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Brenda's age is 3 times Layton's age. In 4 years, she will be twice as old as Layton by then. What are their present ages?
Find an equation of the line passing through the pair of points. Write the equation in slope intercept form.
The X variable is the number of errors on a math test, and the Y variable is the person's level of satisfaction with his/her performance.
Which of the following sets of polynomials n K[x], K commutative are K-modules:(a) all polynomials of degree exactly.
Find both the minimum and maximum values of U=6x1+10x2+7 (graphically) subject to the constrains 2x1+5x2=0, and x2>=0
Find the point of equilibrium for a system that has a demand equation of p=49-0.0003X and a supply equation of p=33+0.00002X
You want to make a statement about the variability in the costs of personnel shelters. After collecting sample data (cost in $K).
What effect would this have on the economy? If you decide not to eliminate pennies what can you do to keep minting costs lower?
For each intercept, show your algebra, then state the intercept using correct function notation and as an ordered pair.
Find an equation of the exponential function y=g(x) , whose graph passes through the 2 given points.
Determine whether the given function is linear or nonlinear? If the function is linear, determine the slope.
One parking garage offers unlimited parking at a flat rate per month. Another garage offers an hourly rate for parking.
To Emile, because he likes math problems, I leave a choice. He can have one of two inheritances. He must make his choice before leaving the office today.
Let phi be a homomorphism of a ring R with unity onto a nonzero ring R'. Let u be a unit in R. Show that phi (u) is a unit in R'.
Show that every maximal ideal of R is prime and if R is finite, show that every prime ideal is maximal.
If A is an ideal of R and S is a subring of R, then S+A is a subring, A, and (S intersecting A) are ideals of S+A and S.
Show that if U is the collection of all units in a ring with unity, then is a group. A reminder was given to make sure to show that U is closed
Let p be a prime. Show that in the ring Z-p (set of integers modulo p) we have (a+b)^p = a^p+b^p for all a, b in Z-p.
If phi: R1 -> R2 is a ring isomorphism, show that phi extends to an isomorphism phi hat : F1 -> F2.
Find [ 2Z : 12Z ], where 2Z is the ring of even integers. If R is assumed to have a unity, what can you say about [ R : I ] ?
Prove that a module over a polynomial ring C[t] is a finite dimensional vector space with a linear operator that plays the role of multiplication by t.
Now let I be the set of all functions f(x) an element of R such that f(1)=0. Show that I is a maximal ideal of R.
Given two elements a,b in the Euclidean ring R their least common multiple c ? R is an element in R such that a | b and b | c.
Prove that the units in a commutative ring with a unit element form an abelian group.
Prove that a necessary and sufficient condition that the element 'a' in the Euclidean ring is a unit is that d(a) = d(1).