### Solving Systems of Equations with Three (3) Variables (Unknowns)

2x + y + 2z = 3 x + 6y + 3z = 4 3x - 2y + z = 0

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2x + y + 2z = 3 x + 6y + 3z = 4 3x - 2y + z = 0

Please see the attachment for the description of the problems.

1) Find the degree measure of the angel marked Z 2) High-Risk Funds Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she m

4. The St. Marks community bbq served 250 dinners. a child's plate cost 3.50 and an adult's plate cost 7.00. A total of 1347.50 was collected. how many of each type of plate was served? 8. Deep thought granola is 25% nuts and dried fruit. Oat dream granola is 10% nuts and dried fruit. How much of deep thought and how much of

Let T be a tree of order at least 4, and let e1, e2, e3 belong E(T^), T^ means Complement of T. Prove that T+e1 +e2+ e3 is planar. Please, draw the graph and explain it step by step.

Prove that if T Є L(V) is diagonalizable then V = im(T) + ker(T) (+ = direct sum) (Hint: Use a basis of eigenvectors. The eigenvectors of the eigenvalue zero are a basis for the null space, and the remaining eigenvectors are a basis for the image) See attached file for full problem description. keywords: matrix

(5) Let R be a ring with 1 and M a left R-module. If N is a submodule of M, the annihilator of N in R is defined to be: {r in R/rn=0 for all n in N} Prove that the annihilator of N in R is a two-sided ideal of R.

Solve the system of equations graphically. Then classify the system as consistent or inconsistent and the equation as dependent or independent. 6. 2y = 6 - x, 3x - 2y =6 14. y - x = 5, 2x - 2y = 10 16. y = 3 - x. 2x + 2y = 6

Please see the attached file for the fully formatted problems.

UNIT FIVE DB B: Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: ? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? ? Which one of the basic functions (linear,

Let K={k1,....km} be a conjugacy class in the finite group G. a) Prove that the element K=k1+k2+....km is the center of the group ring R[G] (check that g^-1Kg=K for all gin G) b) Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki. Prove that an el

1. An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% profit on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork. 2. A professor

Find a linear function f(x) = mx + b whose graph has the given slope and y-intercept. 6. Slope: 4/5 ; y-intercept: (0,28) Find an equation of the line having the given slope and containing the given point 14. m = 3, (-2, -2) Find an equation of the line containing the given pair of points. 28. (-4, -7) and (-2, -1

1. Find k if the following system of equations has a unique solution 2x + (k - 1)y = 6 3x + (2k + 1)y = 9 2. Find k if the following system of equations has infinite solutions kx + 3y = k - 3 12x + ky = k 3. Find k if the following system of equations has no solution 3x + 2y = 6 kx + (k - 1)y = 9

See attached file for full problem description. When converting from Fahrenheit degrees to Celsius degrees, a well known formula is used: C= 5(F - 32) / 9

See attached file for full problem description. 1. Find the slope of the line passing through the points (-8, -3) and (-2, 2). A) B) C) D) 2. Give the coordinates of the point graphed below. A) (4, 0) B) (-4, 0) C) (0, 4) D) (0, -4) 3. Find the slope of the graphed line.

Please see the attached file first. I did the proof, but it's weak, since I can't find a way to argue why every odd order subgroup has to be a subgroup of the cyclic odd order subgroup K of index 2, and by the divisibility argument it still could be a subgroup of G and not to be contained entirely in K.

Jill, Karen, and Betsy studied a total of 93 hours last week. Jill's and Karen's study time totaled only one-half as much as Betsy's. If Jill studied 3 hours more than Karen, then how many hours did each one of the girls spend studying?

3x/2 - 2y/3 = 10 1/8x + 1/4y=5

Determining the equation for a matrix and confirming the inverse, eigenvalues Details: I have think the answer to question (a) is theta^2 [(1-p)I + pJ]. But when I am multiplying the sigma and the sigma inverse I still have "stuff" at the tail end of the identity......being added. I know I should be left with the identity if t

Prove that every regular tournament is strong. Hints Here we need to first figure out something more about outdegrees and indegrees and orders of regular digraphs. Try to find a regular digraps with 3, 4, 5 ,6 vertices, and generalize. D is a regular tournament if there is k such that outdegree x = k and indegree x = n-k

Flying against the jetstream, a jet travels 1890km in 3 hours. Flying with the jetstream, the same jet travels 4650km in 5 hours. What is the speed of the jet in still air, and what is the speed of the jetstream?

Two rainstorms occurred in one week in a certain area. In the first rainstorm 35ml of rain fell per hour, and in the second rainstorm 20ml of rain fell per hour. Rain fell that week for a total of 45 hours for a total rainfall of 1200ml. How long was each of the two rainstorms?

Draw the line whose y-intercept is -7 and whose x-intercept is 4.

3.2 prove that a graph G is a forest if and only if every induced subgraph of G contains a vertex of degree at most 1. Please can you explain in here when the graph G is a forest and induced subgraph.

1. (Solve system by the substitution method. Determine whether the equations are independent, dependent or inconsistent.) 2x - y = 3 2y = 4x - 6 2. (Solve system by the substitution method. Determine whether the equations are independent, dependent or inconsistent.) y = 3(x - 4) 3x - y = 12 3. (Solve sy

Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent. 1. -3x + y = 3 2x - 3y = 5 2. x + 3(y - 1) = 11 2(x - y) + 8y = 28 3. 1/3x - 1/6y = 1/3 1/6x + 1/4y = 0

Flying against the jetstream, a jet travels 2600km in 4 hours. Flying with the jetstream, the same jet travels 6060km in 6 hours. What is the speed of the jet in still air, and what is the speed of the jetstream?

A motorboat travels 485KM in 5 hours going upstream and 714 km in 6 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

A child in an airport is able to cover 380 meters in 4 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover325 meters in 5 minutes. What is the child's running speed on a sti