At Ned's newsstand, 4 magazines cost $24.00 how many magazines could you buy with $60.00 help

Answers

Answer 1
11. But probably if their is tax like 10 lol. But 11
Answer 2

You can buy 10 magazines in $60.

What is unit rate?

A unit rate means a rate for one of something.

Given that, the cost of 4 magazines is $24.00

For 4 magazine → $24

So, for 1 magazine = 24/4 = $6

So, in $60,

60/6 = 10

Hence, you buy 10 magazines in $60.

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Related Questions

A and B are complementary. If mB=26 degrees what is the measure of A?

A and B are complementary. If mB=26 degrees what is the measure of A?

Answers

Answer:

26

Step-by-step explanation:

complementary means same. so A and B are 26.

A car travels a distance of 1280 metres at an average speed of 64 kilometres per hour.
Ра:
Calculate the time it takes for the car travel this distance,
Give your answer in seconds​

Answers

Answer:

The answer is 20 hours

Step-by-step explanation:

This is becuase 1280 divided by 64 equals 20.  There are no unit coversions.

In time t = 0.02 hour the car travels a distance of 1280 meters with a speed of 64 kilometers per hour.

Given that,
A car travels a distance of 1280 meters at an average speed of 64 kilometers per hour.

What is speed?

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
Time  = distance/speed
Time. t = 1.280 / 64

t = 0.02 hours

Thus, In time t = 0.02 hour the car travels a distance of 1280 meters with a speed of 64 kilometers per hour.

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product of (2+x) and (2-x) is​

Answers

Use FOIL,

\((2+x)(2-x)=4-2x+2x-x^2=4-x^2\).

Answer:

4 - x²

Step-by-step explanation:

(2 + x)(2 - x)

Each term in the second factor is multiplied by each term in the first factor

= 2(2 - x) + x(2 - x) ← distribute both parenthesis

= 4 - 2x + 2x - x² ← collect like terms

= 4 - x²

The length of a diagonal of a square field is 200m .find the length of a side in meters and the area of the field in hectares

Answers

The area of the square field is 2 hectares. It's important to note that a hectare is a unit of area commonly used in measuring land. One hectare is equal to 10,000 square meters.

To find the length of a side of the square field, we can use the Pythagorean theorem. In a square, the length of the diagonal forms a right triangle with two sides equal in length (the sides of the square).

Let's denote the length of a side of the square as s. Then, according to the Pythagorean theorem, we have:

s^2 + s^2 = (200)^2

2s^2 = 40000

Dividing both sides by 2, we get:

s^2 = 20000

Taking the square root of both sides, we find:

s = sqrt(20000) ≈ 141.42 meters

Therefore, the length of each side of the square field is approximately 141.42 meters.

To find the area of the square field in hectares, we need to convert the length from meters to hectares. 1 hectare is equal to 10,000 square meters.

The area of the square field can be calculated by squaring the length of the side:

Area = (141.42)^2 ≈ 20000 square meters

To convert this to hectares, we divide by 10,000:

Area in hectares = 20000 / 10000 = 2 hectares

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Which table represents a nonlinear function?

Which table represents a nonlinear function?

Answers

Answer:

Choice C

Step-by-step explanation:

The only one that isn't a linear function is table C. If we take a look at table D (because it's easier and without any negatives) the x values decreases by two every time and the y values increase by 4 every time. Then when we look at table C, the x value increase by 5 which is good. But the y value increases by 2 then 4 then 8, which is why this table isn't a linear function.

The only one that is a nonlinear function is table Choice C.

What is linear function?

In mathematics, linear refer to a proportional behaviour that can be modelled with a line, the functions that model this behaviour are called linear functions, and their graphs are lines.

Now, linear expression refers to an expression which has variables with an exponent equal to one.

But Nonlinear functions have a slope that varies between points.

If we take a look at table D because it's easier and without any negatives then we can see that the x values decreases by two every time and the y values increase by 4 every time.

Thus when we look at table C, the x value increase by 5 which is good. But the y value increases by 2 then 4 then 8, which is not a linear function.

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Question 3 - 1 Point
Dec 14, 8:58:20 AM
ZA and ZB are complementary angles. If m_A = (2x + 30) and m
ZB= (6x 12), then find the measure of ZA.
Submit Answer
Answer:

Answers

Answer:

m∠A=42

Step-by-step explanation:

Since they are complementary they must add up to 90°.

(2x+30)+(6x+12)=90

We can just remove parenthesis since you can't really do anything with them.

2x+30+6x+12=90

Combine like terms.

8x+42=90

Do inverse to find the value of x.

8x=48

x=6

Now since we are looking for the m∠A and not x we need to replace the x with the value of x in the ∠A equation.

(2(6)+30)

(12+30)

m∠A=42

Please see the image below(math)

Please see the image below(math)

Answers

Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

AD = 3DB = 7AH = 9HC = y

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

Just go down the row and say yes no yes no in order!you don't have to type the whole thing out

Just go down the row and say yes no yes no in order!you don't have to type the whole thing out

Answers

Answer:

1) yes

2) no

3) yes

4)no

5)no

Step-by-step explanation:

what is the quotient

what is the quotient

Answers

\(5x + 2 + \frac{7}{x - 2} \)

Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. A zoo has 17 monkeys and 12 chimpanzees. 12 to 17, 12:17, 17 60 12, 17:12, 1 C 17 to 22. 17:22 • D 1740 12. 12:12 17 to 12. 12:17 12

Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. A

Answers

Answer: B

in three ways we have;

\(17\text{ to }12,\text{ }17\colon12,\text{ }\frac{17}{12}\)

Explanation:

We want to write the ratio of the situation in three ways, comparing the first quantity to the second quantity.

Given that;

A zoo has 17 monkeys and 12 chimpanzees

so, we want to compare the number of Monkeys to the number of Chimpanzees.

There are 17 Monkeys to 12 Chimpanzees.

\(17\text{ to }12\)

Writing in other ways, we have;

\(17\colon12\)

and lastly in fraction;

\(\frac{17}{12}\)

Therefore, in three ways we have;

\(17\text{ to }12,\text{ }17\colon12,\text{ }\frac{17}{12}\)

Solve the system of equations below.

Solve the system of equations below.

Answers

Answer:

B

Step-by-step explanation:

So we have the system of equations:

\(x-2y=3\\2x-3y=9\)

To solve, we can use the substitution method. First, add 2y to both sides in the first equation:

\(x=3+2y\)

Now, substitute this into the secon equation:

\(2(3+2y)-3y=9\)

Distribute the 2:

\(6+4y-3y=9\)

Combine like terms:

\(6+y=9\)

Subtract 6 from both sides:

\(y=3\)

So, the value of y is 3.

Substitute this back into the original equation to find x. Thus:

\(x=3+2(3)\)

Multiply:

\(x=3+6\)

Add:

\(x=9\)

So, our answer is (9,3)

And we're done!

The lifting force, f, exerted on an airplane wing varies jointly as the area, a, of the wing's surface and the square of the plane's velocity, v. the lift of a wing with an area of 230 square feet is 14,100 pounds when the plane is going 240 miles per hour. find the lifting force on the wing if the plane slows down to 150 miles per hour.

Answers

The lifting force (f) is given by the formula, f = kav², where k is the constant of variation. It is given that the lifting force varies jointly as the area (a) of the wing's surface and the square of the plane's velocity (v).

f = kav² ----- (1)

The given values are:

a = 230 sq. ft.

v1 = 240 mph

f1 = 14100 lbs

v2 = 150 mph

We need to find the lifting force (f2) when the plane slows down to 150 miles per hour. Now, we need to find the value of the constant of variation (k). We have,

f1 = kav1²

14100 = ka (230) (240)²

14100 = ka (230) (57600)

14100 = 13248000a

k = 14100 / (13248000a) ----- (2)

We can substitute equation (2) into equation (1).We have,

f = 14100 / (13248000a) x a x v² ----- (3)

We can substitute the given values into equation (3).

We have,

f2 = 14100 / (13248000a) x a x 150²

f2 = 14100 / (13248000 x 230) x 150²

f2 = 563 / 5064 x 22500

f2 = 2493.24324324

The lifting force on the wing if the plane slows down to 150 miles per hour is 2493.24324324 pounds.

Answer: 2493.24324324.

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A piecewise function f(x) is defined as shown. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayout Which table could be used to graph a piece of the function? A 2-column table has 3 rows. The first column is labeled x with entries 0, 16, 40. The second column is labeled y with entries 90, 85, 75. A 2-column table has 3 rows. The first column is labeled x with entries 0, 40, 200. The second column is labeled y with entries 90, 40, 0. A 2-column table has 3 rows. The first column is labeled x with entries 40, 120, 200. The second column is labeled y with entries 75, 30, 0. A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.

Answers

Answer:

(D)The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.

Step-by-step explanation:

The piece-wise function, f(x) is defined as follows:

\(f(x)=\left\{\begin{array}{ccc}-\frac{5}{4}x+90 &0\leq x<40\\\\-\frac{3}{8}x+75 &40\leq x\leq 200\end{array}\right\)

\(f(0)=-\frac{5}{4}*0+90=90\\\\f(16)=-\frac{5}{4}*16+90=70\\\\f(40)=-\frac{3}{8}*40+75=60\\\\f(120)=-\frac{3}{8}*120+75=30\\\\f(160)=-\frac{3}{8}*160+75=15\\\\f(200)=-\frac{3}{8}*200+75=0\)

Therefore, the table which could represent the function is that which satisfies the points above.

In option D

\(\left|\begin{array}{c|c}x&f(x)\\--&--\\40&60\\160&15\\200&0\end{array}\right|\)

The correct option is D

Answer:

D

Step-by-step explanation:

edge2020

a lump sum of $2000 is invested at 4.2% compounded continuously. (a) write the function for the model that gives the future value of the investment in dollars after t years. f(t)

Answers

The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t

Give, a lump sum of $2000 is invested at 4.2% compounded continuously.

Hence we have:

P = $2000

rate of interest = 4.2%

years = t

we know that A = Pe^rt

Substitute the above values in the formula.

Amount = f(t)

f(t) = 2000.e⁰·°⁴²t

hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t

Therefore we get the required function.

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Please help!!!!!
what is 20% of 35

Answers

Answer:

7

Step-by-step explanation:

Laura borrowed a total of $18,000 from two different banks to start a business. One bank charged the equivalent of 6% simple
Interest, and the other charged 7.5% interest. If the total interest after 3 years was $3330, determine the amount borrowed from
each bank.
Part: 0/4
Part 1 of 4
Let x represent the principal on the business loan at 6%.
Then,
is the remaining amount borrowed at 7.5%.

Answers

Step-by-step explanation:

Let x be the amount invested at 6% so that 18000-x is the amount invested at 7.5% both in dollars.

The total interest in 3 years is $3330 so we can write: 0.06x(3)+0.075(18000-x)(3)=3330

Solve for x:

0.06x(3)+0.075(18000−x)(3)=3330

Step 1: Simplify both sides of the equation.

0.06x(3)+0.075(18000−x)(3)=3330

0.06x(3)+−0.225x+4050=3330(Distribute)

0.18x+−0.225x+4050=3330

(0.18x+−0.225x)+(4050)=3330(Combine Like Terms)

−0.045x+4050=3330

−0.045x+4050=3330

Step 2: Subtract 4050 from both sides.

−0.045x+4050−4050=3330−4050

−0.045x=−720

Step 3: Divide both sides by -0.045.

−0.045x/−0.045=−720/−0.045

x=16000

x=16000

So, the amounts borrowed are:

Bank at 6% = 16000

Bank at 7.5% = 2000

Find m∠XYZ, best answer gets Brainliest

Find mXYZ, best answer gets Brainliest

Answers

Answer:

162

Step-by-step explanation:

theorem <w+<x=<y

5x+2+8x+4=15x-18

13x+6=15x-18

6+18=15x-13x

24=2x

12=x

------------

xyz=15x-18

15(12)-18

180-18

=162

4. Communicate Precisely When you graph a quadratic function, the
y-intercept appears to be 1, and the x-intercepts appear to be -4 and 2.5.
Which values represent the solution(s) to the related equation of the
function? How can you check? Explain

Answers

Answer:

solo respondo esto por los puntos

Which of the following statements is correct? A. Steven Strange is single and is claimed as a dependent by his parents. Steven has salary income of $15,000 and files his own tax return. The basic standard deduction for Steven is $15,350. B. Wanda (gross income: $5,000) is married and files a separate tax return (MFS). Since Wanda's gross income ($5,000) is smaller than the basic standard deduction for MFS ($12,550), she does not have to file her tax return. C. In general, a $1 deduction for AGI is better than a $1 non-refundable tax credit. D. A greater deduction from AGI leads to a greater deduction for AGI. E. All of above are incorrect. 2. Which of the following statements is incorrect regrading a self-employed taxpayer? A. Qualified job-related expenses (e.g., auto, travel, gift expenses) are classified as deduction for AGI. B. If 30% of the travel time is business purpose, transportation expense (e.g., airfare) is not deductible. C. In addition to the $0.575 per mile auto expenses, the self-employed taxpayer who chooses the standard mileage method (rather than the actual cost method) can claim deduction on depreciation, gas and oil, repair, insurance, license expenses. D. The auto expenses related to commuting between home and his/her job are not qualified for deduction. E. Job-related education expenses where the education maintains or improves current job skills are deductible.

Answers

The correct statement is: E. All of the above are incorrect.

Statement A is incorrect because the basic standard deduction for 2021 is $12,550 for single filers, not $15,350.

Statement B is incorrect because the gross income threshold for filing a separate tax return (MFS) in 2021 is $5, as opposed to the basic standard deduction for MFS.

Statement C is incorrect because a non-refundable tax credit directly reduces the amount of tax owed, whereas a deduction for AGI reduces taxable income before calculating the tax liability. Therefore, a non-refundable tax credit is generally more valuable than a deduction for AGI.

Statement D is incorrect because a greater deduction from AGI does not necessarily lead to a greater deduction for AGI. Deductions from AGI reduce taxable income, while deductions for AGI are claimed before calculating AGI.

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In a classroom with 45 students, there were twice as many girls as boys. How many of each were there?

Answers

Answer:

90

Step-by-step explanation:

Dialogue (sometimes spelled dialog in American English) is a written or spoken conversational exchange between two or more people, and a literary and theatrical form that depicts such an exchange.

Answer:

Girls are twice as many as the boys.

So let's assume girls to be 'x' and boys to be 'y' and adopt the simultaneous equation method to find out the answer to X and Y.

Firstly, let's us establish that: x + y = 45

Secondly, for every boy there are two girls. So,

2y = x.

We have the value for the 'x' here in the equation, so we will substitute that in the first equation:

2y + y = 45

3y = 45

y = 15

Boys are 15.

Put this answer into any of the equations now, we will the first one:

x + 15 = 45

x = 30

Girls are 30.

Step-by-step explanation:

Hope this helps

Crown me as brainliest:)

Is the temperature measured in Celsius proportional to the temperature measured in Fahrenheit?

Answers

Answer:

The relationship between Fahrenheit and Celsius is directly proportional

The relationship between Celsius and Fahrenheit demonstrates that the two units are directly proportional to one another.

Is there a proportional link between the temperature scales?

No. because the ratio is different (no constant of proportionality). The relationship between Celsius and Fahrenheit demonstrates that the two units are directly proportionate to one another. It suggests that as the temperature rises on the Celsius scale, the temperature rises as well on the Fahrenheit scale. Fahrenheit and Celsius have a proportionate relationship. Both follow the various unit differences between each scale and have varying water freezing points. There is one place where the Fahrenheit and Celsius scales meet. At both -40 °C and -40 °F, they are equal. To determine when two temperature scales are equal to one another, the straightforward technique is to set the

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The smaller triangle is a pre-image of the bigger triangle. The center of dilation is (1, −1). What is the scale factor used to create the dilation? −4 −14 14 4.

Answers

The correct answer is 14 because distance from center of dilation to point on pre-image is 14 times the distance from center of dilation to corresponding point on image

We can solve this problem using the formula of the scale factor of dilation which is given below:

Scale factor of dilation = (image distance)/(pre-image distance)

In the above formula, the image and pre-image distances are measured from the center of dilation.

Let us assume that the scale factor is x.

The vertices of the two triangles are labeled as follows:

Pre-image triangle vertices: A(-2,2), B(-1,3), and C(-3,3)

Image triangle vertices: A′(10,-14), B′(6,-10), and C′(14,-10)

Now, we can calculate the image and pre-image distances using the distance formula and the Pythagorean theorem.

Pre-image distance between A(-2,2) and B(-1,3) is

AB = √[(3 - 2)^2 + (-1 + 2)^2]

= √2

Pre-image distance between A(-2,2) and C(-3,3) is

AC = √[(3 - 2)^2 + (-3 + 2)^2]

= √2

Pre-image distance between B(-1,3) and C(-3,3) is

BC = √[(3 - 3)^2 + (-1 + 3)^2]

= 2

Pre-image perimeter of the triangle ABC is

P₁ = AB + AC + BC

= √2 + √2 + 2

= 2√2 + 2

The image distances are measured between the center of dilation (1,-1) and the vertices of the image triangle.

We can calculate the image distance between two points (x1,y1) and (x2,y2) using the formula below:

Image distance between (x1,y1) and (x2,y2) = x2 - x1 or y2 - y1

Let us calculate the image distances between the center of dilation and the vertices of the image triangle.Image distance between (1,-1) and A′(10,-14) is

10 - 1 = 9

Image distance between (1,-1) and B′(6,-10) is

6 - 1 = 5

Image distance between (1,-1) and C′(14,-10) is

14 - 1 = 13

Image perimeter of the triangle A′B′C′ is

P₂ = A′B′ + B′C′ + C′A′

=  √(9² + 13²) + √(5² + 9²) + √(13² + 5²)

= 39.25 + 10.3 + 14.42

≈ 64.97

Scale factor of dilation = (image distance)/(pre-image distance)

= P₂/P₁

= 64.97/(2√2 + 2)

≈ 14.

Hence, the correct option is 14.

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19 divided 800 (estimated)

Answers

Answer:

0.02375

Step-by-step explanation:

sana po nakatulong☺

19/800 is 0.02375 okay

1 is 3 . 3 is 5 . 5 is 4 . 4 is 4 .
What is 7? Explain why.

Answers

Answer:

5

Step-by-step explanation:

seven has 5 letters

Please answer !!!!!!!! Will mark brainliest !!!!!!!!!!!!

Please answer !!!!!!!! Will mark brainliest !!!!!!!!!!!!

Answers

Answer:

B)

D)

Step-by-step explanation:

B) 1 and 13 are x intercepts so true

D) greatest profit is when price is 7; after that profit is getting smaller because function is decreasing

Multiplying Polynomials Multiple Choice
Need to know what goes in blanks and final answer

Multiplying Polynomials Multiple ChoiceNeed to know what goes in blanks and final answer

Answers

Answer:

6x² - 19x + 10

Step-by-step explanation:

Given

(3x - 2)(2x - 5)

Each term in the second factor is multiplied by each term in the first factor, that is

3x(2x - 5) - 2(2x - 5) ← distribute both parenthesis

= 6x² - 15x - 4x + 10 ← collect like terms

= 6x² - 19x + 10

Looking at the two terms, 7a4b2c2 and 14abc6, what is the GCF do the coefficients?

Looking at the two terms, 7a4b2c2 and 14abc6, what is the GCF do the coefficients?

Answers

Greatest Common Factor is also shortened as G.C.F . Greatest Common Factor can be used as the greatest or highest number that divides exactly into two or more numbers.

The GCF for the coefficients is 7. Option A is the correct option.

From the question, we are given two terms 7a4b²c² and 14abc⁶

The coefficient for 7a4b²c² = 7

The coefficient for 14abc⁶ = 14

Solving for the GCF,

The factors of 7 are: 1, 7

The factors of 14 are: 1, 2, 7, 14

Then the greatest common factor is 7.

Therefore, the GCF for the coefficients is 7 . Option A is the correct option.

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How many different 8-letter permutations can be formed from 6 identical h's and two identical t's?.

Answers

The required permutations are given as 168 letters will be formed.

Given that,
How many different 8-letter permutations can be formed from 6 identical h's and two identical t's is to be determined.

What are permutation and combination?

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
A total number of combinations = 8!
The number of repetitions,  = 5!.2!
Permutation of letters = 8!/[5!.2!]

Thus, the required permutations are given as 168 letters will be formed.

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Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems. 1. 2. 3. maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0. maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0. maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.

Answers

The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

1. Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems.
maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

Now, To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 3/4), (0, 0), and (3, 0).

        z = x₁ + 2x₂ = (0) + 2(3/4)

                    = 1.5z = x₁ + 2x₂ = (0) + 2(0) = 0

                        z = x₁ + 2x₂ = (3) + 2(0) = 3

The maximum value of the objective function z is 3, and it occurs at the point (3, 0).

Hence, the optimal solution is (3, 0), and the optimal value of the objective function is 3.2.

maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function,

        evaluate the objective function at each corner of the feasible region:

                                (0, 0), (3, 0), and (2, 5).

                          z = x₁ + x₂ = (0) + 0 = 0

                          z = x₁ + x₂ = (3) + 0 = 3

                           z = x₁ + x₂ = (2) + 5 = 7

The maximum value of the objective function z is 7, and it occurs at the point (2, 5).

Hence, the optimal solution is (2, 5), and the optimal value of the objective function is 7.3.

maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 1), (2, 0), and (5, 1).

                         z = 3x₁ + 4x₂ = 3(0) + 4(1) = 4

                      z = 3x₁ + 4x₂ = 3(2) + 4(0) = 6

                      z = 3x₁ + 4x₂ = 3(5) + 4(1) = 19

The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

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