Question 1-4
A punch bowl contained 4 liters of soda, 5 liters of orange juice, and 2 liters of raspberry juice.
Select the statements that are true.
The ratio of the entire punch bowl to the juices is 9: 11.
The ratio of the entire punch bowl to the orange juice is 11 to 5.
The ratio of orange juice to soda is 4 to 5.
4
The ratio of soda to the entire punch bowl is
11
The ratio of orange juice to raspberry juice is 5 : 2.

1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.

Given that,

We have to find how many different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.

We know that,

Total number of arrangements of 26 different letters= 26!

Let A be the number of arrangements that contains 'the' = 24! ( Total no. Of alphabet= 26 subtract the number That contains 'the' i.e, 3 and add one for 'the' 26-23+1=24)

Let B be the number of arrangements that contains 'aid' = 24! (Total no. Of alphabet minus number of letter in 'aid' and add 'aid' as an alphabet i.e, 26-23+1= 24)

Total no. Of arrangements that contains either sequence 'the' or 'aid'

A or B= (A)+(B)- (A intersection B)

24! +24! -22! = 1.239x10²⁴

Therefore, 1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.

To learn more about letter visit: https://brainly.com/question/27833473

#SPJ4

The area of the polygons sorted in ascending order of area is:

Rectangle  = 4

Triangle = 12

Square = 13

In geometry, a polygon is a planar shape defined by a restricted number of straight line segments linked to form a closed polygonal chain.

Area of the triangle is:

[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2

Where Ax and Ay are the x and y coordinates of A's vertex. The same is true for the x and y notations of the B and C vertices.

Given,

A(-4-3), B(1, -3), C(-1,2)

We have

[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2

= 24/2

= 12

As a result, the area of the triangle is 12.

We use the distance formula to calculate the area of the rectangle. The equation is as follows:

d² = (x₂ - x₁)² + (y₂-y₁)²

Where (x₁, x₂) are the first point's coordinates and (y₁, y₂) are the coordinates of the second point.

Assuming that the vertices are labeled as follows:

A(7,9), B(6,9), C(6,5), D(7,5), then

AB² = (6-7)² + (9-9)²

AB² = 1 + 0

AB = 1

BC² = (6-6)² + (5-9)²

BC² = 0² + -4²

BC = 4

CD² = (7-6)² +(5-5)²

CD² = 1² + 0²

CD = 1

DA² = (7-7)² + (9-5)²

DA² = 0² +4²

DA = 4

As is typical of a rectangle, we can deduce that AB = CD and BC = DA

Since the Area of the rectangle is AB x CD OR BC x DA

The area of the rectangle =4 x 1 = 4

We may also calculate the length of the square's sides using distance methods.

We only need the length of one side because the area of a square is provided as L2.

Hence,

AB = 3.60555

Hence the area of the square =3.60555²

= 12.9999908025

Area of the square is 13

Thus, the polygons are placed in increasing area order as follows:

Rectangle = 4

Triangle = 12

Square = 13

To know more about polygon, visit:

https://brainly.com/question/24464711

#SPJ1

Answer:

log 58.875/ log 13

Step-by-step explanation:

log 58.875/ log 13

Answer:

green

Step-by-step explanation:

green

The following is a code in python.

Python is a popular computer programming language used to create software and websites, automate processes, and analyze data. Python is a general-purpose language, which means it can be used to make many different types of programs and isn't tailored for any particular issues.

One of Python's biggest benefits is the variety of libraries and frameworks it offers. Everything from data visualization, machine learning, data science, natural language processing, and complex data analysis uses the Python Library, from NumPy to TensorFlow.

#Specify the function in

DefinedSum(tu)

# Verify whether the tuple contains 0

if len(tu) == 0

#Then, give back 0

return 0

#Otherwise

else:

#invoke the recursive function.

return tu[0]+Sum (tu[1:])

Set a variable of the tuple type

tu=(2,5,1,8,10)

#print, then invoke the function.

 print("The total of tuple is:"), sum(tu),

Output:

The sum of tuple is: 26

Here, we define the method "sum()" and send the parameter "tu" to the function, which saves the value of the tuple type.

If the length of the tuple is 0, then the if conditional expression should verify the condition and return 0.

If not, invoke the function, return the tuple's total (which is determined recursively), and exit.

Last but not least, initialize the "tu" variable of the tuple type, print, then run the sum function.

To learn more about python, click the following link :-

https://brainly.com/question/14239610

#SPJ1

True, With an 80-person sample size, we are selecting from a skewed-right distribution, hence the sampling distribution mean should likewise be skewed-right.

80 people make up the sample that was taken from the population distribution with a right skew. We may infer that the sampling distribution of the sample means would be close to normalcy given the size of the sample.

In general, the distribution is normal.

The central limit theorem states that as sample size increases, the sample mean distributions become normal, with standard deviations equaling n and mean values approximating the population mean, regardless of the underlying distribution's form. In other words, the sample means sampling distribution turns roughly normal.

Learn more about the skewed-right distribution at

https://brainly.com/question/1604092?referrer=searchResults

#SPJ4

The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

Given that:

2Ax = 0.08

Ax = 0.2

A fully discrete whole life insurance issued to (x) is 1000.

Firstly we have to find out the value of variance S.

Variance S = (insurance issued)^2 * [2Ax - Ax^2]/(1- Ax)^2

Variance S = (1000)^2 * [0.08 -  0.2^2]/(1- 0.2)^2

Variance S = (1000)^2 * [0.04]/.64

Variance S = (1000)^2 * .0625

Variance S = 62500

Standard deviation of S = (insurance issued) * [[tex]\sqrt{2Ax - Ax^2}[/tex]]/(1- Ax)

Standard deviation = 1000 * [[tex]\sqrt{0.08 - 0.2^2}[/tex]]/(1- 0.2)

Standard deviation = 1000 * 0.2/0.8

Standard deviation = 1000 * 1/4 = 250

The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

To learn more about the standard deviation visit: https://brainly.com/question/12402189

#SPJ4

Answer:

24π m

Step-by-step explanation:

r = 12 m

C = 2πr

C = 2 × π × 12 m

C = 24π m

Answer: $1.05 per orange

Step-by-step explanation:

12.33 - 2.88 = 9.45

9.45 ÷ 9 = 1.05

The dimensions of the package of maximum volume that can be sent are 20 inches by 40 inches.

Let us represent the length of the square cross-section of the postal package with x, and the width of the package with y.

So, the perimeter is given by the equation -

y + 4x = 120

y = 120-4x    -----------(1)

the volume will be

V = [tex]x^{2} y[/tex]        -----------(2)

Now, substitute (1) in (2), and we get,

V = [tex]x^{2}[/tex] (120-4x)

V = 120[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]

Differentiating with respect to x, we get,

V' = 240x - 12[tex]x^{2}[/tex]

V'=0

hence, 240x - 12[tex]x^{2}[/tex] = 0

12[tex]x^{2}[/tex] = 240x

dividing by 120x on both sides,

hence, x=20

Now, we know that,

y = 120 - 4x

y = 120-4(20)

y = 120-80

y=40

Hence, the dimensions that maximize the volume of the package are 20 inches by 40 inches.

Read more about maximum volumes:

brainly.com/question/10373132

#SPJ4

P(4, 7.25) are the coordinates of circumcentre of the triangle

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect

Given: The vertices R(-2,5), S(-6, 5), T(-2,-1)​

Let P(x,y) be the circumcentre of triangle. Then,

PR = PS = PT

PR² = PS²

(x-(-2))² + (y-5)² = (x-(-6))² + (y-5)²

(x+2)² + (y-5)² = (x+6)² + (y-5)²

x²+4x+4 + y²-10y+25 = x²+12x+36 + y²-10y+25

12x-4x = 36 -4

8x = 32

x = 32/8 = 4

Also, PS² = PT²

(x-(-6))² + (y-5)² = (x-(-2))² + (y-(-1))²

(x+6)² + (y-5)² = (x+2)² + (y+1)²

x²+12x+36 + y²-10y+25 = x²+4x+4 + y²+2y+2

12x-4x-10y-2y = 4+2-36-25

8x-12y = -55 .......(1)

put x= 4 into (1):

8x-12y = -55

8(4)-12y = -55

32 -12y = -55

-12y = -55-32

-12y = -87

y = 7.25

Therefore, the coordinates of circumcentre of the triangle are P(4, 7.25)

Learn about the circumcenter of a triangle on:

brainly.com/question/29482852

#SPJ1

The expression to find out the total length of its beak and tongue that sticks out is b+t.

When Rufous-tailed hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters, the length is 28 millimeters.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information illustrated, Guevara’s feeders take pictures of the birds’ tongues sticking out as they sip nectar.

A hummingbird’s beak is b millimeters long and its tongue sticks out t millimeters past its beak.

The expression to find out the total length will be:

= Length of beak + Length of tongue

= b + t

The length when the hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters is:

= 20 + 8

= 28 millimeters

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

answer:

(1/y)^3(1/z)^4

step-by-step explanation:

negative exponents just move the number to the denominator. so all you have to do is move the y & z to the denominator to change the exponents to positive. hope that helps!

The fourth figure is a function as it passes the vertical line test.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

By vertical line test which is drawing a vertical line anywhere in a graph of a function if it only intersects only at one point, it is a function.

learn more about functions here :

https://brainly.com/question/12431044

#SPJ1

The predetermined overhead rate for the recently completed year was closest to $28.56 par labor - hour.

What is Labor - hour?

4 to 8 hours or more are typical for active labor. Your cervix will expand on average at a rate of 1 cm per hour. What you can do: Seek encouragement and support from your labor partner and your medical team. To ease your discomfort, try deep breathing and relaxation exercises.

Given:

Longobardi corporation bases its predetermined overhead rate on the estimated labor- hours for the upcoming year.

At the beginning of the most recently completed year, the corporation estimated the labor-hours for the upcoming year at 46,000 labor- hours.

The estimated variable manufacturing overhead was $6.25 per labor-hour and the estimated total fixed manufacturing overhead was $1,026,260.

The actual labor- hours for the year turned out to be 41,200 labor-hours.

Estimated total manufacturing overhead

= $1,026,260 + ($6.25 per labor- hour X 46,000 labor - hours)

= $1,313,760

Predetermined overhead rate

= $1,313,760 / 46,000 labor-hours

= $28.56 per labor-hour

Hence, the predetermined overhead rate for the recently completed year was closest to $28.56 par labor - hour.

To know more about labor - hour, click on the link

https://brainly.com/question/24924489

#SPJ4

Answer:

Step-by-step explanation:

do 21 ÷ 4 = 5.25

Now we have 5.25 miles for each inch. So all we have to do is multiply 5.25 by 13 to find the answer:

5.25 × 13 = 68.25

Let me know if this helped!

The inequality contain -12 in its solution is  x + 5 ≤ -4.

What is inequality?

The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things.

We have to find from the given inequalities which inequality has -12 in its solution.

Consider, the given inequalities

(1)  x + 6 < -8

⇒ x < - 8 - 6

⇒ x < -14

This inequality does not contain -12 in its solution.

(2) x + 4 ≥ - 6

⇒  x ≥ -6 - 4

⇒ x ≥ - 10

This inequality does not contain -12 in its solution.

(3) x - 3 > -10

⇒  x  > -10 + 3

⇒  x > -7

This inequality does not contain -12 in its solution.

(4) x + 5 ≤ -4

⇒  x ≤ - 4 - 5

⇒  x ≤ -9

This inequality contain -12 in its solution.

Hence, the inequality contain -12 in its solution is  x + 5 ≤ -4.

To know more about inequality, click on the link

https://brainly.com/question/24372553

#SPJ4

The linear equation for the attendance in terms of the price, p is

2600= -150p + 3650

A =m*p + b

where A= attendance , m = slope , b = y-intercept and p = price

When p=11 then A=2000 , i  e , (11, 2000).

When p= 7 , then A=2600, i .e ,  (7 , 2600).

m= (b-d)/(a-c)

=> m = (2600-2000)/(7 - 11)

        = -150

Therefore , 2600= -150p + b

To get the value of b,

putting the value of p in the obtained equation,

we get,

2600= -150 * 7+ b

2600 = -1050 + b

b = 3650

Hence , our equation becomes

2600= -150p + 3650

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on

To learn more about linear equation

https://brainly.com/question/28882406

#SPJ4

Two blueberry farms are similar in shape. the ratio of the side lengths of the farms is 6 : 7 then  $337.50  is the cost to dig a trench  around the  larger blueberry farm

The farms are sized with a ratio of 4:5 which means that the perimeter of the larger farm can be found by subtracting the perimeter of the smaller farm from that of the total of both farms which can be found by the following formula where it is assumed to be x.

4/(4+5) * x = 360 yards

4x = 360 * 9

x = (360 * 9) / 4

x = 810 yards

Size of larger farm = 810 - 360 = 450 yards

If it costs $0.75 to dig a trench per yard, the total cost for the larger farm is;

= 450 * 0.75

= $337.50

learn more about of farm here

https://brainly.com/question/18572338

#SPJ4

The program should print the integers according to this formula is

nums[0][0]=a;

nums[0][1]=b;

nums[1][0]=c;

nums[1][1]=d;

nums[0][2]= nums[0][0] + nums[0][1]; //a+b

nums[1][2]= nums[1][0] + nums[1][1]; //c+d

nums[2][0] = nums[0][0] + nums[1][0]; //a+c

nums[2][1] = nums[0][1] + nums[1][1]; //b+d

//sum = (a+b) + (c+d) + (a+c) + (b+d)

nums[2][2] = nums[0][2] + nums[1][2] + nums[2][0] + nums[2][1];

The nums array is 2 dimensional as shown below.

row, column column 0 column 1 column 2

row 0 a b a+b

row 1 c d c+d

row 2 a+c b+d (a+b)+(c+d)+(a+c)+(b+d)

The first index of an array always starts from 0.

Thus, nums[rows][columns] is used to access each element of the array.

The sum of first row elements is to be stored in the last index of row0, that is in nums[1][2].

Thus we equate nums[0][2] = nums[0][0] + nums[0][1]

Similarly, for 2nd row; nums[1][2] = nums[1][0] + nums[1][1]

The sum of first column is to be stored in last index of column0.

Thus, nums[2][0] = nums[0][0] + nums[1][0]

and for 2nd column,

nums[2][1] = nums[0][1] + nums[1][1].

Thus, the answer is--  

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

nums[0][0]=a;

nums[0][1]=b;

nums[1][0]=c;

nums[1][1]=d;

nums[0][2]= nums[0][0] + nums[0][1]; //a+b

nums[1][2]= nums[1][0] + nums[1][1]; //c+d

nums[2][0] = nums[0][0] + nums[1][0]; //a+c

nums[2][1] = nums[0][1] + nums[1][1]; //b+d

//sum = (a+b) + (c+d) + (a+c) + (b+d)

nums[2][2] = nums[0][2] + nums[1][2] + nums[2][0] + nums[2][1];

To learn more about  program visit:https://brainly.com/question/11023419

#SPJ4

The equation of the line is y = -1/4x + 15/4

From the question, we have the following parameters that can be used in our computation:

Slope = -1/4

Point = (3, 3)

The equation of a line is calculated using

y = m(x - X) + Y

Where

m = Slope = -1/4

(x, y) = Point = (3, 3)

Substitute the known values in the above equation, so, we have the following representation

y = -1/4(x - 3) + 3

So, we have

y = -1/4x + 3/4 + 3

Evaluate

y = -1/4x + 15/4

Hence, the equation is y = -1/4x + 15/4

Read more about linear equations at

https://brainly.com/question/13738662

#SPJ1

Answer: I need the Problem?

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.

When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.

Zero denotes the absence of a correlation: There is no propensity is for variables to change simultaneously.

Thus, when two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.

To know more about the negative correlation, here

https://brainly.com/question/16913516

#SPJ4

A shooter has a 27.92% chance of hitting the target at least 13 times.

This probability mass function in this type of binomial distribution is the quantity of successes ("x").

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The required number of wins is five since we are concerned with the likelihood that target will be hit exactly five times.(i.e., x = 13).

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Therefore, there is a 27.92% chance that a shooter will hit its target at the very most 13 times.

To know more about the binomial distribution, here

brainly.com/question/9325204

#SPJ4

Answer:

y - 9 = -18/13(x + 5)

Step-by-step explanation:

This is the UML diagram for the development of the program, in which Shapes 2D is the superclass and Circle, Square, Triangle, Rectangle, Rhombus, and Parallelogram are subclasses.

​​​​​​​This is the program in C++ demonstrating the above classes.

#include<iostream>

using namespace std;

class shapes

{

public:

   string name;

   string color;

   virtual void getAttributes()=0;

};

class Circle: public shapes

{

public:

   float radius;

   Circle(string n,string c, float r)

   {

       name=n;

       color=c;

       radius=r;

   }

   float getPerimeter()

   {

       return(2*(3.142)*radius);

   }

   float getArea()

   {

       return((3.142)*(radius*radius));

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Square:public shapes

{

public:

   float side;

   Square(string n,string c, float s)

   {

       name=n;

       color=c;

       side=s;

   }

   float getPerimeter()

   {

       return(4*side);

   }

   float getArea()

   {

       return(side*side);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Triangle:public shapes

{

public:

   float base;

   float height;

   float side1;

   float side2;

   float side3;

   Triangle(string n,string c)

   {

       name=n;

       color=c;

   }

   float getPerimeter()

   {

       cout<<"Enter side1\n";

       cin>>side1;

       cout<<"Enter side2\n";

       cin>>side2;

       cout<<"Enter side3\n";

       cin>>side3;

       return(side1+side2+side3);

   }

   float getArea()

   {

       cout<<"Enter base\n";

       cin>>base;

       cout<<"Enter height\n";

       cin>>height;

       return((0.5)*base*height);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Rectangle:public shapes

{

public:

   float length;

   float breadth;

   Rectangle(string n,string c, float l,float b)

   {

       name=n;

       color=c;

       length=l;

       breadth=b;

   }

   float getPerimeter()

   {

       return(2*(length+breadth));

   }

   float getArea()

   {

       return(length*breadth);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Rhombus:public shapes

{

public:

   float diagonal1;

   float diagonal2;

   float side;

   Rhombus(string n,string c)

   {

       name=n;

       color=c;

   }

   float getPerimeter()

   {

       cout<<"Enter Side\n";

       cin>>side;

       return(4*side);

   }

   float getArea()

   {

       cout<<"Enter diagonal 1\n";

       cin>>diagonal1;

       cout<<"Enter diagonal 2\n";

       cin>>diagonal2;

       return((0.5)*diagonal1*diagonal2);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Parallelogram:public shapes

{

public:

   float base;

   float height;

   Parallelogram(string n,string c, float b,float h)

   {

       name=n;

       color=c;

       base=b;

       height=h;

   }

   float getPerimeter()

   {

       return(2*(base+height));

   }

   float getArea()

   {

       return(base*height);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

int main()

{

   int choice;

   while(1)

   {

       cout<<"\n\nEnter your choice :";

       cout<<"\n1 for Circle\n";

       cout<<"2 for Square\n";

       cout<<"3 for Triangle\n";

       cout<<"4 for Rectangle\n";

       cout<<"5 for Rhombus\n";

       cout<<"6 for Parallelogram\n";

       cin>>choice;

       system("cls");

       switch(choice)

       {

       case 1:

           {

               float r;

               cout<<"Enter radius\n";

               cin>>r;

               Circle c("Circle","Yellow",r);

               c.getAttributes();

               cout<<"Perimeter : "<<c.getPerimeter()<<endl;

               cout<<"Area : "<<c.getArea()<<endl;

           }break;

       case 2:

           {

               float side;

               cout<<"Enter side\n";

               cin>>side;

               Square s("Square","Red",side);

               s.getAttributes();

               cout<<"Perimeter : "<<s.getPerimeter()<<endl;

               cout<<"Area : "<<s.getArea()<<endl;

           }break;

       case 3:

           {

               Triangle t("Triangle","Green");

               t.getAttributes();

               cout<<"Perimeter : "<<t.getPerimeter()<<endl;

               cout<<"Area : "<<t.getArea()<<endl;

           }break;

       case 4:

           {

               float l,b;

               cout<<"Enter Length and breadth\n";

               cin>>l>>b;

               Rectangle r("Rectangle","Blue",l,b);

               r.getAttributes();

               cout<<"Perimeter : "<<r.getPerimeter()<<endl;

               cout<<"Area : "<<r.getArea()<<endl;

           }break;

       case 5:

           {

               Rhombus r("Rhombus","Purple");

               r.getAttributes();

               cout<<"Perimeter : "<<r.getPerimeter()<<endl;

               cout<<"Area : "<<r.getArea()<<endl;

           }break;

       case 6:

           {

               float b,h;

               cout<<"Enter base\n";

               cin>>b;

               cout<<"Enter height\n";

               cin>>h;

               Parallelogram p("Parallelogram","Pink",b,h);

               p.getAttributes();

               cout<<"Perimeter : "<<p.getPerimeter()<<endl;

               cout<<"Area : "<<p.getArea()<<endl;

           }break;

       }

   }

}

To learn more about objects and classes,

https://brainly.com/question/21113563

#SPJ4

Answer:

15. x = 4

16. x = 7

Step-by-step explanation:

15.

CD/ ED = DG / DF

48 / (5x - 2) = 40 / (2x + 7)

48 (2x + 7) = 40 (5x - 2)

96x + 336 = 200x - 80

200x - 96x = 336 + 80

104x = 416

x = 4

16.

ST / PL = TU / LM

(x + 1) / 72 = (2x - 3) / 99

99 (x + 1) = 72 (2x - 3)

99x + 99 = 144x - 216

144x - 99x = 99 + 216

45x = 315

x = 7

Answer:

15.  x = 4

16.  x = 7

Step-by-step explanation:

Similar Triangles

In similar triangles, corresponding sides are always in the same ratio.

If ΔCDG ~ ΔEDF then:

From inspection of the given diagram:

Therefore:

[tex]\implies \sf CD : ED = DG : DF[/tex]

[tex]\implies 48 : (5x-2) = 40 : (2x+7)[/tex]

[tex]\implies \dfrac{48}{(5x-2)} = \dfrac{40}{(2x+7)}[/tex]

[tex]\implies 48(2x+7)=40(5x-2)[/tex]

[tex]\implies 96x+336=200x-80[/tex]

[tex]\implies 416=104x[/tex]

[tex]\implies x=\dfrac{416}{104}[/tex]

[tex]\implies x=4[/tex]

If ΔSTU ~ ΔPLM then:

From inspection of the given diagram:

Therefore:

[tex]\implies \sf ST : PL = TU : LM[/tex]

[tex]\implies (x+1) : 72 = (2x-3) : 99[/tex]

[tex]\implies \dfrac{(x+1)}{72}= \dfrac{(2x-3)}{99}[/tex]

[tex]\implies 99(x+1)=72(2x-3)[/tex]

[tex]\implies 99x+99=144x-216[/tex]

[tex]\implies 315=45x[/tex]

[tex]\implies x=\dfrac{315}{45}[/tex]

[tex]\implies x=7[/tex]