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# Graphs and Functions

### Use the four color theorem

Use the four color theorem to prove that every outerplanar graph is 3-colorable.

### Graph

Graph each line and shade appropriate portion . for every case there constrains x â?¥ 0 and y â?¥ 0 . Find coordinates of all corner points: intersection between given lines and intersection between lines and x- or y-axis . x + y â?¤ 5 -x + y â?¤ 3

### Apply graphing technique to find solutions.

Use graphing technique to find solutions 1. 3x - 4y ≤ 12 2. 2x + y ≤ 4 3. 5x - 3y ≥ 15 4. x + y ≥ -2 x - 2y ≤ 4 5. x + y ≤ 4 0 ≤ x ≤ 2 y ≥ 0 6. 3x + 4y ≤ 12 x - y ≤ 4 x ≥ 0 Draw the line, use (0,0) test to find on what side of the line is the solution and shade

### Piece wise defined function

Not: this is a piece wise defined function x^(2) + 5, if x<b Let f(x) = d, if x=b x^(2) - 8x, if x>b a) Find b such that lim f(x) exists. x->b Note: Enter does not exist if no b exists which make the limit well defined. b=_________ b

### The slope of the secant line

Consider the function f(x)= sqrt(7x+6) We will take steps to find the tangent line to the graph of f at the general point (x,f(x)), and use it to find a tangent line with a specific property. (a) For any point (x,f(x)) on the graph of f, let (x+h,f(x+h)) be another point on the graph of f, where h [cannot]= 0 . The slope

### Solving, drawing the graph and explaining

4. Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion. Maximize 20x + 5y Subject to: 2x + y > 15 x + y < 5 y < 5 x, y > 0

### Point slope form for an equation

Use the point-slope form of the linear equation to find an equation of the line with the given slope and passing through the given point. Then write the equation in standard form. Slope -2/3; through (4,5)

### verbal description of the variation

The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the speed and inversely as the radius of the curve. it takes 3000 pounds of force to keep a 2000 pound car from skidding with radius 400 at 40mph. What force is needed to keep the same car from skidding when it tak

### Blocks of a given graph and expansion to a 4-critical graph

For n∈N, let G be the graph with vertex set {v_0,...,v_3n} defined by v_i↔v_j if and only if |i-j|≤2 and i+j is not divisible by 6. a) Determine the blocks of G. b) Prove that adding the edge v_0 v_3n to G creates a 4-critical graph.

### range of scores on the final exam

The professor counts his midterm as 2/3 of the grade and his final as 11/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put her average between 70 and 79 inclusive?

### Linear Equations and Slope

1. given the following equation, 5x - 3y = 15; solve for y. 2. Verify that the ordered pair (5, -2) is a solution to the equation 2x + 3y = 4 3. for the following equations: 5x - 2y = 14: find x if y = 4 find y if x = 2/5 4. find the slope and the y-intercept of the line represented by the equation: 2x + y =

### Assessing Slopes and Intercepts

3.1-72 Graph the line defined by the equation . Find the y values for the following values of x: When x = -7: -7 + 4y = 5 4y = 12 y = 3 When x = -3: -3 + 4y = 5 4y = 8 y = 2 When x = 1: 1 + 4y = 5 4y = 4 y = 1 When x = 5: 5 + 4y = 5 4y = 0 y = 0 When x = 9: 9 + 4y = 5 4y = -4 y = -1 x y -

### properties of the Stone-Weierstrass Theorem

Let be a compact interval and let A be a collection of continuous functions on which satisfy the properties of the Stone-Weierstrass Theorem [Stone-Weierstrass Theorem: Let K be a compact subset of and let A be a collection of continuous functions on K to R with the properties: a) The constant function belongs to A. b) I

### The slopes of a line

1)Find an equation of the line, say y=mx+b, which passes through the point (â?'7,â?'5) and is perpendicular to the line 4x+4y=â?'16 y=_________ 2) What is the shortest distance from the point (â?'7,â?'5) to the line 4x+4y=â?'16?

### reflection of the graph

Looking for step-by-step solutions on how to solve for the different algebra problems. Please show all work on a word document or excel sheet. 7. Which point on the graph makes this relation not a function? 8. Given find the value of 9. 10. Find the domain and range of the function.

### Prove that the delta(S) must contain an odd number of edges

Let G=(V,E) be a 3-regular graph (i.e. one in which all nodes have degree 3), and let S SUBSET V be any subset of the nodes such that |S| is odd. Prove that the cut delta(S) must contain an odd number of edges. Please refer to attachment for proper formatting.

### Use the intercepts to graph the equation.

Please help with these problems: Please show the steps. 1. Use the intercepts to graph the equation and also show graph x+5y=10 2. Graph the system of equalities and also show graph yâ?¥-4 xâ?¥6 3. Solve the system of equations. What is the solution? (type ordered pair) X + 3y=3 (1) X = 5 -3y (2) 4. Solve

### Slope of the Line: Equations

1. Find the slope of the line that passes through the given pair of points: a) (4,5) and (3,8) b) (2, 2) and (4, 4) 2. Find an equation of line that passes through the point (2, 4) and has slope m = 1. 3. Find an equation of line that passes through the two given points: (2, 1) and (3, 5). 4. Write the equation in s

### Intersecting and perpendicular lines

In your own words, explain the difference between intersecting and perpendicular lines. Can two lines exist that are not intersecting or parallel? Explain your answer. Next, I want you to find an example of intersecting, perpendicular, and parallel lines from the "real world". You will explain each of the three examples and

### Properties of Functions

Explanation is on file attatched. 1. A student was given the function f(x) = x2 and asked to write the result of translating this function 1 unit to the left. The student wrote the following: g(x) = (x+1)2. Is this statement correct? Explain 2. The length of time that it takes for a pendulum to make one complete swing de

### Graphing of functions: f(x) = |x|^x

Use Graphing Utilities to examine a function of x : f(x) = |x|^x Lots of analysis of grpah of f(x)=|x|^x so please inspect the attachment for full treatise

### Liner regression equation for OLLU

OLLU has the following data for the studentsâ?? enrollment from year 2005 to 2009. What is the estimated enrollment for 2010 by utilizing a liner regression equation? year actual enrollmemt 2005 2533 2006 2612 2007 2656 2008 2689 2009 2701

### Show that g1 and g2 are continuous.

If f: R^n --> R is continuous on R^n and alpha<beta, show that the set {x in R^n: alpha <= f(x) <= beta} is closed in R^n. Let f be continuous on R^2 to R^n. Define the function g1,g2 on R to R^n by g1(t)=f(t,0) and g2(t)=f(0,t). Show that g1 and g2 are continuous.

### Creating two dimensional graphs

Create a two dimensional graph using the following example: How much time you spend on the phone each day.

### Application problem with a linear function

Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 6.4. With 55 gallons of fuel in its tank, the airplane has a weight of 2252 pounds. What is the weight of the plane with 22 gallons of fuel in i

### Algebra

. Determine whether the system is consistent, inconsistent, or dependent. 3x + 2y = 15 6x + 4y = 30 (Points : 1) Consistent Dependent Inconsistent 7. Carla invested \$23,000, part at 16% and part at 15%. If the total interest at the end of the year is \$3,500, how much did she invest at 16%? (Poin

### Elementary Theorem in Graph Theory

Prove the following theorem: For any graph G, either G or its complement is connected.

### Quantitative Reasoning

1. Data-Information Relationship A. What is the difference between data and information? What is needed for business decision-making? Data, information or both? If you think data is different from information, which comes first? Data or information? B. Raw data is a list of words or numbers. The purpose of descriptive stat

### Trains A and B are traveling in the same direction on parallel tracks.

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and train B is traveling at 60 miles per hour. Train A passes a station at 10:10 A.M. If train B passes the same station at 10:25 A.M., at what time will train B catch up to train A?

### Conversion Problem

The height in feet of a particular theme park ride is modeled by the function h(t) = -16t2 + 70t + 90, where t is the time in seconds after the ride starts. When does the ride reach its maximum height? What is that maximum height?