The only solution to the system of inequalities y < −x+5 and y ≥ 3x+1 is (1,3).
What are the inequalities?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
For the inequality y < -x + 5, any point below the line y = -x + 5 will satisfy the inequality. For the inequality y ≥ 3x + 1, any point on or above the line y = 3x + 1 will satisfy the inequality.
To find the solutions that satisfy both inequalities, we can shade the region that is below the line y = -x + 5 and also on or above the line y = 3x + 1. This region is the shaded triangle bounded by the lines y = -x + 5, y = 3x + 1, and the x-axis.
Therefore, the solutions to the system of inequalities are the points in this shaded triangle. To check which options are solutions, we can substitute the values of x and y given in each option into both inequalities and check if they satisfy both.
(0,2): y < -x + 5 is true because 2 < -0 + 5. y ≥ 3x + 1 is false because 2 < 3(0) + 1. Therefore, (0,2) is not a solution.(1,3): y < -x + 5 is true because 3 < -1 + 5. y ≥ 3x + 1 is true because 3 ≥ 3(1) + 1. Therefore, (1,3) is a solution.(2,1): y < -x + 5 is true because 1 < -2 + 5. y ≥ 3x + 1 is false because 1 < 3(2) + 1. Therefore, (2,1) is not a solution.(3,6): y < -x + 5 is false because 6 ≥ -3 + 5. y ≥ 3x + 1 is true because 6 ≥ 3(3) + 1. Therefore, (3,6) is not a solution.Hence, the only solution is (1,3).
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Complete question:
Which of the following are solutions to the system of inequalities y < −x+5 and y ≥ 3x+1?
Select all that apply.
a. (0,2)
b. (1,3)
c. (2,1)
d. (3,6)
Identify the solution for the system of equations and explain its meaning using the context from the real-world problem.
I GOT THE ANSWER BUT I NEED THE EXPLANATION
The linear equation in this situation is y=20x which will have its solution as per the values of 'x'.
Explain about the System of Linear Equations?A collection of more that two linear equations is known as a system of linear equations. It's possible for a linear equation to have a number of variables.There are numerous uses for a system of linear equations. Real-world problem like assessing cost, distance, lifespan, profit, etc., as an example. Every unknown quantity can be found for a given quantity by using it.For instance, the cost of a good for a certain amount can be determined using a linear equation.
If a unit of a single product costs $20, the equation would be y=20x.In this case, x is the quantity of items and y is the price.The linear equation in this situation is y=20x.
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n the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 125 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 132 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
First, we need to find the number of people who went to the pool in the second, third, and fourth weeks.
Number of people in second week = 1,120 - 125 = 995
Number of people in third week = 995 + 145 = 1,140
Number of people in fourth week = 1,140 - 132 = 1,008
To find the percent decrease, we need to find the difference between the number of people in the first week and the fourth week, and then divide by the number of people in the first week.
Difference between first and fourth weeks = 1,120 - 1,008 = 112
Percent decrease = (112/1,120) x 100% = 10%
Therefore, the percent decrease in the number of people who went to the pool over these four weeks is 10%.
Suppose your boss proposes an alternative form of payment. For the first day of each month, you’ll earn a penny. Thereafter, each workday your wages will double what they were the day before. If there are 20 workdays in a month, how much would you make for the month?
We will make ₹1,048,575 for the month. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?The four basic operations, often referred to as "arithmetic operations", are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.
We are given that for the first day of each month, a penny is earned. Thereafter, each workday wages will double what they were the day before.
Now, since there are 20 workdays in a month so, the total amount earned is as follows:
⇒ 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1,024 + 2,048 + 4,096 + 8,192 + 16,384 + 32,768 + 65,536 + 131,072 + 262,144 + 524,288
⇒ ₹ 1,048,575
Hence, we will make ₹ 1,048,575 for the month.
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Use the diagram of the cylinder to answer the question. Use 3.14 for π and round to the nearest tenth. SHOW PROOF PLEASE
803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.
What is the surface area of a solid?Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.
According to the given information:The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given values, we get:
Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8
= 401.92 + 401.92
= 803.84 square inches
the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.
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pls show work i’m struggling
The distance between points A and B is 6 units.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
We are given that;
The points= (-1.4) and B (5.-2)
Now,
To find the distance between points A (-1.4) and B (5.-2), we can use the distance formula:
d = [tex]\sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.
Substituting the values we have:
[tex]\sqrt{(5 - (-1))^2 + (-2 - (-4))^2}[/tex]
d = [tex]\sqrt{(5 + 1)^2 + (-2 + 2)^2}[/tex])
d = [tex]\sqrt{(6^2 + 0^2)}[/tex]
d = [tex]\sqrt{36}[/tex]
d = 6
Therefore, by the distance formula answer will be 6 units.
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Dan has 16 pencils. Quentin gives him
5 more pencils. Choose all the ways you
can use to find how many pencils Dan
has in all.
016 +5
o 16 + 4+
o 16-5
16 + 5
Because Dan has 16 pencils and he gets 5 more
The equation Q=2s2+4sh represents the surface area, Q, of a cracker box in the shape of a square prism with a base side length of
In square prism , A cracker box in the shape of a square prism with a base side length of [tex]SA - \frac{2S^{2} }{4S} = h[/tex].
What is square prism?
The bases of a square prism are square, and the other four faces are rectangles. A square prism is a cuboid object in three dimensions.
Angles and sides that are in opposition to one another are congruent. A magnet bar is an illustration of the shape of a square prism.
we know that'
The formula to calculate the surface area of a square prism is
[tex]Q = 2s^{2} + 4sh[/tex]
subtract 2s² both sides
SA - 2s² = 4sh
Divide by 4s both sides
[tex]SA - \frac{2S^{2} }{4S} = h[/tex]
Rewrite
[tex]SA - \frac{2S^{2} }{4S} = h[/tex]
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Find the centroid of the region bounded by the given curves y=2-x^2 , y=x
The centroid of the region is at the point (0, 2/5).
What is the centroid of the region bounded by the curves?To find the centroid of the region bounded by the curves y=2-x² and y=x, we first need to find the limits of integration and the expressions for the x-coordinate and y-coordinate of the centroid.
The curves intersect at (1,1) and (-1,1), so we will integrate over the interval [-1,1].
To find the x-coordinate of the centroid, we need to evaluate the following integral:
x' = (1/A) ∫[a,b] xf(x) dx
where;
A is the area of the region (which we can find by integrating the difference between the two curves).A = ∫[a,b] (f(x) - g(x)) dx
In this case, f(x) = 2 - x² and g(x) = x, so
A = ∫[-1,1] (2 - x² - x) dx
= [2x - (1/3)x³ - (1/2)x²] | from -1 to 1
= (4/3)
Now we can evaluate the x-coordinate of the centroid:
x' = (1/A)∫[-1,1] x*(2-x²-x) dx
= (1/(4/3))∫[-1,1] (2x - x³ - x²) dx
= (3/4) [(x²/2) - (1/4)x⁴ - (1/3)x³] | from -1 to 1
= 0
So the x-coordinate of the centroid is 0.
To find the y-coordinate of the centroid, we need to evaluate the following integral:
y' = (1/A) ∫[a,b] (1/2) [f(x)² - g(x)²] dx
y' = (1/(4/3)) ∫[-1,1] (1/2)[(2-x²)² - x²] dx
= (3/4)[(8/15)x⁵ - (2/3)x³ + (1/2)x] | from -1 to 1
= (2/5)
So the y-coordinate of the centroid is 2/5.
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Kristoff needs to fill in the blanks below to factor x2 - 12x + 20. Which of the following is
NOT true about the missing values?
The factor that both trinomials have in common is; C: (x + 2)
How to factor polynomials?In mathematics, a polynomial is defined an expression that consists of variables that are also referred to as indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² - 7x - 18
The trinomial of james is;
x² - 7x - 18
Factorizing this gives;
x² + 2x - 9x - 18
= x(x + 2) - 9(x + 2)
= (x + 2)(x - 9)
The trinomial of Kaitlin is;
x² + 14x + 24
Factorizing this gives;
x² + 12x + 2x + 24
= x(x + 12) + 2(x + 12)
= (x + 2)(x + 12)
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guys pls give the correct answer quickly
The True statement is:
All the four function cut the y axis at (0, 3)
What is Intercept?The point at which the line or curve crosses the graph's axis is referred to as the intercept. When a point crosses the x-axis, it is referred to as the x-intercept. When a point crosses the y-axis, it is referred to as the y-intercept.
We have Four function
f(x) = 4[tex](2)^x[/tex] -1
g(x) = 3[tex](1/4)^x[/tex]
h(x) = [tex](1/2)^x[/tex] + 2
k(x) = -[tex]3^x[/tex] + 4
We have represented all the graph given below.
First, there is no function whose have negative y intercept.
Only f(x) have negative x intercept.
But all the four function cut the y axis at (0, 3)
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√49is a
√50is a
V/127 is a non-perfect
125 is rational because it is equal to a
square and therefore
square and therefore
and therefore irrational.
number.
√49 is a rational number. √50 is an irrational number. √127 is an irrational number. 125 is a rational number because it is equal to a perfect cube of the whole number 5.
What does an irrational number look like?A real number is considered to be irrational if it cannot be written as a simple fraction. It cannot be described using a ratio. When p and q are numbers and q is not identical to 0, N is not equivalent to p/q if N is irrational. An illustration of this is the illogic of the integers
Why are certain numbers irrational?A actual number that's unable to be written as the ratio between two integers—that is, as p/q, where both p and q both are integers—is an irrational number.
√49 is a rational number because it is equal to 7, which is a whole number.
√50 is an irrational number because it cannot be expressed as a fraction of two integers and it is not a perfect square.
√127 is also an irrational number because it cannot be expressed as a fraction of two integers and it is not a perfect square.
125 is a rational number because it can be expressed as 5^3, which is a perfect cube of the whole number 5.
Therefore, the correct statements are:
√49 is a rational number.
√50 is an irrational number.
√127 is an irrational number.
125 is a rational number because it is equal to a perfect cube of the whole number 5.
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NEED HELP ASAP!!!
An auto mechanic's current annual gross wage is $47,500. For retirement, the mechanic wants to have enough saved to live off 80% of the current annual gross wage and draw 4% the first year. What is the total amount the mechanic will need in retirement savings to meet their retirement income goal?
A. $590,000
B. $950,000
C. $1,520,000
D. $900,500
The total amount the mechanic will need in retirement savings to meet their retirement income goa is (B) $950,000, the correct option is B
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
We are given that;
Annual gross wage= $47,500
Percentage saved= 80%
Draw in 1 year=4%
Now,
To calculate the total amount the mechanic will need in retirement savings to meet their retirement income goal, we can follow these steps:
Determine the retirement income goal: The mechanic wants to live off 80% of their current annual gross wage, which is:
0.8 x $47,500 = $38,000 per year
Calculate the amount of savings needed to generate the retirement income: The mechanic wants to draw 4% of their savings in the first year, so the amount of savings needed to generate $38,000 per year is:
$38,000 / 0.04 = $950,000
Therefore, by the given interest rate answer will be $950,000.
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ALL
A cube lies inside a cylinder as shown The sides of the cube measure 3.2 inches and the diameter of the cylinder is 4.5 inches. What is the geometric probability of the cube? Use 3.14 for pl and round to the nearest tenth
06
0.16
0.46
0.36
The geometric probability of the cube is 0.64
How to determine the geometric probability of the cube?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Cube side length, l = 3.2 inchesDiameter of cylinder, d = 4.5 inchesHeight of cylinder, h = 3.2 inchesNext, we calculate the volumes of the cube and the cylinder using the following formulas
V(Cube) = l³
V(Cylinder) = πr²h
So, we have
V(Cube) = 3.2³ = 32.768
V(Cylinder) = 3.14 * (4.5/2)² * 3.2 = 50.868
The geometric probability of the cube is then calculated as
P = V(Cube)/V(Cylinder)
So, we have
P = 32.768/50.868
Evaluate
P = 0.64
Hence, the probability is 0.64
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A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was 36,800. Assume this trend continues. Let p(x) = population, and x = years since 2012. Answer the questions. -Expected Population in year 2014 =
- Predicted year when population will reach 54000 =
- The rate of population changes = ?
- The number of years for the population doubled since 2008 =
Using the equation, we found the following:
1) Expected Population in the year 2014 = 41100
2) Predicted year when the population will reach 54000 = 2020
3) The rate of population changes = 2150
4) The number of years for the population doubled since 2008 =9.12
What is a linear equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
Given,
the population in 2008 = 28,200
the population in 2012 = 36,800
The population is growing linearly.
Assume a linear equation,
p(x) = 36800 + kx
where,
p(x) = population
x = years since 2012.
k = increase in population
p(0) = 36800
p(-4) = 36800 - 4k
28200= 36800 -4k
4k = 36800 - 28200
k = 2150
Then the linear equation becomes,
p(x) = 36800 + 2150x
1) Population in 2014
x = 2014 - 2012 = 2
From the equation,
p(2) = 36800 + 2150 * 2 = 41100
2) x when p(x) = 54000
From the equation,
54000 = 36800 + 2150x
2150x = 17200
x = 8
Year = 2012 + 8 = 2020
3) Rate of population change = (population in 2012 - population in 2008) / number of years = 36800-28200 / 4 = 2150
4) Population doubled since 2008
p(x) = 2 * 28200 = 56400
We have to find x , when p(x) = 56400
Using the linear equation,
56400 = 36800 + 2150x
x = 9.12
Therefore using the equation, we found the following:
1) Expected Population in the year 2014 = 41100
2) Predicted year when the population will reach 54000 = 2020
3) The rate of population changes = 2150
4) The number of years for the population doubled since 2008 =9.12
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the number of cars in a parking lot are no more than 7.
Let c be the number of cars in the parking lot
Answer: C is less than or equal to 7
Step-by-step explanation: because the numbers of cars are not less nor greater than 7
What is solve for k=
Answer:
k=77
steps:
k/11=7
k=7*11
k=77
Answer:
k = 77Step-by-step explanation:
[tex]\tt \cfrac{k}{11} =7[/tex]
The opposite of division is multiplication, so we need multiply both sides by 11:-
[tex]\tt \cfrac{k}{11}\times 11 =7\times 11[/tex]
[tex]\tt k=7\times 11[/tex]
[tex]\tt k=77[/tex]
______________________
Hope this helps! :)
a) Write a similarity statement.
b)lf BC = 2 and DC = 10. AD =
Step-by-step explanation:
a) BD/AD=AB/AC=AD/CD; BD/AB=AB/BC=AD/AC; AD/AB=AC/BC=CD/AC;
b) if BC=2 and DC=10, then it is possbile to write:
BD/AD=AB/AC=AD/10; BD/AB=AB/2=AD/AC; AD/AB=AC/2=10/AC, then
AC/2=10/AC and AC²=20. According to the Pyphagorean's theorem AD²=AC²+CD² and AD=√120≈10.96
If the given sample variance is 17.56, what is the standard deviation?
According to the preceding statement, then standard deviation becomes 4.19 if the sample variance is given as 17.56.
How to interpret a standard deviation?A measurement of a data set's departure from the mean is referred to as "standard deviation" (or ""). Whereas a large variance shows that the numbers are more spread, a lower number suggests that its data are clustered around the mean. The standard deviation is a measure of how volatile your collected data is generally. It displays the standard deviation for every score with respect to the mean.
We must consider the square root of both the sample covariance matrix to determine the standard deviation.
= √17.56
≈ 4.19
Hence, their standard deviation is around 4.19
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Hamburgers can be purchased from two different popular fast food restaurants. Restaurant A sells 11 burgers for $14.52, and Restaurant B sells 2 burgers for $2.58. Which restaurant offers the best value per hamburger, and what is its amount?
Restaurant A for $1.29
Restaurant B for $1.29
Restaurant A for $1.32
Restaurant B for $1.32
Answer: Restaurant B
Step-by-step explanation:
First, Divide 14.52 by 11 as shown below to get the cost per burger for Restaurant A:
14.52/11 = 1.32
Next, divide 2.58 by 2 for the cost of the burger at Restaurant B:
2.58/2 = 1.28
Now we can see that Restaurant B's burgers are 4 cents cheaper than Restaurant A.
Good Luck!
An
18
inch pizza from Pizza Pi has
12
servings and
1
,
725
calories. Kayla has enough pizza for each person to eat one slice. If Kayla has
8
,
625
calories worth of pizza, how many people does she feed?
Answer:
60Step-by-step explanation:
We need to divide 8625/1725
I used calculator and got 5.
Kayla has 5 pizzas.
Each pizza has 12 slices so we multiply 5x12.
That is 60.
FAQ:
Why do we multiply 5 by 12?
Answer: Each pizza has 12 slices. If we want to know how many slices 2 pizzas have, we would multiply 12 by 2. The ratio of pizza to slice is 12:1.
Pizza is 12x bigger than individual slice
(I want pizza now)
Measure of arc ML=76 Degrees and Measure of Angle JLK = 54 Degrees. What is the value of X
The value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Measure of arc ML=76 Degrees and
Measure of Angle JLK = 54 Degrees
We have to find the value of x
O is the centre of the circle.
As we see the figure angle L is corresponding to 54 degrees.
x=54
Hence, the value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.
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What is the distance from Point A to BC?
The least distance by Pythagorean theorem is equal to √5. (Correct choice: B)
How to determine the least distance of a point to a line
In this problem we find the representation of a point and a line on Cartesian plane. There is a least distance between the point and the line when the line segment between them is perpendicular to the line. The line segment AC fulfill these features. Given the location of points A and C, we can determine the distance by means of Pythagorean theorem:
d = √[(Δx)² + (Δy)²]
Where:
d - DistanceΔx - Change in variable x.Δy - Change in variable y.If we know that A(x, y) = (1, 3) and C(x, y) = (3, 2), then the least distance between the point and the line:
d = √[(3 - 1)² + (2 - 3)²]
d = √[2² + (- 1)²]
d = √5
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?????????????????????????
Answer:
(-5, 2)
Step-by-step explanation:
We can see that the g(x) is a translated form of f(x) using the formula:
y = (x - h)³ + k,
where (h, k) is the origin of the graph's translation.
We can assign the following h and k values based on the given g(x):
g(x) = (x + 5)³ + 2
h = -5
k = 2
Finally, we can form an ordered pair (h, k):
(-5, 2)
9 How do Jaden's questions about the missing students influence the development of the plot?
Page 9
A
By causing the Puppetmaster to challenge her curiosity
B
By emphasizing the close connection between the players and the Puppetmaster
C
By persuading the teachers to begin a search for them
D By highlighting the entertainment value that the game provides each player
11133-feb 2017023 12:29 PM
00 ON
Jaden's questions about the missing students influence the development of the plot in many ways.
What is number?Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used in all areas of mathematics, including algebra, geometry, calculus, and statistics. Numbers are used to represent quantities and can be represented in a variety of ways, such as numerals, symbols, words, and graphs. Numbers can be used to measure and compare objects, define relationships between objects, and help solve problems.
Firstly, they cause the Puppetmaster to challenge her curiosity. The mysterious disappearances of the students compel the Puppetmaster to find out why they have gone missing, and to take measures to ensure that no one else goes missing. This encourages the Puppetmaster to become more involved in the game, and creates tension between her and the other players.
Secondly, Jaden's questions emphasize the close connection between the players and the Puppetmaster. The players rely on the Puppetmaster for guidance and safety, and her actions in response to Jaden's questions demonstrate her commitment to the players' wellbeing. This serves to strengthen the bond between the players and the Puppetmaster.
Thirdly, Jaden's questions persuade the teachers to begin a search for the missing students. By raising awareness of the situation, Jaden encourages the teachers to take action to investigate the disappearances and to protect the remaining students.
Finally, Jaden's questions highlight the entertainment value that the game provides each player. Her questions demonstrate her enthusiasm for the game, which encourages the other players to play with greater enthusiasm. This serves to increase the intensity of the game, and to make the game more exciting for all involved.
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Hi! Can someone please help me with this math question? Thanks!
Answer:
Quadratic since it times by 4 every time
Step-by-step explanation:
the number of square units for the area because Area=LW so A=10x10 which is 100 and perimeter is P=2L=2W so that would be P=2(10)+2(10) which is 40, therefore, the area is greater
The number of square units for the area of the square is greater than the number of units for the perimeter.
How can the area and perimeter of a square be calculated?The area of a square is calculated using the formula below:
Area of square = (length of side)²
The length of the side of the square = 10 units
Ares of the square = 10 * 10
Area of the square = 100 units
The perimeter of a square = 4 * length of the side
Perimeter of a square = 4 * 10
The perimeter of a square = 40
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Complete question:
One side of a square is 10 units. Which is greater the number of square units for the area of the square or the number of units for the perimeter?
what is the answer?????????????????
Surface Area of cuboid = 2 (lb + bh + hl)
According to the question :
length = x, width = x-5, height = 0.5x
250 = 2 ( x × (x-5) + (x-5) × 0.5x + 0.5x × x )
250 = 2 ( x² - 5x + 0.5x² - 2.5x + 0.5x²)
250 = 2 ( x² - 5x + x² - 2.5x )
250 = 2 ( 2x² - 7.5x )
250 = 4x² - 15 x
4x² - 15x -250 = 0
Mr. and Mrs. Smith took their children on a trip to the Grand Canyon. When they left home, Mrs. Smith noted the odometer read 5,478.18 miles. When they arrived at the Grand Canyon, she noted that the odometer read 6,010.63. How far had the family-driven?
Mr Smith looks their children 1 times 1
find the image coordinates of a triangle with the coordinates M(0,4), N(4,2), and P(2,-2), dilated by a scale facotr of three
The image triangle has vertices after the dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).
How to determine image coordinates of the triangleTo find the image coordinates of a triangle after dilation, we need to multiply the coordinates of each point by the scale factor.
In this case, the scale factor is 3.
So the image coordinates of the triangle with vertices M(0,4), N(4,2), and P(2,-2) after dilation by a scale factor of 3 are:
M' = (3 * 0, 3 * 4) = (0, 12)
N' = (3 * 4, 3 * 2) = (12, 6)
P' = (3 * 2, 3 * (-2)) = (6, -6)
Hence, the image triangle has vertices M'(0,12), N'(12,6), and P'(6,-6).
In summary, the image coordinates of the triangle after dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).
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Problem is down below Please find the answer.
[tex](2x-1)^{2} = 25 \iff (2x-1)^{2} = 5^{2}\\[/tex]
[tex]x > 0 \implies 2x - 1 = 5 \iff 2x = 5 + 1 \iff 2x = 6 \implies \bf x = 3\\[/tex]
[tex](3y-1)^{2} = 36 \iff (3y-1)^{2} = 6^{2}\\[/tex]
[tex]y > 0 \implies 3y-1 = 6 \iff 3y = 6 + 1 \iff 3y = 7 \implies \bf y = \dfrac{7}{3}\\[/tex]
⇒
[tex]\dfrac{3x - y}{x+y} \cdot \dfrac{1}{7} = \dfrac{3(3) - \frac{7}{3} }{7(3+\frac{7}{3} )} = \dfrac{9 - \frac{7}{3} }{7(\frac{16}{3})} = \dfrac{\frac{27-7}{3} }{7(\frac{16}{3})}=\\[/tex]
[tex]= \dfrac{\frac{20}{3} }{\frac{112}{3}} = \dfrac{20}{3} : \dfrac{112}{3} = \dfrac{20}{3} \cdot \dfrac{3}{112} = \dfrac{20}{112} = \bf \dfrac{5}{28}\\[/tex]