systems of equations in #2. Show all your steps/work.
4.) Solve the following system of equations in 3 variables. Show all your steps/word.
x - 2y -z = 82x - 3y + z = 234x - 5y + 5z = 53
5.) Explain the three types of solutions of system of equations can have?
Find a nonzero matrix A in M2x2(R) satisfying v ?. Av = 0 for all v ∈ R2 - Show that α and β are projections satisfying ker(α) = ker(β) if and only if αβ = α and βα = β.
Explain what happens to the focusing distance y as the object moves far away from the lens. Explain what happens to the focusing distance y as the object moves closer and closer to the lens.
Let G = C* be the multiplicative group of nonzero complex numbers. Is the map f: G --> G a homomorphism, provided f is given by i) f(z) = iz, ii) f(z) = z^2, iii) f(z) = |z|, iv) f(z) = z-bar? Justify your answer.
Make the number in standard notation
Make a graph and find the intervals.
Solving logarithmic expression without calculator
The sum of two numbers is 72. One of the numbers is six more than twice the other. What are the two numbers?
Line passes through the point (5,1) and has a slope of 2 write an equation for this line. Find the equation for the line 1,-5 and -4,3
Compute an equation for the circle
Graph each of the equations on one rectangular coordinate system. (Hint: You must get y by itself before graphing.) Scale the graph accordingly; you will need your x-axis and y-axis to go to at least 100.
(If the expression is an exponential form, write it in radical form. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers)-m √(?2y?^5 )
Suppose that the monthly cost of a long-distance phone plan (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of 0.09
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