The counterexample must satisfy the hypothesis of the conditional statement which is the correct answer would be option (B).
What is a Counterexample?A counterexample is an example in which the hypothesis is correct but the conclusion is incorrect.
Since A counterexample is used to show that a conditional assertion is untrue.
So, just one counterexample is required to prove a statement untrue.
Also, when employing a counterexample to prove a conditional assertion untrue.
The counterexample must then meet the hypothesis of the conditional statement.
As a result, the correct statement concerning the counterexample is;
The conditional statement's hypothesis must be satisfied by the counterexample.
Hence, the correct answer would be option (B).
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Figure A has a perimeter of 48 m and one of theside lengths is 18 m. Figure B has a perimeter of 80 m.What is the corresponding side length of Figure B?
We have to use proportions to solve this question.
According to the given information, the perimeter of Figure A is to the sidelength of that figure as the perimeter of Figure B is to the sidelength of that figure:
[tex]\begin{gathered} \frac{48}{18}=\frac{80}{x} \\ x=\frac{80\cdot18}{48} \\ x=30 \end{gathered}[/tex]The corresponding sidelength of Figure B is 30.
the graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the domain of the function.
The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.
What is domain of a function?The domain of a function is the complete set of possible values of the independent variable.
Also a domain of a function refers to "all the values" that go into a function.
From the graph the domain of the function of the volume of the of liquid in the bucket is calculated as follows;
The minimum value of the volume of liquid in the bucket = 0
The maximum value of the volume of liquid in the bucket = 7.5 liters
The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}
0 ≤ V ≤ 7.5 liters
Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.
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calculate the area of this trapiziuem
Answer:
............where is it?
Of the 120 families, approximately___pay more than $5710 annually for day car per child.
1) Considering a Normal Distribution, then we can write out the following:
[tex]P(X>5710)=P(X-\mu>5710-6000)=P(\frac{X-\mu}{\sigma}>\frac{5710-6000}{1000})[/tex]Note that we're dealing with probabilities.
2) Let's find out the Z-score resorting to a table, we get:
[tex]Z=\frac{x-\mu}{\sigma}=\frac{5710-6000}{1000}=-0.29[/tex]2.2) So we can infer from 1 and 2:
[tex]P(X>5710)=P(Z>-0.29)=0.6141[/tex]Notice that this distribution refers to 120 families
Harriet sells prints of her photographs, and is deciding what her minimum order should be during a sale. The equation that relates to her profit, y, from a minimum order of size x is 12x - 4y = 48.
Part A
What are the x-intercept and the y-intercept of the graph of her profit?
A. X-intercept: 3; y-intercept: -12
B. X-intercept: 4; y-intercept: 12
C. X-intercept: 4; y-intercept: -12
D. X-intercept: 3; y-intercept: 12
Part B
What should her minimum order size be, to make a profit?
Consider the given linear equation,
[tex]12x-4y=48[/tex]PART A
Substitute y=0 to obtain the x-intercept,
[tex]\begin{gathered} 12x-4(0)=48 \\ 12x=48 \\ x=4 \end{gathered}[/tex]Thus, the x-intercept is 4 .
Substitute x=0 to obtain the y-intercept,
[tex]\begin{gathered} 12\mleft(0\mright)-4y=48 \\ -4y=48 \\ y=-12 \end{gathered}[/tex]Thus, the y-intercept is -12 .
Therefore, option C is the correct choice
PART B
The linear equation can also be written as,
[tex]\begin{gathered} 4y=12x-48 \\ y=\frac{12}{4}x-\frac{48}{4} \\ y=3x-12 \end{gathered}[/tex]The minimum limit to make a profit can be calculated as,
[tex]\begin{gathered} y>0 \\ 3x-12>0 \\ 3x>12 \\ x>\frac{12}{3} \\ x>4 \end{gathered}[/tex]Note that the order of photograph must be an integer. The next integer after 4 is 5.
So the minimum order size to make a profit should be 5.
Proofs involving a transversal
Thus, it is clear that the lines RS and TV in the preceding diagram are parallel to each other
What are the properties of parallel lines?If you extend a set of lines indefinitely, they will remain parallel and never cross each other even though they are on the same plane. The symbol || represents the collection of parallel lines. All parallel lines are always equally spaced apart. Investigate the characteristics of parallel lines.
When two lines in a plane are stretched infinitely in both directions and do not cross, they are said to be parallel.
To solve the given question we know,
angle 1= angle 2 and lines RV // TS
angle 4= angle 3(interior angles on parallel lines are equal)
angle 1=angle 4 (vertically opposite angles are equal )
angle 1= angle 3 (angle 4=angle 1)
angle 4=angle 2( angle 1=angle 4)
Now we can see that the sum of base angles of the diagram will be 180 because
180-angle 3= angle STV
angle 4=angleSTV+180 (angle 3=angle4)
we proved that the diagram is a parallelogram because base angles of the same side are supplementary:
Therefore , we can conclude that the lines RS // TV in the preceding diagram .
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4. Sean bought 1.8 pounds of gummy bears and 0.6 pounds of jelly beans and paid $10.26. He went back to the store the following week and bought 1.2 pounds of gummy bears and 1.5 pounds of jelly beans and paid $15.09. What is the price per pound of each type of candy?Directions: For each problem - define your variables, set up a system of equations, and solve.
Let
the price of gummy bears per pound = x
the price of jelly beans per pound = y
[tex]\begin{gathered} 1.8x+0.6y=10.26 \\ 1.2x+1.5y=15.09 \\ 1.2x=15.09-1.5y \\ x=12.575-1.25y \\ \\ 1.8(12.575-1.25y)+0.6y=10.26 \\ 22.635-2.25y+0.6y=10.26 \\ -1.65y=10.26-22.635 \\ -1.65y=-12.375 \\ y=\frac{-12.375}{-1.65} \\ y=7.5 \\ \\ 1.8x+0.6y=10.26 \\ 1.8x+0.6(7.5)=10.26 \\ 1.8x+4.5=10.26 \\ 1.8x=10.26-4.5 \\ 1.8x=5.76 \\ x=\frac{5.76}{1.8} \\ x=3.2 \end{gathered}[/tex]price per pound of gummy bear = $3.2
price per pound of jelly beans = $7.5
crate A exerts a force of 8320N and a pressure of 64N/cm2. crate B exerts a force of 9860N and a pressure of 29N/cm2. find the difference between the base areas of the crates in cm2
Answer:
difference in base areas = 210 cm²
Step-by-step explanation:
In order to calculate the difference in the base areas of the crates, we first need to find the base area of each crate.
To calculate the base area, we can use the formula for pressure and rearrange it to make area the subject:
[tex]\boxed{Pressure = \frac{Force}{Area}}[/tex]
⇒ [tex]Area = \frac{Force}{Pressure}[/tex]
Therefore:
•Base area of crate A = [tex]\mathrm{\frac{8320 \ N}{64 \ N/cm^2}}[/tex]
= 130 cm²
• Base area of crate B = [tex]\mathrm{\frac{9860 \ N}{29 \ N/cm^2}}[/tex]
= 340 cm²
Now that we know the base areas of each crate, we can easily calculate the difference between them:
difference = 340 cm² - 130cm²
= 210 cm²
Need help answering all these questions for the black bird. Exponential equation for the black bird: g(x) = 2^x-8 + 1King Pig is located at (11,9)Moustache Pig is located at (10,4)
Given:
Exponential equation for the black bird is,
[tex]g(x)=2^{x-8}+1[/tex]Required:
To find the starting point of bird and graph the given function.
Explanation:
(1)
The bird starting point is at x = 0,
[tex]\begin{gathered} g(0)=2^{0-8}+1 \\ \\ =2^{-8}+1 \\ \\ =1.0039 \\ \\ \approx1.004 \end{gathered}[/tex](2)
The graph of the function is,
Final Answer
(1) 1.004
(2)
Which of the following expressions is equal to -x2 -36
OA. (-x+6)(x-6i)
OB. (x+6)(x-6i)
OC. (-x-6)(x-6i)
OD. (-x-6)(x+6i)
The expression equivalent to -x² - 36 is the one in option C.
(-x - 6i)*(x - 6i)
Which of the following expressions is equal to -x² - 36?We can rewrite the given expression as:
-x² - 36 = -x² - 6²
And remember that the product of a complex number z = (a + bi) and its conjugate (a - bi) is:
(a + bi)*(a - bi) = a² + b²
Then in this case we can rewrite:
-x² - 6² = -(x² + 6²) = - (x + 6i)*(x - 6i)
= (-x - 6i)*(x - 6i)
The correct option is C.
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If triangles MNP is an equilateral triangle, find x and the measure of each side.
The value of x = 13
Each side of the equilateral triangle is: 27 units.
What is an equilateral Triangle?A triangle is classified or defined as an equilateral triangle if all its sides are of the same length. This means, all equilateral triangles have side lengths that are congruent.
Since triangle MNP is said to be an equilateral triangle, all its sides would be equal to each other. Therefore:
MN = NP = MP
Given the following:
MN = 4x - 25
NP = x + 14
MP = 6x - 51
Thus:
MN = NP
Substitute
4x - 25 = x + 14
4x - x = 25 + 14
3x = 39
x = 39/3
x = 13
MN = 4x - 25 = 4(13) - 25 = 27
MN = NP = MP
NP = 27
MP = 27
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Solve for r.
r - 15 / -1 = -4
Answer:
r=19
Step-by-step explanation:
15-r=-4
r=19
:]
Rewrite the expression (17x3 – 12x2 + 6x - 4)/(x – 1) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor, using the synthetic division method.
Given that
The equation is
[tex]\frac{17x^3-12x^2+6x-4}{x-1}[/tex]and we have to convert it into the form of
[tex]\begin{gathered} q(x)+\frac{r(x)}{b(x)} \\ where\text{ q\lparen x\rparen is quotient, r\lparen x\rparen is remainder, and b\lparen x\rparen is divisor.} \end{gathered}[/tex]Last year, Mrs.Sclair’s annual salary was $88,441. This year she received a raise and now earns $96,402 annually. She is paid weekly. a. What was her weekly salary last year? Round to the nearest cent. b.What is Mrs.Sclair’s weekly salary this year? Round to the nearest cent. c.On a weekly basis, how much more does Mrs.Sclair earn as a result of her raise?
We have the following:
old salary: $88441
new salary: $96402
The year is approximately 52 weeks, therefore:
a. old salary for week:
[tex]\begin{gathered} \frac{88441}{52}=1700.8 \\ \end{gathered}[/tex]b. new salary for week:
[tex]\frac{96402}{52}=1853.9[/tex]c. weekly raise
[tex]1853.9-1700.8=153.1[/tex]Write the following expression in its simplest form-2/3(9/2x + 15/2)
Given the expression
-2/3(9/2x + 15/2)
Open the parenthesis;
= -2/3(9/2 x) - 2/3(15/2)
= -18x/6 - 30/6
= -3x - 5
Hence the expression in its simplest form is -3x - 5
HELP ME PLEASE !!!
REASONING An absolute value function is positive over its entire domain. How many x-intercepts does the graph of the function have?
● None
01
02
O Infinite
The absolute value function can intersect a horizontal x-axis at zero, one, as well as two points.
What is meant by the absolute value function?The absolute value function is usually thought to provide the distance between two numbers on a number line. Algebraically, the output is the value without regard to sign for whatever the input value is. The corner point where the graph changes direction is the most essential characteristic of the absolute value graph. This point is depicted as the origin. When the input is zero, the graph of an absolute value function would then intersect the vertical axis.Thus, depending on the way the graph has indeed been shifted and reflected, it could or might not intersect the horizontal axis.
The absolute value function can intersect the x-axis at zero, one, or two points.
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savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?
The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.
How is the amount required to have a saving of $50,000 ?The compound interest formula is expressed as;
P = A / (1 + r/n)^nt
Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.
Given the data in the question;
Accrued amount A = $50,000Interest rate r = 6%Compounded monthly n = 12Elapsed time t = 30 yearsPrincipal P = ?First, convert rate from percent to decimal.
Rate r = 6%
Rate r = 6/100
Rate r = 0.06 per year
To determine the principal, plug the given values into the formula above and solve or P
P = A / (1 + r/n)^nt
P = $50,000 / (1 + 0.06/12)^( 12 × 30 )
P = $50,000 / (1 + 0.05)³⁶⁰
P = $50,000 / (1.05)³⁶⁰
P = $8,302.10
Therefore, the principal investment is $8,302.10.
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Enter the solution to the inequality below. Enter your answer as an inequality.
Use =< for and >= for >
√x ≥ 17
Answer here
SUBMIT
The solution of the inequality is [tex]x \geq 289[/tex].
What is inequality?
Inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ( [tex]\neq[/tex]) " to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.
The given inequality is, [tex]\sqrt{x} \geq 17[/tex]
Taking square on both sides, we get
[tex]x\geq 289[/tex].
Therefore, the solution of the inequality is [tex]x \geq 289[/tex].
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the number 0.3333... repeats forever; therefore, its irrational
The statement is false, the number can be rewritten as:
0.33... = 3/9
So it is a rational number, not irrational
Is the statement true?Here we have the statement:
"the number 0.3333... repeats forever; therefore, its irrational"
This is false, and let's prove that.
our number is:
0.33...
Such that the "3" keeps repeating infinitely.
If we multiply our number by 10, we get:
10*0.33... = 3.33...
If we subtract the original number we get:
10*0.33... - 0.33... = 3
9*0.33... = 3
Solving that for our number we get:
0.33... = 3/9
So that number can be written as a quotient between two integers, which means that it is a rational number.
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Ziba brought 4 bottles of water to the park. Each bottle held 6 ounces of water. Ziba drank an equal number of ounces of water each hour. If she was at the park 3 hours, how many ounces of water did she drink each hour
By taking the quotient between the total volume and the number of hours, we conclude that she drinks 8 ounces per hour.
How many ounces of water did she drink each hour?
We know that Ziba has 4 bottles, each one with 6 ounces, so the total volume of water is:
V = 4*6 ounces = 24 ounces.
We know that she drinks that in 3 hours, so the amount that she drinks each hour is:
24 oz/3 = 8 oz
She drinks 8 ounces of water each hour.
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20 >= 4/5 w
Solve the inequality. Grab the solution
Solve the inequality. Grab the solution
-8<-1/4m
In inequality 20 >= 4/5 w, w is 25 or any real no. lower than< 25 and in inequality -8<-1/4m, m = any real no. greater than> 24 is are the solution.
What is inequality?An inequality compares two values and indicates whether one is lower, higher, or simply not equal to the other.
A B declares that a B is not equal.
When a and b are equal, an is less than b.
If a > b, then an is bigger than b.
(those two are called strict inequality)
The phrase "a b" denotes that an is less than or equal to b.
The phrase "a > b" denotes that an is greater than or equal to b.
We have give the inequality to solve
20 = 4/5w
w = 20 × 5/4
= 25 or any real no. lower than< 25
Let -8 = -1/4m
m = -8 × -4
m = 24
so m = any real no. greater than> 24
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Hi, can you help me answer this question please, thank you!
Given:
The test claims that night students' mean GPA is significantly different from the mean GPA of day students.
Null hypothesis: the population parameter is equal to a hypothesized value.
Alternative hypothesis: it is the claim about the population that is contradictory to the null hypothesis.
For the given situation,
[tex]\begin{gathered} \mu_N_{}=\text{ Night students} \\ \mu_D=Day\text{ students} \end{gathered}[/tex]Null and alternative hypothesis is,
[tex]\begin{gathered} H_0\colon\mu_N=\mu_D \\ H_1\colon\mu_N_{}\ne\mu_D \end{gathered}[/tex]Answer: option f)
The function P(m) below relates the amount of time (measured in minutes)
Steve spent on his homework and the number of problems completed.
It takes as input the number of minutes worked and returns as output the
number of problems completed.
P(m) = 12 +9
Which equation below represents the inverse function M(p), which takes the
number of problems completed as input and returns the number of minutes
worked?
OA. M(p) = 6p + 54
OB. M(p) = 6p - 54
OC. M(p) = 54p - 6
OD. M(p) = 54p + 6
The inverse function of a function f in mathematics exists a function that reverses the operation of f. The number of problems completed as input and returns the number of minutes worked exists m(p) = 6p - 54.
What is meant by inverse function?An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.
Given: P(m) = (m/6) + 9
Determine the inverse function
P(m) = (m/6) + 9
Represent P(m) as P
P = (m/6) + 9
Swap the positions of P and m
m = (p/6) + 9
We are to make p the subject.
Subtract 9 from both sides, then we get
m - 9 = (p/6) + 9 - 9
m - 9 = (p/6)
Multiply through by 6
6(m - 9) = (p/6) × 6
simplifying the above equation, we get
6(m-9) = p
6 m-54 = p
Rearranging the above equation, we get
p = 6m - 54
Swap the positions of P and m
m = 6p - 54
m(p) = 6p - 54
Therefore, the correct answer is option C. M(p)=6p - 54
The complete question is:
The function below relates the amount of time (measured in minutes) Steve spent on his homework and the number of problems completed.
It takes as input the number of minutes worked and returns as output the number of problems completed.
P(m) = (m/6)+9
Which equation below represents the inverse function M(p), which takes the number of problems completed as input and returns the number of minutes worked?
A. M(p)=54p + 6
B. M(p)=54p - 6
C. M(p)=6p - 54
D. M(p)=6p + 54
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Answer:6p-54
Step-by-step explanation:
what is the area of a circular pool with a diameter of 36 ft?
Answer:
1,017.36ft^2
Explanation:
Area of the circular pool = \pi r^2
r is the radius of the pool
Given
r = d/2
r = 36/2
r = 18ft
Area of the circular pool = 3.14(18)^2
Area of the circular pool = 3.14 * 324
Area of the circular pool = 1,017.36ft^2
Randy has $12 which he decides to put into his savings account. Every week Randy does chores to earn a $6 allowance which he continues to save and put into his savings account.Like Randy, Becky decides to be more responsible with her money and also save her money. Right now she owes her parents $8. Becky also earns $7 a week for doing chores, If both Randy and Becky save up beginning today whose savings account would reach $50first?A. RandyB. BeckyC. They would reach $50 at the same time.D. There is not enough given information to determine who will save up $50 first
Randy's initial money = $12
Randy's earnings per week = $6
Becky's initial money = -$6 (she owes )
Becky's earnings per week = $7
Number of weeks: x
The equation for each:
• Randy:
50 = 12 + 6x
• Becky:
50 = -6 + 7x
Solve each for x:
Randy:
50= 12 + 6x
50-12 = 6x
38 = 6x
38/6=x
x= 6.3
Becky:
50= -8 + 7x
50+8 =7x
58=7x
58/7=x
x= 8.28
Randy will take 6.33 weeks and Becky 8.28 weeks.
Answer:
A. Randy
You are told that a 95% confidence interval for the population mean of a normally distributed variable is 17.3 to 24.5. if the population was 76, what was the sample standard deviation?
The sample standard deviation of the population with confidence interval of 95% is 13.57
What is standard deviation?Standard deviation gives a value that measures how much the given value differ from the mean.
How to find the sample standard deviationGiven data form the question
95% confidence interval
population mean of a normally distributed variable is 17.3 to 24.5
population was 76
Definition of variables
confidence interval = CI = 95%
mean = X = 17.3 to 24.5
taking the average, X = 21.45
standard deviation = SD = ?
Z score = z = 1.96
from z table z score of 95%confidence interval = 1.96
sample size = n = 76
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]24.5=21.45+1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]24.5-21.45=1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]3.05=1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]\frac{3.05}{1.96} =\frac{SD}{\sqrt{76} }[/tex]
[tex]1.5561 =\frac{SD}{\sqrt{76} }[/tex]
SD = √76 * 1.5561
SD = 13.56577
SD ≈ 13.57
The standard deviation is solved to be 13.57
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What is the distance from Point B (-1, 11) to line y = -1/3x - 6?
Answer in simplest radical form
The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.
The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).
Comparing the equation y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.
It is clear that the coefficient of x, A = -1 ÷ 3.
The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.
Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,
d = 15.811.
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I need help on this please!
Answer:
y = -2x + 2
Step-by-step explanation:
so to find the slope of the graph we must do (rise)/(run)
when we see the graph we see that when it goes DOWN 2 it also goes RIGHT 1
RISE is up or down
RUN is left or right
since it is down it is negative
so
-2 / 1
that is just -2
that is the slope
the equation for slope intercept is y = mx + b where m is the slope and b is the y intercept
so far it is y = -2x + b
the y intercept is where it crosses the y axis
that point is 2 based off of the graph
so
y = -2x + 2 is your answer
a. Find the value of x given that r ll s.The measure of angle 1 = (63-x)The measure of angle 2 = (72-2x)b. Find the measure of angle 1 and the measure of angle 2.
In the given illustration, angle 1 and angle 2 are corresponding angles.
Note that corresponding angles in parallel lines are congruent.
angle 1 measures (63 - x)
angle 2 measures (72 - 2x)
Since both angles are congruent with each other, equate the angles :
[tex]\begin{gathered} 63-x=72-2x \\ \text{Solve for x, put the variables to the left side and the constant to the right side :} \\ -x+2x=72-63 \\ x=9 \end{gathered}[/tex]The measure of angle 1 will be :
[tex]63-9=54[/tex]The measure of angle 2 will be :
[tex]72-2(9)=54[/tex]ANSWERS :
a. x = 9
b. angle 1 = 54 degrees
angle 2 = 54 degrees
What point in the feasible region maximizes the objective function?
x>0
Y≥0
Constraints
-x+3≥y
{ y ≤ ½ x + 1
objective function: C = 5x - 4y
Answer:
(3, 0)
Maximum Value of Objective Function = 15
Step-by-step explanation:
This is a problem related to Linear Programming(LP)
In linear programming, the objective is to maximize or minimize an objective function subject to a set of constraints.
For example, you may wish to maximize your profits from a mix of production of two or more products subject to resource constraints.
Or, you may wish to minimize cost of production of those products subject to resource constraints..
The given LP problem can be stated in standard form as
Max 5x - 4y
s.t.
-x + 3 ≥ y
y ≤ 0.5x + 1
x ≥ 0, y ≥ 0
The last two constraints always apply to LP problems which means the decision variables x and y cannot be negative
It is standard to express these constraints with the decision variables on the LHS and the constant on the RHS
Rewriting the above LP problem using standard notation,
Let's rewrite the constraints using the standard form:
- x + 3 ≥ y
→ -x - y ≥ -3
→ x + y ≤ 3 [1]
y ≤ 0.5x + 1
→ -0.5x + y ≤ 1 [2]
The LP problem becomes
Max 5x - 4y
s. t.
x + y ≤ 3 [1]
-0.5x + y ≤ 1 [2]
x ≥ 0 [3]
y ≥0 [4]
With an LP problem of more than 2 variables, we can use a process known as the Simplex Method to solve the problem
In the case of 2 variables, it is possible to solve analytically or graphically. The graphical process is more understandable so I will use the graphical method to arrive at the solution
The feasible region is the region that satisfies all four constraints shown.
The graph with the four constraint line equations is attached. The feasible region is the dark shaded area ABCD
The feasible region has 4 corner points(A, B,C, D) whose coordinates can be computed by converting each of the inequalities to equalities and solving for each pair of equations.
It can be proved mathematically that the maximum of the objective function occurs at one of the corner points.
Looking at [1] and [2] we get the equalities
x + y = 3 [3]
-0.5x + y = 1 [4]
Solving this pair of equations gives x = 4/3 and y = 5/3 or (4/3, 5/3)
Solving y = 0 and x + y = 3 gives point x = 3, y =0 (3,0)
The other points are solved similarly, I will leave it up to you to solve them
The four corner points are
A(0,0)
B(0,1)
C(4/3, 5/3)
D(3,0)
The objective function is 5x - 4y
To find the values of x and y that maximize the objective function,
plug in each of the x, y values of the corner points
Ignoring A(0,0)
we get the values of the objective function at the corner points as
For B(0,1) => 5(0) - 4(1) = -4
For C(4/3, 5/3) => 5(4/3) - 4(5/3) = 20/3 - 20/3 = 0
For D(3, 0) => 5(3) - 4(0) = 15
So the values of x and y which maximize the objective function are x = 3 and y = 0 or point D(3,0)