Please help please ! No fake answers pls

In the diagram, what are the values of x and y?

Please Help Please ! No Fake Answers Pls In The Diagram, What Are The Values Of X And Y?

Answers

Answer 1

Answer:

B

Step-by-step explanation:


Related Questions

You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys and girls are in class?


3 more boys; 5 for every 4

Answers

Answer:

By using the given ratio, we will see that there are 15 boys and 12 girls.

How we can find the number of boys and girls in the class?

The given information is:

There are 3 more boys.

There are 5 boys for every 4 girls.

Now, notice that in the ratio we have a difference of 1 boy, so if we want to have a difference of 3 boys, we must multiplicate it by 3, then we get:

3*15 boys for every 3*4 girls (remember that you can multiply both quantities on the ratio and it does not change).

15 boys for every 12 girls.

Now the difference is 3.

15 - 12 = 3

So we can conclude that there are 15 boys and 12 girls.

Step-by-step explanation:

sam and taylor own and operate a car wash service. sam cleans the interior of each car and taylor cleans the exterior. the time it takes sam to finish the interior has a mean of 202020 minutes with a standard deviation of 6.46.46, point, 4 minutes. the time it takes taylor to finish the exterior has a mean of 181818 minutes with a standard deviation of 4.84.84, point, 8 minutes. both of their finishing times are approximately normally distributed. suppose we select a car at random, and define the random variable ddd as the difference between their finishing times. we can assume that their times are independent. find the probability that they finish within 101010 minutes of each other.

Answers

They have a 0.77 chance of finishing within 10 minutes of each other.

What is probability?

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

mean of the difference between their times is the difference of the expected (or mean) times for each person,

=20-18

=2

standard deviation,

=√((6.4)²+(4.8)²)

=8

The probability,

=0.77

The probability that they finish within 10 minutes of each other is 0.77.

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(4x)
(2x + 6)°
What is the value of x?

Answers

Answer:

8[tex]x^{2} \\[/tex] + 24x

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The coordinates of the vertices of quadrilateral ABCD are A(-5, 1), B(-2, 5), C(5, 3), and D(2, -1).
Drag and drop the choices into each box to correctly complete the sentences.
The slope of AB is!
Quadrilateral ABCD is
0
the slope of BC is
the slope of CD is!
because
¹0
and the slope of AD is!

Answers

The slope of AB is 4/3, the slope of BC is -2/7, the slope of CD is 4/3 and the slope of AD is -2/7. The Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel in a parallelogram.

The vertices of Quadrilateral ABCD are A(−5, 1) , B(−2, 5) , C(5, 3) , and D(2, −1) .

The slope between 2 points is:- m=(y2-y1) / (x2-x1)

The slope of AB :

m= (5-1) / (-2-(-5))

m= 4/3                 ........................(1)

The slope of BC :

m= (3-5) / (5-(-2))

m= -2/7                 ..........................(2)        

The slope of CD :

m= (-1-3) / (2-5)

m= 4/3                  ............................(3)

The slope of AD :

m= (-1-1) / (2-(-5))

m= -2/7                  .............................(4)

Therefore,

The slope of AB is (1) 4/3, the slope of BC is (2) -2/7, the slope of CD is (3) 4/3, and the slope of AD is (4) -2/7.

Quadrilateral ABCD is a (5) parallelogram because (6) both pairs of opposite sides are parallel.

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Which graph represents the
function f(x)=4/x

Answers

Answer:

See Answer

Step-by-step explanation:

The equation − 2 x + 3 = 6 − 2 x has no solution. Which step would change the given equation so that it has infinitely many solutions? A. adding 3 to the left side of the equation B. adding 6 to the left side of the equation C. subtracting 3 from the left side of the equation D. subtracting 6 from the left side of the equation

Answers

Hhhhhhhhhhhh
The answer is D

answer these questions. ( find the variables)


1. n + 7 = 10


2. c - 2+ = 7


3. a x 3 = 15


4. a / 5 = 9


5. 9z + 2 = 38


6. 17 + 3n = 47


7. 7y - 7 = 21


8. 3x + 90 = 147


9. 26/ y + 3 = 16


10. 147 - 3x + 90

Answers

Answer:

1)3

2)9

3)5

4)45

5)4

6)10

7)4

8)19

9)2

10)unable (no equal sign?)

Step-by-step explanation:

Find the lengths of the hypotenuses (x) of the triangle whose legs are given

1) 7cm,24cm

Answers

c^2 = 625
c = 25
hyp = 25

Answer:

The length of the hypotenuse is 25 cm.

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse.

Pythagorean theorem states

[tex]a^2+b^2=c^2[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the legs or sides of the triangle.

The hypotenuse is [tex]c[/tex].

We can solve for [tex]c[/tex] by taking the square root of both sides of the equation.

[tex]c=\sqrt{a^2+b^2}[/tex]

We are given

[tex]a=7\\b=24[/tex]

Lets evaluate [tex]c.[/tex]

[tex]c=\sqrt{7^2+24^2}[/tex]

[tex]c=\sqrt{49+b^2}[/tex]

[tex]c=\sqrt{49+576}[/tex]

[tex]c=\sqrt{625}[/tex]

[tex]c=25[/tex]

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The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. what is the weight of a randomly selected pack of gum that has a z-score of 3.11? a. 39.6 grams b. 44.7 grams c. 49.5 grams d. 54.6 grams

Answers

Answer:

Step 1: Obtain the mean and standard deviation of the weights of packs of chewing gum. The weights of packs of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation 2.- grams. Step 2: Obtain the z-score of the randomly selected pack of gum. The z-score of the randomly selected pack of gum is 3.11. Step 3: Determine which of the following statements is true: The weight of this pack of gum is lighter than the mean weight by 3.11 standard deviations The weight of this pack Of gum is heavier than the mean weight by 3.11 standard deviations The weight of this pack Of gum is lighter than the mean weight by 2.4 standard deviations The weight of this pack Of gum is heavier than the mean weight by 2.4 standard deviations

Follow the attachment I have linked below and hopefully you are able to follow the instructions

4. building code does not permit building a house that is more than
35 feet tall. An architect working on the design shown at right would like
the roof to be sloped so that it rises 10 inches for each foot of horizontal
run.
(a) Given the other dimensions in the diagram, will the builder be allowed
to carry out his plan?
(b) Two vertical supports (shown dotted in the diagram) are to be placed
6 feet from the center of the building. How long should they be?

Answers

The builder will be able to execute his idea based on the other measurements in the illustration.

Explain about the inches?

In the traditional system of measurement, one inch can be referred to as a unit of length. Inches of length are either denoted by in or by ". 5 inches, for instance, can be expressed as 16 inches or 16".

Initially, 1 inch was equal to the breadth of a man's thumb. In the 14th century, King Edward II of England decreed that 3 grains of barley laid end to end and lengthwise made up 1 inch.

Historically, there have been many different standards for what an inch is exactly, but since the international yard was adopted in the 1950s and 1960s, the inch has been based on the metric system and defined as precisely 25.4 mm.

Building codes prohibit the construction of homes that are taller than 35 feet.

The building is 22 feet tall in the diagram.

                  = 35 - 22

                  = 13 feet

so the builder is allowed to carry out is plan

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15. Graph the inequality y> |x + 1|-1. Which point is NOT part of the solution?
O
O
O
O
(-1,2)
(1,3)
(-1,0)
(1,-1)

Answers

The solution for the inequality y > |x + 1| - 1 is -x - 2 > y > x and the coordinate (1, -1) is not a part of the solution so, option D is correct. The graph is attached below.

What is inequality?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

Given:

y > |x + 1| - 1

Solve the inequality as shown below,

y + 1 > |x + 1|

y + 1 > -(x + 1) and y + 1 > x + 1

y + 1 < -x - 1  and  y + 1 > x + 1

y < -x - 1 - 1  and y > x + 1 - 1

y < - x  -2 and y > x + 0

y < -x - 2  and y > x

Thus, the solution is -x - 2 > y > x.

Plot the graph by putting the values of x and find y then join the points.

Put the values from the option to check,

From y > x option 4 is not part of the solution as -1 < 1.

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nine congruent circles are inscribed in a square with a side length of 126. if a point in the square is chosen at random, what is the probability that the point is not in a circle?

Answers

There is a 21.5% chance that a point in a square with nine congruent circles drawn there won't be within one if it is chosen at random.

It is given to us that :

Nine congruent circles are inscribed in a square

The square has a side length of 126

We have to find out the probability that the point is not in a circle, if a point in the square is chosen at random.

It is known that the square has a side length of 126.

=> Area of the square = [tex](Length)^{2}[/tex]

=> Area of the square = [tex]126^{2}[/tex]

=> Area of the square = 15876 ------ (1)

It is also known to us that nine congruent circles are inscribed in the square that has a side length of 126.

=> Diameter of each circle = 126/3

=> Diameter of each circle = 42

=> Radius of each circle = 21  ------ (2)

We know that the area of a circle is given as -

Area of circle = [tex]\pi r^{2}[/tex]  ------ (3)

where,

r = radius of the circle

Substituting the value of r from equation (2) in equation (1), we have

Area of circle = [tex]\pi r^{2}[/tex]

=> Area of circle = [tex]\pi (21)^{2}[/tex]

=> Area of circle = 1385.44

=> Area of 9 circles = 12468.96    ----- (4)

Now, we can say that -

Area not in a circle = Area of square - Area of 9 circles

=> Area not in a circle = 15876 - 12468.96 [From equation (1) and (4)]

=> Area not in a circle = 3407.04    ------ (5)

We know that the probability of a outcome is given as -

Probability = Number of favorable outcomes/Total number of outcomes

So, the probability that the point is not in a circle can be calculated as -

Probability = Area not in a circle/Area of square

=> Probability = 3407.04/15876

=> Probability = 0.215

=> Probability = 21.5%

Thus, if there are nine congruent circles inscribed in a square and a point in the square is chosen at random, the probability that the point is not in a circle is 21.5%.

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Marissa just bought 100 acres of land. She wants to grow apple, peach, and cherry trees on her land. Color the
model to show how the acres could be distributed for each type of tree. Using your model, complete the table.

Answers

Answer:

Step-by-step explanation:

Robb’s Fruit Farm consists of 100 acres on which three different types of apples grow. On 25 acres, the farm grows Empire apples. Mcintosh apples grow on 30% of the farm.

if a sample includes 27 people, the degrees of freedom used in the formula to estimate the population variance would be

Answers

The degrees of freedom for the sample variance is equal to the number of data points in the sample minus 1, so for a sample of 27 people, the degrees of freedom would be 26.

The degrees of freedom for the sample variance is calculated by taking the number of data points in the sample and subtracting 1. In this case, the sample size is 27 people, so the number of degrees of freedom is 26. This is because we need to account for one degree of freedom in order to calculate the overall variance of the sample. The degrees of freedom is important in estimating the population variance because it helps to determine the size of the sample necessary to accurately estimate the population variance. By knowing the degrees of freedom, we can better understand the accuracy of our estimates and adjust our sample size accordingly.

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you are making a cake and have already put in all of the ingredients except the eggs. you go to the refrigerator and find that there are no eggs, which results in the condition known as

Answers

The condition known as "eggless baking" is a common problem when baking cakes and other desserts.

It can be caused by not having eggs in the refrigerator or by forgetting to add them to the recipe. Without eggs, the cake batter lacks structure and will not hold together when baked. Without the proteins from the eggs, the cake will be denser and less moist.

Additionally, the cake may not rise as much as desired and the texture may be crumbly or gummy. To solve this problem, you can try substituting other ingredients such as mashed bananas, applesauce, or yogurt. However, it is best to add eggs if possible to ensure the best results.

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Jamie has 2 ½ packs of sunflower seeds to cover 150 sq ft. Based on this
information, what is the number of sq ft that 1 pack of sunflower seeds will
cover?

Answers

Answer:

60 ft.^2

Step-by-step explanation:

Known area/number of packs= A / number of packs for A, where A= area of interest

150/2.5=A/1

A=60

A dance squad needs at least $800 to buy new dance outfits. They have saved $350
already. -They are selling tickets to a dance performance for $10 each. They need to sell
x tickets to have enough money to buy the new dance outfits. Which inequality
represents the situation?

Answers

Answer:

x>=45 is the req. inequality

The inequality equation for the number of tickets to be sold is x ≥ 45

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number of tickets to be sold be x

Let the total amount of money to be saved be = $ 800

The amount of money already saved = $ 350

So , the remaining amount of money = $ 800 - $ 350 = $ 450

The cost of each ticket = $ 10

So , the cost of x tickets = 10x

Now , the number of tickets to be sold to raise $ 450 is given by

10x ≥ 450   be equation (1)

On simplifying the equation , we get

Divide by 10 on both sides of the equation , we get

x ≥ 45

Therefore , the number of tickets to be sold is 45

Hence , the inequality is x ≥ 45

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A family member has two and one fourth yds of ribbon, and you add three fifths yds to it. How much ribbon would you each get if you split the total amount in half?

fifty seven over forty
fifty seven over twenty
twenty seven over forty
forty seven over twenty

Answers

The required amount of the ribbon, when split into half, is 57 / 20. Option A is correct.

What is the fraction?

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
A family member has two and one-fourth yds of ribbon, and you add three-fifths yds to it,
So,
= 2 1/4 + 3 / 5
= 9 / 4 + 3 / 5
= 57 / 20

Now,

Half of the ribbon = [57 / 20] × [1/2] = 57 / 40

Thus, the required amount of the ribbon, when split into half, is 57 / 20. Option A is correct.

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The mean of the numbers 5, 2x, 4 and 3 is 5. Find the value of x.​

Answers

Answer:

(5 + 2x + 4 + 3)/4 = 5

(12 + 2x)/4 = 5

3 + 1/2x = 5         (multiply by 2

6 + x = 10

x = 4

The numbers are 5, 8, 4 and 3.

Step-by-step explanation:

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The graph of f(x) = 7x is stretched vertically by a factor of five. Which of the following is the equation of the new graph, g(x)? A. g(x) = 5(7x) B. g(x) = 7(5x) C. g(x) = 5(7x) D. g(x) = 7(5x)

Answers

The solution is Option D.

The graph of the function after a vertical stretch of 5 is given by the equation g ( x ) = 5 ( 7ˣ )

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = 7ˣ

The function f ( x ) is stretched vertically by a factor of 5

Let the new function be represented as g ( x )

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

So , the value of the function g ( x ) is given by the equation

g ( x ) = 5 ( f ( x ) )

g ( x ) = 5 ( 7ˣ )

Hence , the function is g ( x ) = 5 ( 7ˣ )

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Which statement describes the rate of change of the line?

Answers

Answer:

20$

Step-by-step explanation:

30 to 50 is 20, 50 to 70 is 20

Anyone Know f(-10)= 4.5,f(-2)=4.5??? Help ASAP

Answers

The linear function of  f(-10)= 4.5,f(-2)=4.5 is y = 4.5.

How to represent linear function?

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, the linear function of f(-10)= 4.5, f(-2)=4.5 can be represented as follows:

Using y = mx + b

4.5 = -10m + b

4.5  = -2m + b

b = 4.5 + 10m

Hence, using substitution,

4.5  = -2m + 4.5 + 10m

4.5 - 4.5 = 8m

m = 0

Let's find b

4.5 = -10(0) + b

b = 4.5

Therefore, the linear function is y = 4.5

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Lengths of pregnancies of women are normally distributed with a mean of 266 days and a standard deviation of 16 days.

What percentage to the nearest hundredth of children are born from pregnancies lasting more than 274 days?

What percentage to the nearest hundredth of children are born from pregnancies lasting less than 246 days?

Answers

The percentage of children are born from pregnancies lasting less than 274 days are 0.02.

The percentage of children are born from pregnancies lasting less than 246 days are 0.02.

What is normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution in statistics.

The normal distribution describes a symmetrical plot of data around its mean value, with the standard deviation serving as the determinant of the curve's width. The "bell curve" is used to visually represent it.

Given:

Lengths of pregnancies of women are normally distributed with a mean of 266 days and a standard deviation of 16 days.

⇒  μ = 266,   σ = 16

Consider, the normal distribution formula

f(x) = (1 / σ√2π) e^(-1/2)(x - μ/ σ)^2

For x = 274,

f(274) = (1 / 16√2π) e^(-1/2)(274 - 266/16)^2

f(274) = 0.02

Hence, the percentage of children are born from pregnancies lasting less than 274 days are 0.02.

For x = 246

f(246) = (1/16√2π) e^(-1/2)(246 - 266/16)^2

f(246) = 0.02

Hence, the percentage of children are born from pregnancies lasting less than 246 days are 0.02.

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1) Kathy is 12 years old and Ben is 16 years old. How many years ago was Ben three times as old as Kathy?
2) Find z if 1 4/11 of z is 45
3) Emma is 10 years old. She asked her father how old he is and he said, "When you are my age, I will be 70." How old is Emma's father?
4) Jame's dog Buddy is 2 years older than his cat Fluffy. Three years ago, Buddy was three times as old as Fluffy. How old are Buddy and Fluffy now?
5) The sum of x and y age is 60. In six years, y will be eight times as old as x will be. How old is x?

Answers

1. Ten years ago, because Kathy was 2 and Ben was 6 (2 • 3).

Which of the following statements is always true?
A. A linear paris formed by complementary angles.
B. If two angles are adjacent, then they are linear pair.
C. If two angles for a linear pair
, then their sum measures 1800
D. In a linear pair, one of the two angles is an acute angle and the other is an obtuse angle.

Answers

The true statement is that A. A linear pair is formed by complementary angles.

What is a linear pair?

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.

Complementary angles are those whose combined angle is exactly 90 degrees. For instance, p angles include 30 degrees and 60 degrees.

In conclusion, based on the information, the correct option is A.

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express cos r as a fraction in simplest terms

Answers

Answer:

[tex]\frac{5}{13}[/tex]

Step-by-step explanation:

If you have studied trigonometry, you will know that [tex]cos(\theta )=\frac{adjacent}{hypotenuse}[/tex], where the adjacent is the side with both the right angle and the angle θ, and the hypotenuse is the diagonal side.

We know here that the hypotenuse is 26.

We know do not know that adjacent where both angle R and the right angle are, but we can find it using Pythagoras' Theorem, something else which you may have studied.

[tex]a^2=c^2-b^2\\a^2=26^2-24^2\\a^2=100\\a = \sqrt{100}=10[/tex]

We now know that the adjacent is equal to 10.

Therefore, we substitute them into the cos ratio, and simplify the fraction.

[tex]cos(R)=\frac{10}{26} =\frac{5}{13}[/tex]

if an athlete is tested in the back squat and is found to have a 1rm of 515 pounds (234 kg), approximately what weight should this athlete lift if he is performing ten repetitions per set?

Answers

This athlete should aim to lift approximately 70-80% of their 1RM for ten repetitions, which would be approximately 360-410 lbs (163-186 kg).

When determining the weight an athlete should lift for a given set of repetitions, it is important to consider the athlete's 1RM. 1RM stands for one-repetition maximum and is the most weight an athlete can lift for one repetition. Generally, when lifting for a set of repetitions, athletes should aim to lift 70-80% of their 1RM. In this case, the athlete has a 1RM of 515 lbs (234 kg). If this athlete was performing ten repetitions per set, they should aim to lift approximately 360-410 lbs (163-186 kg). This is a good starting point for the athlete and can be adjusted as needed depending on how it feels.

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The U.S. Weather Bureau has a station on Mauna Loa in Hawali that has measured carbon dioxide levels since 1959. At that time , there were 312 parts per million of carbon dioxide in the atmosphere. In 2005 , the figure was 389 parts per million. Find the increase in carbon dioxide levels and the percent of increase . Percent increase:96

Answers

a) By the subtraction operation, the increase in carbon dioxide levels between 1959 and 2005 is 77 parts.

b) The percentage increase in carbon dioxide levels between 1959 and 2005 is 24.7%.

What is the percentage increase?

The percentage increase is found by determining the difference between the original and final values through subtraction operation.

The difference is then divided by the original value, multiplied by 100.

The carbon dioxide levels in 1959 = 312 parts per million

The carbon dioxide levels in 2005 = 389 parts per million

The increase in dioxide levels from 1959 to 2005 = 77 parts per million (389 - 312)

The percentage increase = 24.68% (77/312 x 100)

= 24.7%

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If m<2 = 63°, then m<3 is:
63°.
27°
117°
None of these choices are correct.

Answers

Answer:

63°

Step-by-step explanation:

since they are in the form of vertically opposite angle.

find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.

Answers

The area under the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].

Consider the following parametric equations:[tex]$$x=t^2-3 t \text { and } y=\sqrt{t} \text { and the } y \text {-axis. }$$[/tex]

The objective is to find area enclosed by the curve using the formula.

The area under the curve is given by parametric equations x=f(t), y=g(t),  and is traversed once as t increases from α to β, then the formula for calculating the area under the curve:

[tex]$$A=\int_\alpha^\beta g(t) f^{\prime}(t) d t$$[/tex]

The curve has intersects with y-axis. so x=0

[tex]$$\begin{aligned}t^2-3 t & =0 \\t(t-3) & =0 \\t & =0 \text { or } t=3\end{aligned}$$[/tex]

Now we have to draw the graph,

Let f(t)=[tex]t^2-3 t, g(t)=\sqrt{t}$[/tex]

Differentiate the curve f(t) with respect to t.

[tex]f^{\prime}(t)=2 t-3[/tex]

Now, find the area under the curve use the above formula.

[tex]\begin{aligned}A & =\int_0^3(\sqrt{t})(2 t-3) d t \\& =\int_0^3(2 t \sqrt{t}-3 \sqrt{t}) d t \\& =\int_0^3\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t \\& =\left[2 \frac{t^{\frac{5}{2}}}{\frac{5}{2}}-3 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^3 \\& \left.\left.=\left[\frac{4 t^{\frac{5}{2}}}{5}-2 t^{\frac{3}{2}}\right]_0^3\right]^{\frac{5}{2}}\right] \\\\\end{aligned}$$[/tex]

[tex]& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right][/tex]

[tex]$\begin{aligned}& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right] \\& =\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}-0 \\& =\frac{6 \sqrt{3}}{5}\end{aligned}[/tex]

Therefore,  the area of the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].

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