How to sketch graph of
9,907 results, page 78

Physics Help
A graph of wavelength vs. 1/frequency should be a straight line. What are it's slope and yintercept? I'm not given any graphs or numbers, just this question. And I know that Velocity = frequency x wavelength And that slope is found by rise/run and m= y2y1/x2x1 obviously. So... 
Trigonometry
Solve 2cos^2θ/2 = cos2θ for 0º≤θ≤360º. (Hint: Graph each side of the equation and find the points of intersection.) A) ≈73.8º; 260.4º B) ≈141.3º; 218.7º C) ≈225.7º; 315.8º D) ≈51.7º; 138.2º 
Algebra: Steve
I already asked this question,I just wanted to clarify the answer. Problem: The polynomial f(x) has degree 3. If f(1)=15, f(0)=0, f(1)=5, f(2)=12, then what are the xintercepts of the graph of f? Steve: clearly, f(0) = 0 so, f(x) = ax^3+bx^2+cx = x(ax^2+bx+c) 1(ab+c) = 15... 
Physics
a BALL IS THROWN UPWARD WITH AN INITIAL VELOCITY OF 9.8 M/S FROM THE TOP OF A BUILDING. FILL A TABLE BELOW SHOWING THE BALLS POSITION,VELOCITY, and ACCELERATION AT THE END OF EACH OF THE 1ST 4SEC OF MOTION TIME(s) POSITION(M) VELOCITY(M/S) 1 2 3 4 Acceleration (M?S^2) Fill in ... 
Is this correct? Algebra
9. Joe wants to fence a rectangular pen for his goats. the length of the pen should be at least 60 ft, and the distance around should be no more than 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen? I want to know if I am correct... ... 
mathematics
using a graph plot the following points: point 1 (1,0), point 2 (1,1), point 3( 1,2), point 4(2,2)draw lines to connect from point 1 to point 3 to point 4, the lines you have just drawn most resemble which of the following letters of the alphabet? x, o, n, or l. 
Math please help
Carol has a collection of 100 stamps the graph below shows the percentage of stamps she has from each country how many more of Carols stamps are from France than from Norway? France: 24%, England:22%, Norway:29%, Italy:25%. a.) 5 stamps* b.) 24 stamps c.) 29 stamps d.) 53 stamps 
graphs2
x + 2y = 4 How do I graph this?can you please help? I answered this below. If you are having trouble you must tell us exactly what the problem is. What don't you understand about taking the next step? that is the problem.I got the other one but how do i do this if the y is 2y... 
Physics
The brakes on your automobile are capable of slowing down your car at a rate of 4.2 m/s^2. a) If you are going 145 km/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 90 km/h speed limit? b) Graph x vs. t and v vs. t for such... 
mathalgebra
Find three different ordered pairs that are solutions of the question x=2 and you have to use 1,0,1 for thje subsitut of y or x i don't know.im so confused please help i don't know the ansrer math is hard I can see why you are confused so am I. If x = 2, that is just a ... 
Chemistry
A sample of O2 gas is placed in a sealed 1.00 L flask and pressure is measured as temperature is changed. The data are plotted and the slope of the resulting line is equal to 0.00400 atm/K. The line passes through the origin of the graph. There are (blank) g of O2 gas in the ... 
Economics
Graph A New Equilibrium: Y axis represents Quantity (hours per semester) 0, 25, 50, 75, 100, 125, 150 X axis represents Price of Tutoring (per hour) 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, $50 Question: Determine the approximately size of market surplus or shortage that would ... 
Science
10. A single weed in plot 6 has a genetic mutation that allows its cells to transport herbicide out through the cell membrane before the weed is harmed. Suppose a student allows weeds to grow in plot 6 and then periodically treats them with herbicide. Represent this ... 
Calculus 1A
I am so confused! The problem is: Verify the given linear approximation at a=0. Then determine the values of x for which the linear approximation in accurate to within 0.1. LN(1+x) ≈ x I found f(0) = 0 and f'(0) = 1 I have an equation: LN (1+x) (.1) < x < LN(1+x... 
Physics spring constant
Astronauts are in space so there is no gravity, but they wish to weight themselves. The spring constant is 265 N/m. The question shows a graph; the y is the position in meters while the x is the seconds. I do not wish for an answer, but the way in which i'm supposed to tackle ... 
Math
which statement are always true about a scatter plot with a positive trend? Choose two The point will form a straight line•• As the x value increases the y value increases The point will show a general upward trend left to right on the graph•• There will not be any ... 
Math PLZZZ HELP!!!
always true about a scatter plot with a positive trend? Choose two The point will form a straight line•• As the x value increases the y value increases The point will show a general upward trend left to right on the graph•• There will not be any outliers Correct me 
PreCalc
Does y=1/x have an inverse? It is a onetoone function, so it should be the inverse equation is the same??? yes, the inverse is the same. Check it with G(f(x)) So, when drawing the inverse, it is just the same graph? 
Math
geometry On the coordinate plane, draw a rectangle ABCD with vertices at A (1,4), B(5,4), C(5,1) and D (1,1). Then graph and describe the new rectangle formed when you subtact 3 from each coordinate of the vertices in rectangle ABCD. 
Calculus
Given the graph of f'(x) with f(x) continuous on all reals, find the intervals f(x) is concave up and down and find the X values of the points of inflection. I did points 2 concave down to 2 then concave up 4. 
MathGeometry
B is in the interior of angle AOC. C is in the interior of angle BOD. D is in the interior of angle COE. The measure of angle AOE is 162 degrees, COE is 68 degrees, and the measures of angles AOB, COD, and DOE are all equal. The question is to find the measure of angle DOA. (... 
Calculus Need of Urgent help
find the indicated limits, if they exist. 1. lim (3x^3+x^2+1)/(x^3+1) x> infinity 2. find the slope of the tangent line to the graph of the given function at any point: f(x) = 2x +7 Could anyone please, please, please explain to me how to do these problems? It seems like ... 
Calculus
Hi it's me again I need help with this too and I promise to never use this site again! I feel so ashamed for asking :( Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.The answer has to have the antiderivative too. ... 
Math
1. Does the graph represent linear relationship? Why or why not? 2. Are the slopes of the lines the same or different? How can you tell? 3. Is the statement true: Line P has a greater slope than line Q true false 4. How many solutions does this system have? one solution ... 
Calculus
"The line x+y = 0 is tangent to the graph of y = F(x). Find F(x) if F'(x) = x". I know how to find the antiderivative of F'(x), but I don't know how to use the tangent line to find my constant. 
Math
How can I graph this equation: (xsquared + ysquared  1)cubed = xsquared times ycubed ? Is there a polar form of the equation? 
trig
I need to state the period and 2 consecutive asymptotes on the graph for the following questions. 1: y = 3 tan pi*x period: pi (?) asymptotes: ? 2: y = 2 sec 4x period: ? asymptotes: ? 3: y = csc (x/3) period: ? asymptotes: ? 4: y = 3 cot (pi*x/2) period: ? asymptotes: ? If ... 
math
graph the line with slope 1/2 passing through the point(5,2) find the slope of the line 5x+5y=3 write answer in simplest from consider the line 2x4y=4 what is the slope of a line perpendicular to this line. what jis the slope of a line parallel to this line 
math
The following graph shows the growth of the median home value in a particular region of the United States starting in 1996. The graphs starts in 1996 and shows the trend through the year 2000; therefore x = 0 represents the year 1996 and x = 4 is 2000. 
PHYSICS
Given: The initial position of the block is the origin; i.e., x = 0 at t = 0 . Consider down the track to be the positive xdirection. A block with an initial velocity v0 slides up and back down a frictionless incline. Which graph best represents a description of the velocity ... 
Maths
A mathematics class has 200 members. If there is 12% absentee rate per class meeting, find: a) mean, variance and standard deviation number of students who will be absent from each class. b) Draw the probability table and distribution graph of the number of the students absent. 
Statistics
A mathematics class has 200 members. If there is 12% absentee rate per class meeting, find: a) mean, variance and standard deviation number of students who will be absent from each class. b) Draw the probability table and distribution graph of the number of the students absent. 
TRIG
I need to state the period and 2 consecutive asymptotes on the graph for the following questions. 1: y = 3 tan pi*x period: pi (?) asymptotes: ? 2: y = 2 sec 4x period: ? asymptotes: ? 3: y = csc (x/3) period: ? asymptotes: ? 4: y = 3 cot (pi*x/2) period: ? asymptotes: ? 
Calculus
the area of the first quadrant region bounded by the yaxis, the line y=4x and the graph of y=xcosx is approximately: a) 4.50 square units, b) 4.54 square units, c) 4.56 square units, d) 4.58 square units, e) 5.00 square units 
math
Book 1 255 book 2 235 book 3 178 book 4 299 book 5 150 book 6 67 book 7 82 book 8 267 book 9 188 book 10 142 book 11 281 book 12 138 book 13 326 book 14 264 book 15 103 ^ number of pages What would be the best graph or display to represent your Home Library Statistics data? Why? 
Chemistry
Hey; I'm currently in a kinetics class and I am trying to do a prelab for a lab that we haven't learned the material for yet and I'm really stuck, and we unfortunately don't have a textbook for the class so I was hoping someone could help. We have the compound mxylene and it ... 
micro
which of the following statements is true of the oligopoly that can cover its varible costs and si in equilibrium? a:p=mc=atc b:p>mc c:p>mr and p=mc d:p<mc and mr=MC and WHy What is "si"? Graph an oligopolist, facing a downward sloping demand curve. Draw in your ... 
math
9x+5greater than or equal to 40 or 7x+3greater than or equal to 11 solve and graph I got the answer of x greater than or equal 5 or x is greater than or equal to 2 as the solution to this equations, but how do i put this into a soltuion set the way that they want it set up... 
Chemistry
1. As the intermolecular forces between molecules increase in magnitude, do you expect each of the following to increase, decrease or remain the same? My answers: Viscosity: increase Boiling point: increase Vapor pressure: decrease Surface tension: increase Heat of ... 
Chemistry
1. As the intermolecular forces between molecules increase in magnitude, do you expect each of the following to increase, decrease or remain the same? My answers: Viscosity: increase Boiling point: increase Vapor pressure: decrease Surface tension: increase Heat of ... 
math
The graph of a function is horizontally compressed by a factor of 5 and vertically compressed by a factor of 2 Find an equation for this compressed function in terms of the function f(x) 
Math
My values are: 0.075 0.025 0.1 0.075 0.1 0.125 0.05 0.125 0.025 0.15 0.125 0.025 What would be an appropriate scale to go by on a bar graph. 
Calculus: drwls, please
First, I appreciate your help, and this is very kind of all of you to help us. Now, this problem we are both sick of: we are to use transformations of f(x)= 1/x or f(x)=1/x^2 to graph the rational function: f(x)= 1/x 4. I tried using the information you gave me, but my graphs... 
Statistics
USA snapshot presented a bar graph depicting business travelers’ impression of wait times in airport security lines over the past 12 months. Statistics were derived from Travel Industry Association of American Business Traveler Survey of 2034 respondents. Is this a ... 
Math
Which of the following types of information is suited for display on a doubleline graph? A. annual changes in Melody’s height and weight from 5 to 10 years old B. number of Democrats and Republicans in the Senate during the past decade C. monthly sales of two different ... 
physic
Crall and Whipple attached a fan to a cart placed on a level track and then released the cart. They made a positionversustime graph (see figure below) and fit a curve to these data such that x = 0.036 m + (0.0080 m/s)t + (0.10 m/s2)t2. (a) Find the velocity as a function of ... 
calculus
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x=9y^2 y=1 x=0 about the yaxis. I am able to find the volume of other questions, but this one got me stumped. I tried drawing out the graph, but I can't really ... 
calculus
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x=9y^2 y=1 x=0 about the yaxis. I am able to find the volume of other questions, but this one got me stumped. I tried drawing out the graph, but I can't really ... 
11th grade Algebra II
if the roots of ax^2+bx+c=0 are real, rational, and equal, what is true about the graph of y= ax^2+bx+c? 1.) it intersects the xaxis at two distinct points. 2.) it lies entirely below the xaxis 3.) it lies entirely above the xaxis 4.) it is tangent to the xaxis i think the... 
US History
'Take a poll of your classmates to find out what they trust about the federal government and what they mistrust about it. Compile the answers into a list. Then use the list to make a bar graph of the top five answers.' Since I don't have classmates (.) I figured I'd ask you ... 
math
Tamar is crating a veritcal bar graph to show how far each of her friends loves from school the data are in the table shown. Friend 1 2 3 4 5 6 7 8 9 10 Distance 7 8 9 9.5 6.5 16 7 7.5 8 10 from school (miles) What numbers are appropriate for Tamar to use to label the vertical... 
MATH
Tamar is crating a veritcal bar graph to show how far each of her friends loves from school the data are in the table shown. Friend 1 2 3 4 5 6 7 8 9 10 Distance 7 8 9 9.5 6.5 16 7 7.5 8 10 from school (miles) What numbers are appropriate for Tamar to use to label the vertical... 
math
Tamar is crating a veritcal bar graph to show how far each of her friends loves from school the data are in the table shown. Friend 1 2 3 4 5 6 7 8 9 10 Distance 7 8 9 9.5 6.5 16 7 7.5 8 10 from school (miles) What numbers are appropriate for Tamar to use to label the vertical... 
Algebra
Jan is a photographer. She earns $42.50 for each picture she sells. It costs Jan $850.00 per month to maintain her photography lab. Write an equation that represents the relationship between Jan's monthly profit (P) and the number of pictures (x) she sells. What does the x... 
Math
Which of the following options best describes the function graphed below? A graph shows a slanting straight line that starts at the origin and goes up. Nonlinear increasing Nonlinear decreasing Linear increasing Linear decreasing I believe the answer is C. but I also think its... 
Math
Sara was mixing punch for a party from a recipe that calls for 3 parts ginger ale mixed with 2 parts pineapple juice. She graphed the people served compared to the total mixture. Use the point shown on her graph to compute the ginger ale need to serve 20 people. 
math
a paintball is hot at a wheel that has a radius of 40 cm. it hits the very bottom of the wheel next to the road while the car is stopped at the red light. as the light turns green, the wheel rolls, and so does the paint. if it takes 3 seconds for the wheel to make one full ... 
math
a paintball is hot at a wheel that has a radius of 40 cm. it hits the very bottom of the wheel next to the road while the car is stopped at the red light. as the light turns green, the wheel rolls, and so does the paint. if it takes 3 seconds for the wheel to make one full ... 
Math
which of the following types of information is not suited for display on a double line graph A: the change in rainfall based on the change in temperature B: the number of and different colors of car in parking lot C: the increase in value of jewelry for each year owned D: the ... 
math,correction
can someone please correct this for me. i have to graph: y = 3/4x + 2 so the points i got for plotting is: (4,1),(0,2),(4,5) then i just connect the points to get the line. If they plot on a line the answer is correct. y= 3/4 x + 2 is a line, and all solutions have to be on ... 
MATH plz helo check my answer
3 ≤ 2x  5 < 13 i thing the answer is 1 < x < 9 and how would you graph this on a number line so MY NUMBER LINE IS 1 TO 9, SO AT 1 i have a closed circle and at 9 i have a open circle and its shaded in is it right 
Math 1
AT&T:$0.08 per minute,$5 monthly fee VOIP:(cable phone):free calls,$35 monthly fee Cell:$40 for first 400 minutes,$0.25 per minute after 400 equation for each? how to graph? 
algebra 1
The graph shows the relationship between the total amount of money that Carly will have left, y, if she buys x packs of baseball cards. How much money will she have if she doesn't buy any packs of baseball cards? 
Science
The two variables of interest in this lab are: "percent change in mass" of bag and "sucrose molarity" in the bag solution. On a graph of these two variables, which would be the independent variable, and which would be the dependent variable? 
algebra
Help would be greatly appreciated!!! This gets really confusing for me. Write an inverse variation equation. If y varies inversely with x and y=2 when x=4…. a. Find K. b. Write a general equation. c. Use your equation to find y when x=8 Draw a chart to show at least 5 ... 
Physics
create a graph with your data of rotational speed vs radius. independent variable goes on x axis. which is x axis and which is y axis out of radius and rotational speed 
math
Here is the question I have to answer. Find the area of the specified figure. Show how you can use the formula for area to find the answer. I know you can't see the graph but can you direct me in the right direction of solving these. I don't know if there a formula you use or ... 
GEOMETRY HELPPPPP MEEEE PLEASSEEEEE!!!
Find the lengths of the diagonals of this trapezoid. trapezoid on a graph with points (a,0), (b,c), (b,c), (a,0) negative a and b are on the left side (a is on bottom and b is on top) and positive a and b are on the right side (a is on bottom and b is on top) please please ... 
Math
Graph and identify the coordinates of a rectangle with a length of at least 5 units and a width of at least 2 units. Each vertex of the rectangle must be in a different quadrant. Two of the points must have rational coordinates that are not integers. 
algebra
Graph the following function using the technique of shifting, compressing, strecthing and/or reflecting Find domain and range of the function g(x)=2sqrtx3+7 domain=___ (interval notation) range=_____ (interval notation) 
Math
1. Graph and identify the coordinates of a rectangle with a length of at least 5 units and a width of at least 2 units. Each vertex of the rectangle must be in a different quadrant. Two of the points must have rational coordinates that are not integers 
math
draw a square on the graph paper whose each side of the length 5 centimetre and then make partition of the square into 25 small squares as soon in figure 1.1 each square is small square have its height and length 1 centimetre 
Alg 1
Graph 4x+y>6 5y<=x20 Then give 2 ordered pairs that solve it& 2 ordered pairs that don't solve it 
math
Graph the following equations; calculate the slope, xintercept, and yintercept, and label the intercepts on the graph. 1. A temperature of 41 degrees F is equivalent to 278.2 degrees K, while a temperature of 86 degrees F is equivalent to 303.2 degrees K. Find the equation ... 
Science help
Will someone please check my work for me? Molecules involved in a chemical reaction must meet to react. What is this concept called? entropy enthalpy collision theory< reaction rate 2. Which of the following equations is used to describe reaction rates? ∆H  T&#... 
trig
Is this formula continous on the interval (1,1) h(theta)=(theta)sin(theta) How do you enter theta into the calculator to graph the function. Also, am I suppose to plug in the numbers into the function to determine if it is continous 
HS Calculus/math
x=2sint y=3cost 0<[smaller and equal to] t <[larger and equal to] pie find a cartesian equation for the parametrized curve what portion of the graph of the cartesian equation is traced by the parametrized curve? 
Geometry
when you have a graph with just dots and the dots make a figure. Then the dots on the outside are the posts and the inside dots are trees. what equation can i use to get the area of the figure using only posts and trees? 
math
Maggie is driving home from college. She drives at a constant speed for 2 hours and then lowers her speed for the next two hours. Which graph best illustrates Maggie's trip home from college? 
Maths
I don't get this Find the equation of the line given the following information: m=UD, x=5 And I have to find the equation. Then it says: Identify the slope and y intercept from the following equations: y=8, m=___, b=___ I also have to graph it. But if it's UD, isn't there no ... 
science
how do you rearrange 1.1513/sqrt(f)=ln(Re*sqrt(f)/2.51) to get it in terms of f and also rearrange it in terms of Re? if you identify an initial estimate of the solution for f when Re=5000 how do you plot on a scatter graph (using something like 0 to 0.1 in increments of 0.01... 
MATH
1. Maximize z = 16x + 8y subject to: 2x + y ≤ 30 x + 2y ≤ 24 x ≥ 0 y ≥ 0 Graph the feasibility region. Identify all applicable corner points of the feasibility region. Find the point(s) (x,y) that maximizes the objective function z = 16x + 8y. 
math
Maximize z = 16x + 8y subject to: 2x + y ≤ 30 x + 2y ≤ 24 x ≥ 0 y ≥ 0 Graph the feasibility region. Identify all applicable corner points of the feasibility region. Find the point(s) (x,y) that maximizes the objective function z = 16x + 8y. 
Reiny and steve do this for me please
1. Consider the functions f(x)=1/(x)+4 and g(x)=2/(x). Graph f and g on the same grid. a) Determine the points of intersection of the two functions. b) Show where f(x)<g(x). c) Solve the equation 1/(x)+4=2(x) to check your answer to part a). d) Solve the inequality 1/(x)+4&... 
math. can someone do this for me please....
* Consider the functions f(x)=1/x +4 and g(x)=2/x. Graph f and g on the same grid. a)Determine the points of intersection of the two functions. b)Show where f(x)<g(x). c)Solve the equation 1/x +4=2/x to check your answer to part a). d)Solve the inequality 1/x +4<2/x to ... 
Algebra
The bar graph which is 4% whole mil, 8% milk for cream and 30% cream shows the milk fat percentages in three dairy product s. How many pounds each of whole milk and cream should be mixed to form 200 lb of milk for cream cheese? 
physics
In physics what are the dependent variables between 0 and 2 on a line graph? I must use the rounded number to mark off intervals along the axis. The intervals must be the same amount each time (count up by the same number). 
math
1. Find the median of the following set of numbers. = B 45, 21, 54, 22, 65, 61 A) 54 B)49 1/2 C) 45 D)48 1/2 2. The following scores were recorded on a 100point examination: 95, 75, 76, 86, 96, 71, 68, 81, 95, 76, 69, 82, 93, 88, 94 Find the mean and median final examination ... 
Math
The base of a solid S is the simicircular region enclosed by the graph of y = the sqrt of [4x^2] and the xaxis. If the cross sections of S perpendicular to the xaxis are squares, the the volume of S is...? I've worked this out a few ways using what I know abt finding the ... 
math
A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a ... 
Algebra
Could someone be nice enough to check my answers please? 1)Identify a pattern and find the next number in the pattern. 2,3,8,13 my answer; 18 2)Name the property of real numbers illustrated by the equation. 4(x+4)=4x16 my answer; distributive property 3)Solve the compound ... 
Math
The following data shows the number of potatoes in twenty 2 kg bags. One graph represents Farm A, the other represents Farm B Farm A: 8,9,11,13,13,16,19,19,19,20,21,21,23,25,26,27,30,31,33,33 Farm B: 9,9,11,11,12,13,13,14,15,16,17,17,18,19,20,21,21,22,24,30 You are interested ... 
Math
The following data shows the number of potatoes in twenty 2 kg bags. One graph represents Farm A, the other represents Farm B Farm A: 8,9,11,13,13,16,19,19,19,20,21,21,23,25,26,27,30,31,33,33 Farm B: 9,9,11,11,12,13,13,14,15,16,17,17,18,19,20,21,21,22,24,30 You are interested ... 
Economics
3. Suppose the Clean Springs Water Company has a monopoly on bottled water sales in California. If the price of tap water increases, what is the change in Clean Springs' profitmaximizing level of output, price, and profit? Explain in words and with a graph. I would think that... 
calculus
Using a graphing utility, graph and approximate the zeros and their multiplicity. A.x=0,multiplicity 2;x=7,multiplicity 3 B. x=0,multiplicity 2; x=7,multiplicity 1; x=7, multiplicity 2 C. x=0,multiplicity 3;x=0,multiplicity 2 D.x=0,multiplicity 3;x=7, multiplicity 2 E.x=0,... 
PreCalc
Could somebody please check this for me? Dtermine whether the graph of each equation is symmetric with respect to the origin, the xaxis, the yaxis, and the line y=x or the line y=x. I came up with the line being symmetric to the xaxis, the yaxis, and the line y=x. I'm not... 
math
Hi This is a threepart question: a. the graph y = f(x) in the xyplane has parametrization x=x, y=f(x), and vector formula r(x) = xi + f(x)j. Use this to show that if f is twicedifferentiable, then ((absvalue f''(x))/[1+((f'(x))^2]^3/2 b. use the formula for k in part a to ... 
Graphing
Okay, so I need to make a line graph for career advancement. Would I put the job position on the vertical axis or the horizontal one? And Where would I put the years of experience needed to reach that position? ON the horizontal or vertical? Please help. thank you. 
pre algebra
An area has been reforested. After 5 years , one of the tree is 2 meters tall. After six more years, the same tree is 3.2 meters tall. name 2 ordered pairs that can be used to to graph the information? 
linear programming
Maximize z = 16x + 8y subject to: 2x + y ≤ 30 x + 2y ≤ 24 x ≥ 0 y ≥ 0 Graph the feasibility region. Identify all applicable corner points of the feasibility region. Find the point(s) (x,y) that maximizes the objective function z = 16x + 8y.