Answer:
Step-by-step explanation:
let Rajani be carrying r = 9.725kg
let Mamata be carrying m = 8.500kg
difference = r - m = 9.725 - 8.500 = 1.225kg
hence Rajani is carrying 1.225kg more than Mamata
Let a,b,c be positive real numbers. Prove the inequality
[tex]\displaystyle\\\bf\frac{(a+b)^2}{c} +\frac{c^2}{a} \geq 4b[/tex]
Answer: proved
Step-by-step explanation:
Prove the inequality:
[tex]\displaystyle\\\frac{(a+b)^2}{c} +\frac{c^2}{a} \geq 4b\ \ \ \ \ a > 0\ \ \ \ \ b > 0\ \ \ \ \ c > 0\\[/tex]
Multiply both parts of the inequality by ac (a>0, c>0):
[tex]a(a+b)^2+c*c^2\geq 4abc[/tex]
Simplify the left side of the inequality using the Cauchy inequality:
[tex]\boxed {t+v\geq 2\sqrt{tv} }[/tex]
[tex]a(a+b)^2+c(c^2)\geq 2\sqrt{a(a+b)^2c(c^2)} \\\\a(a+b)^2+c(c^2)\geq 2(a+b)c\sqrt{ac} \\\\a(a+b)^2+c(c^2)\geq 2(ac+bc)\sqrt{ac}\ \ \ \ \ (1)[/tex]
Simplify the right side of the inequality using the Cauchy inequality:
[tex]ac+bc\geq 2\sqrt{acbc} \\\\ac+bc\geq 2\sqrt{abc^2} \\\\ac+bc\geq 2c\sqrt{ab}[/tex]\ \ \ \ \ (2)
Substitute expression (2) into expression (1):
[tex]a(a+b)^2+c(c^2)\geq 2*2c\sqrt{ab} \sqrt{ab} \\\\a(a+b)^2+c(c^2)\geq4abc[/tex]
Hence,
[tex]\displaystyle\\\frac{(a+b)^2}{c} +\frac{c^2}{a} \geq 4b[/tex]
determine if the point (2, -3) is a solution to the system 2x + 5y = 11 and 3x - 2y = 1
Step-1) Determine the value of the x and y variables
To verify if (2, -3) is a solution to the system of equations provided in the question, we will need to determine the value of the x and y variables.
To do this, we will have to compare the coordinates of the point (2, -3) with the "original form" of the coordinate point (x, y). Then, we will have to identify the values (from the coordinates) in their respective order.
Example: (4, 5) = (x, y) ⇒ x = 4; y = 5
Step-2) Substitute the x and y values into one of the equations
The next step is to substitute the value of the variables. This is a required step for the coordinate provided to be verified. Once you substitute the value of the variables, you can move on to the next step process.
Step-3) Simplify the equation completely until it is in simplified form
Then, we will have to simplify the equation completely.
This is also a required step because simplifying is a process where we can convert an expression to a specific numerical value, which can help us create final conclusions to a problem. It can also help us obtain a specific numerical value from any large/small expression provided.
Step-4) Compare both sides and verify if they are equal/not equal
If both sides of the equation do not receive the same value, then the point (2, -3) is not a solution to the provided system of equation.
Part II: Verify if the point is a solution of the equations:Given Information (Provided in the question):
Equation 1: 2x + 5y = 11 Equation 2: 3x - 2y = 1Step-1) Determine the x and y variables from the coordinates:
(2, -3) = (x, y) ⇒ x = 2; y = -3Step-2) Substitute the variables into any equation:
⇒ 2x + 5y = 11 ⇒ 2(2) + 5(-3) = 11Step-3) Simplify both sides of the equation:
⇒ 2(2) + 5(-3) = 11 ⇒ 4 + (-15) = 11 ⇒ 4 - 15 = 11 ⇒ -11 ≠ 11Therefore, (2, -3) is not a solution to the system of equations.
Identify the function given of y=|20x+15|
Hello,
I hope you and your family are doing well!
The function y = |20x+15| is an absolute value function. Absolute value functions have the form y = |f(x)|, where f(x) is a linear function.
In this case, the linear function is 20x+15, so the absolute value function is:
y = |20x+15|
The absolute value function takes the absolute value of the output of the linear function. This means that if the output of the linear function is positive, the absolute value function returns the same value. If the output of the linear function is negative, the absolute value function returns the opposite of that value.
For example, if x = -1, then the output of the linear function is 20(-1)+15 = -5. The absolute value of -5 is 5, so the absolute value function returns y = 5.
On the other hand, if x = 1, then the output of the linear function is 20(1)+15 = 35. The absolute value of 35 is 35, so the absolute value function returns y = 35.
Overall, the absolute value function returns the distance of the output of the linear function from 0, without considering the sign of the output.
----
Please consider giving this answer 5 stars and brainliest if you find it helpful.
Happy Holidays!
Graphing the line with.....
Can you also mark the two points on the graph.
The graph of the linear equation y = (3/2)*x - 7
Can be seen in the image at the end.
How to graph the linear given equation?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we know that the slope is -2 and the y-intercept is -4, then the linear equation is:
y = -2x - 4
To graph that line we need to find two points on it, to get the points we need to replace the value of x.
if x = 0
y = -2x - 4
y = -4
So we have the point (0, -4)
And if x = 1:
y = -2*1 - 4
y = -6
So we have the point (1, -6)
Now we just need to graph these two points and connect them with a line.
You can see the graph below.
Learn more about linear equations:
brainly.com/question/1884491
#SPJ1
Use the graph to answer the question. Where was the object after 2 seconds?
A. 6m
B. 5m
C. 14m
D. 4m
Answer: A. 6m
Step-by-step explanation: the graph shows at the x axis that it is time. so, go to two seconds and then go up to where the line is. it goes up to 6m so that is the answer.
Simplify
A. 8a5
B. 8a6
C. 16a5
D. 16a6
Critique each of the following proposed research plans. Your critique should explain any problems with the proposed research and describe how the research plan might be improved. Include a discussion of any additional data that need to be collected and the appropriate statistical techniques for analyzing the data.
(a) A researcher is interested in determining whether a large firm is guilty of gender bias in setting wages. To determine potential bias, the researcher collects salary and gender information for all of the firm’s employees. The researcher then plans to conduct a "difference in means" test to determine whether the average salary for women is significantly different from the average salary for men.
(b) A researcher is interested in determining whether time spent in prison has a permanent effect on a person’s wage rate. He collects data on a random sample of people who have been out of prison for at least fifteen years. He collects similar data on a random sample of people who have never served time in prison. The data set includes information on each person’s current wage, education, age, ethnicity, gender, tenure (time in current job), and occupation, as well as whether the person was ever incarcerated. The researcher plans to estimate the effect of incarceration on wages by regressing wages on an indicator variable for incarceration, including in the regression the other potential determinants of wages (education, tenure, and so on).
The information provided indicates that the means test is too narrow because it excludes factors like the type of engineer, amount of education, and experience. The type of engineer or educational level may be a reflection of the gender with lower earnings.
Additional information on the factors, including gender, education, and the type of engineer, could enhance the research.
Then, it is advised to build a multiple regression where the wage is the dependent variable and the other four variables are independent variables. The "difference in means" test is not appropriate for identifying gender bias in salary setting due to the significance of the omitted variable.
The variables which are likely useful to add to the regression to control for important omitted variables are excessive drug or alcohol use and their gang activity.
To learn more about regression
brainly.com/question/27426965
#SPJ4
11/x = 13/17 round answer to the nearest tenth
Answer:
To solve this equation, you can use cross multiplication to eliminate the fractional terms. Doing so gives you 11 * 17 = 13 * x. Solving for x gives you x = (11 * 17)/13. Dividing these two numbers gives you approximately x = 8.46. Rounding this number to the nearest tenth gives you x = 8.5. Therefore, the value of x that makes the equation true is approximately 8.5.
Using complete sentences, explain thoroughly what is meant by the given formula:
a 1 =
: 10
an = an-1+4
The meaning of the given formula is that the first term (a₁) is equal to the nth term (aₙ) of a sequence multiplied by 10 and it is also equal to the preceding nth term (aₙ₋₁) of a sequence plus four (4).
What is an arithmetic sequence?In Mathematics, an arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
How to calculate the nth term of an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Based on the information provided, we can logically deduce that the first term (a₁) of the arithmetic sequence can either be calculated by multiplying the nth term (aₙ) by ten 10 or adding four (4) to the preceding nth term (aₙ₋₁) of the arithmetic sequence.
Read more on arithmetic sequence here: brainly.com/question/12401000
#SPJ1
50 POINTS BABY!! PLEASE HELP ASAP
Answer:
I think 50
Step-by-step explanation:
Scott can eat at most 15 muffins without feeling sick. If Scott is feeling sick, which range best describes the number of muffins he might have eaten?
WRITE AS AN INEQUALITY EQUATION
WILL BE REPORTED BY ALL 51 OF MY ACCOUNTS
Answer: Muffins > 15 (Greater than 15)
Step-by-step explanation: If the most Scott can eat without feeling sick is 15 muffins, this means that any more muffins would make him sick. The amount of muffins to make Scott sick would have to be greater than 15.
7. You need to find the height of a nearby tree. Instead of climbing the tree, you decide to
use the length of your shadow and the shadow of the tree. Use the image below to find
the height (h) of the tree to the nearest foot.
The height of a nearby tree is 15ft
What is Application of trigonometry ?
Trigonometry is the study of lengths, heights, and angles through computations involving triangles. There are many applications for trigonometry and its functions in daily life. For instance, it is employed in astronomy to gauge the distances between nearby stars, in geography to gauge the separations between landmarks, and in the satellite navigation system.
According to question
let
The height of tree = h
Angle elevation = α
Given
Length of shadow of tree = 20 ft
height of man = 6 ft
Length of shadow of man = 8 ft
We know that
tanθ = Perpendicular/Base
therefore:
tanα = 6/8 = h/20
⇒ 6*20 = 8h
⇒ 120 = 8h
⇒ h = 120/8
⇒ h = 15
hence, the height of a nearby tree is 15 ft.
To learn more about Application of trigonometry , check out
https://brainly.com/question/29155955
#SPJ1
One month Trey rented three movies and five video games for a total of $35. The next month he rented six movies and two video games for a total of $20. Find the rental cost for each movie and each video game.
The rental cost for each movie and each video game is 2.25.
One month Trey rented three movies and five video games for a total of 35.
3 M + 5V = 33
6 M + 2 V = 24
Divides bottom equation by 2:
3 M + 5 V = 35
3 M + V = 20
subtracts:
4V = 21
V = 21/4 = $5.25
3 M + 5.25 = 12
3 M = 6.75
M = 2.25
Let x = cost to rent a movie and y = cost to rent a video game
3x + 5y = 33
6x + 2y = 24
Multiply the first equation by -2:
-6x - 10y = -66
6x + 2y = 24
Add the equations to get -8y = -42
So, y = 5.25 and x = 2.25.
To learn more about video games visit:
https://brainly.com/question/8910338
#SPJ1
Your family plans to start a small business in your neighborhood. Your father borrows
$10, 000 from the bank at an annual interest rate of 8% rate for 36 months. What is the
amount of interest he will pay on this loan?
The amount of interest he will pay on this loan$12,400.
What is interest?
The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as an annual percentage of the loan amount. The interest rate on the loan is known as this percentage.
Principal = $10,000
Rate = 8%
Time = 36 months, 1 year - 12 months
36 months - 36/12= 3 years
S.I. = PRT/100
10,000*8*3/100
240,000/100 = $2,400
A = P+I = 10,000+2,400= $12,400
To learn more about interest visit:https://brainly.com/question/29480777
#SPJ1
Jason bought two different types of boards to make picture frames. He bought a red cedar board and will cut it into eight 10.25-inch pieces. He also bought a tiger maple board that he will cut into sixteen 10.5-inch pieces. Determine the difference between the boards’ total lengths.
The difference between the boards’ total lengths is 86 inches.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The difference between the total lengths of the boards is the positive value when we subtract one from another.
The total length of the red cedar board is = (8×10.25) = 82 inches.
The total length of the tiger maple board is = (16×10.5) = 168 inches.
∴ The difference is (168 - 82) = 86 inches.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
Susan plans to attend college in 3 years. She will need $ 17,400 for the first-year cost. Her uncle gave her a special gift of $12,000 to use toward the cost. How much must Susan save each month to have enough for the first-year cost?
Answer:
$150 per month
Step-by-step explanation:
Susan plans to attend college in 3 years. She will need $ 17,400 for the first-year cost. Her uncle gave her a special gift of $12,000 to use toward the cost. How much must Susan save each month to have enough for the first-year cost?
17,400 - 12,000 = $5,400 Susan needs to pay in 3 years.
3 years = 36 months
$5,400/36 = $150 per month
3. List all the factors of the number 30. (1 point) 1, 2, 3, 5, 6, 10, 15, 30 2, 3, 4, 10, 20, 30, 40 1, 2, 4, 5, 10, 15, 30 1, 2, 4, 5, 8, 10, 20, 40
Answer:
1,2,3,5,6,10,15,30
Step-by-step explanation:
1*30
2*15
3*10
5*6
A stone is dropped from the edge of a roof, and hits the ground with a velocity of −165 feet per second. Assume the acceleration due to gravity is -32 feet per second squared. How high (in feet) is the roof?
Answer:
425.39 ft
Step-by-step explanation:
[tex]\frac{1}{2}mv^2=mgh\\\frac{1}{2}v^2=gh\\v^2=2gh[/tex]
h = [tex]\frac{v^2}{2g} = \frac{165^2}{2 * 32}=\frac{27225}{64}=425.39ft[/tex]
The measurement of the radius of the end of a log is found to be 8 inches, with a possible error of 1/8 inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.
By using the differentials to approximate the possible propagated error in computing the area of the end of the log is ±2π
The measurement of the radius of the end of a log = 8 inches
The possible error of radius = 1/8 inches
The area of cross section of the end of the log = πr^2
A = πr^2
dA / dr = 2πr
dA = 2πr(dr)
Here the possible error of radius = 1/8 inches
dr = 1/8 inches
Substitute the values in the equation
dA = 2π × 8 × (± 1/8)
= ±2π
Therefore, the possible propagated error in computing the area is ±2π
Learn more about area here
brainly.com/question/22741115
#SPJ4
Use the formula A=P(1+r/n)ⁿ⁺ to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The time when the money will double is 11.6 years
How to determine the time when the money will double?From the question, we have the following parameters that can be used in our computation:
Principal amount, P = $900Rate of interest, R = 6%Number of years = tNumber of times compounded, n = 12 i.e. monthlyWhen the money doubles, the amount is
A = 900 * 2
A = 1800
The compound interest formula is given as
A = P(1 + r/n)^nt
Also from the question, we have
n = 12
This is so because the loan is compounded 12 times in a year as a result of being compounded monthly
Solving further, we replace the variables with their values in the above equation
1800 = 900 * (1 + (6%)/12)^(t*12)
Divide both sides by 900
2 = (1 + (6%)/12)^(t*12)
Also, we have
2 = (1.005)^(t*12)
Take the logarithm of both sides
12t = log(2)/log(1.005)
Evaluate the quotients
12t = 139
Divide both sides by 12
t = 11.6
Hence, the number of years is 11.6 years
Read more about compound interest at:
brainly.com/question/2455673
#SPJ1
Question 4
What is the solution of the equation? Prove your answer to be correct.
1/3(6z + 7.2) = 0.5(8z + 2) - 0.4
a. z = 0.8
b. z = 0.9
c. Z = 2.8
d. z = 3.6
The value of z in the equation 1/3(6z + 7.2) = 0.5(8z + 2) - 0.4 is z=0.9
How to solve the equation?
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division.Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.1/3(6z + 7.2) = 0.5(8z +2) -0.4
(6/3)z + 7.2/3 = (8/2)z + 2/2 - 0.4
2z + 2.4 = 4z + 1 - 0.4
2z - 4z = 0.6 - 2.4
-2z = -1.8
z= 0.9
Hence, the value of z in the equation 1/3(6z + 7.2) = 0.5(8z + 2) - 0.4 is z=0.9
To know more about equation check the below link:
https://brainly.com/question/26310043
#SPJ1
A movie theater has a seating capacity of 367. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $2660 on a sold out night, how many children, students, and adults attended?
Number of children adults and students who attended the theatre is 182 , 91 , 94 respectively
Let Number of Children in theatre = c
Let Number of Adults in theatre = a
Let Number of Students in Theatre =s
Total money earned by selling the tickets = $2660
According to the given information
c + s + a = 367
a = c/2
5c + 7s + 12a = 2660
5c + 5s + 5a = 5(367)= 1835
Using elimination and substitution method
subtract
2s +7a = 2660-1835 = 825
2s +7(c/2) = 2s +7c/2 = 825
4s +7c = 1650
c + s + c/2 = 367
2c + 2s + c =734
2s + 3 c =734
4s + 6c=1468
4s + 7c =1650
c = 182 children
a= 91 adults
s = 367-273 = 94 students
Number of children adults and students who attended the theatre is 182 , 91 , 94 respectively
To know more about Elimination method
https://brainly.com/question/29100420
#SPJ1
a norman window consists of a rectangle surmounted by a semicircle. if the perimeter of a norman window is to be 32 feet, determine what should be the radius of the semicircle and the height of the rectangle such that the window will admit the most light.?4.49 ft.
Therefore, the height of the rectangle and the radius of the semicircle should be 8 feet each in order for the Norman window to admit the most light.
What is the perimeter of a semi circle?The distance along the line defining a half circle's boundary is known as the semi circle's perimeter. It is made up of the diameter of the semi circle, which is a straight line that passes through the center of the circle, and the semi circle's curving arc. For example, he radius of the semicircle and the height of the rectangle such that the window will admit the most light. A semi circle's diameter must be determined before calculating the circumference. This may be accomplished by determining the radius of the semicircle, which is the separation between any two points on the circle and the circle's center. Simply said, the diameter is twice the radius.
How to solve?
If the perimeter of the Norman window is 32 feet, then each side of the rectangle must be 8 feet long. ( using 2(l+b))
The radius of the semicircle must also be 8 feet, as the perimeter of a semicircle is equal to 2 * pi * radius.
To learn more about perimeter of a semi circle, visit:
https://brainly.com/question/14429410
#SPJ4
PLEASE ANSWER CLEARLY WITH THE EQUATION
Aisha is working two summer jobs, making $7 per hour babysitting and $8 per hour landscaping. Last week Aisha worked 2 more hours babysitting than hours landscaping and earned a total of $134. Write a system of equations that could be used to determine the number of hours Aisha worked babysitting last week and the number of hours she worked landscaping last week. Define the variables that you use to write the system.
After solving the provided question, Aisha spent 7.9 hours and 9.9 hours, respectively, working last week as a babysitter and a landscaper.
Which is an equation?A mathematical statement that has at least two terms, both of which contain variables or equal integers, is defined as an equation.
Aisha is reportedly working two summer jobs, earning $7 an hour for babysitting and $8 an hour for gardening.
Let's say you were to watch the children for x hours.
And y would be the amount of hours spent on landscaping.
Last week, Aisha spent two more hours babysitting than a landscaper, earning a total of $134.
[tex]y = x + 2\\7x + 8y = 134\\Substitute the value of y = x + 2 in the equation,\\7x + 8(x + 2) = 134\\7x + 8x + 16 = 134\\15x = 134 - 16\\15x = 118\\x = 118/15\\x = 7.9\\Substitute the value of x = 7.9 in the equation y = x + 2 ,\\y = 7.9 + 2\\y = 9.9\\[/tex]
To more about the equation here:
https://brainly.com/question/649785
#SPJ1
Solve the systems of equations graphed on the coordinate axes below.
The solution of the system of equation y = -x + 3 and y = 3x + 7 will be (-1,4).
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.
As per the given system of equations,
y = -x + 3 and y = 3x + 7
Compare both,
3x + 7 = -x + 3
3x + x = 3 - 7
x = -1
y = -(-1) + 3 = 4
So the solution will be (-1,4).
Hence "The system of equations y = -x + 3 and y = 3x + 7 will have the following solution: (-1,4).".
For more about the equation,
brainly.com/question/10413253
#SPJ1
For the following, find the arc length:
(Use \large \pi=3.14 and round your final answer to the hundredths.)
x=_________
Answer:
x = 10.47
Step-by-step explanation:
circumference = 2 * 10 * π = 20π
centre angle of a circle (in radiant) = 2π
x : 20π = π/3 : 2π
x = (20π * π/3)/ 2π
x = 10 * π/3
x = 10π/3
x = 10.466667
x = 10.47
Which graph shows a proportional relationship between the number of hours of renting a lawn mower and the total amount spent to rent the lawn mower? PLEASE HELP! ASAP
35 POINTS use photo
What is the first equation?
3x - 3y =
What is the second equation?
3x + y=-6
The equations are 3x - 3y = 4 and 3x + 2y = -6.
What is a system of linear equations in matrices?
A system of linear equations can be represented in matrix form using a coefficient matrix, a variable matrix, and a constant matrix. Consider the system, 2x+3y=85 and x−y=−2. The coefficient matrix can be formed by aligning the coefficients of the variables of each equation in a row.
In the given matrix,
The first equation would be
3x - 3y = 4
and the second equation would be
3x + 2y = -6
Hence, the equations are 3x - 3y = 4 and 3x + 2y = -6.
To learn more about the System of linear equations in matrices, visit:
https://brainly.com/question/27929071
#SPJ1
Find how long it takes $2500 to double if it is invested at 6% interest compounded semiannually. Use the formula A=P(1+r/n) to solve the compound interest problem.
It will take approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
After 11.71 years the amount will double to the principal amount
What is Compound interest:Compound interest refers to the interest added to a loan or deposit that depends on both the principal amount and compound interest rate and the number of compoundings in a year.
The formula for the amount in compound interest is given by
Amount, A = P(1+r/n)^ntwhere P = Principal amount
r = Rate of interest
n = Number of compounds
t = Time period
From the given data
Principal amount, p = $ 2500
Rate of interest, r = 6% = 6/100 = 0.06
Number of compounds, n = 2 [ ∵ 12/6 = 2 ]
Here we need to find the time period
Let's assume that after 't' years the amount will be doubled i.e $ 5000
From the given problem,
Amount, A = 2500(1+0.06/2)^2t
= 2500(1+0.06/2)^2t
= 2500(1 + 0.03)^2t
= 2500 (1.03)^2t
As we assumed after 't' years the amount is $ 5000
=> 2500 (1.03)^2t = 5000
=> (1.03)^2t = 5000/2500
=> (1.03)^2t = 2
Apply to log on both sides
=> log (1.3)^t = log 2
=> 2t log (1.3) = log 2
=> 2t = log 2/ log(1.03)
=> 2t = 23.4497722
[ use calculator for log (1.03) and log 2 values]
=> t = 11.7248861
=> t = 11.71 ≅ 11 years
Therefore,
After 11.71 years the amount will double to the principal amount
Learn more about Compound interest at
https://brainly.com/question/25857212
#SPJ4
Which of the options is a solution for the following system of inequalities?
2x+y >3
x-y >1
O (5,-2)
O (0,-5)
O (0,0)
O (0,5)
The solution for the given system of inequalities is (5,-2). which is the correct answer would be an option (A).
The first inequality, 2x + y > 3, can be rewritten in slope-intercept form as y > -2x + 3. This represents a line with a slope of -2 and a y-intercept of (0,3).
The second inequality, x - y > 1, can also be rewritten in slope-intercept form as y < x - 1. This represents a line with a slope of 1 and a y-intercept of (0,-1).
When you graph these two lines, you will get two lines that intersect at some point. The region of the graph that satisfies both inequalities will be the area that is bounded by these lines and lies above or below them, depending on the inequality symbol.
In this case, the solution to the system of inequalities is the region of the graph that is above the line y = -2x + 3 and below the line, y = x - 1. This region is shaded in the graph below.
From the graph, you can see that the solution includes all points in the shaded region. You can also see that points B (0,-5), C (0,0) , and D (0,5) is not included in the solution, while point A (5,-2) included in the solution.
Therefore, the correct answer is A (5,-2).
Learn more about inequalities here:
brainly.com/question/20383699
#SPJ1