Please help! Write a transformation rule that maps the figure to its image. Some might require more than one transformation.
Top triangle: figure
Bottom triangle: image

Based on the triangle sum theorem, the value of x is: 45.

The Triangle Sum Theorem states that in any triangle, the sum of the measures of the interior angles is always equal to 180 degrees. This is true for all triangles, regardless of their size or shape.

The theorem can be proven using Euclidean geometry, which states that the sum of the angles in a triangle is always 180 degrees. This theorem is also known as the "angle sum property" of a triangle.

Therefore:

2x + 10 + 30 + 50 = 180 (based on the triangle sum theorem).

Combine like terms:

2x + 90 = 180

2x = 180 - 90

2x = 90

2x/2 = 90/2

x = 45.

Learn more about triangle sum theorem on:

https://brainly.com/question/7696843

#SPJ1

The equation 6x + 8 = 2(3x + 4) had infinitely many solutions.

The equation 6x + 8 = 2(3x + 4) can be solved by isolating x on one side of the equation. To do this, we can first distribute the 2 on the right side of the equation:

6x + 8 = 6x + 8

Then we can subtract 8 from both sides:

6x + 8 - 8 = 6x + 8 - 8

6x = 6x

Divide both sides by 6

6x/6 = 6x/6

x = x

This means x can assume any value which will make the equation true.

Therefore, the equation had infinitely many solutions.

Learn more about solution of an equation on:

https://brainly.com/question/25678139

#SPJ1

Using Arithmetic progression, There were 4,13,22,31 pupils chosen out of the applicants.

The professor desires to choose four students at random.

A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

The fourth student was chosen at random, followed by every ninth student.

The fourth student is chosen first.

Using the following term formula, which is

=>a + d(n-1) (n-1)

The second student is the one after that.

=>4 + 9(2-1) (2-1)

=>4 + 9(1) (1)

=>4 + 9

=> 13

The third pupil will be

=>4 + 9(3-1) (3-1)

=>4 + 9(2) (2)

=>4 + 18

=> 22

The fourth pupil will be

=>4 + 9(4-1) (4-1)

=>4 + 9(3) (3)

=> 4+ 27

=> 31

To learn more about A.P. from given link

https://brainly.com/question/14321233

#SPJ1

The probability that the system gets damaged is 0.685.

Virus A damages the system with probability 0.4.

Independently of it, virus B damages the system with probability 0.5.

Independently of A and B virus C damages the system with probability 0.2.

We have to find the probability that the system gets damaged.

P(system will not be damaged by virus 1) = 1 - 0.1 = 0.9

P(system will not be damaged by virus 2) = 1 - 0.5 = 0.5

P(system will not be damaged by virus 3) = 1 - 0.3 = 0.7

P(the system will be damaged) = 1 - P(system will not be damaged)

P(the system will be damaged) = 1 - P(system will not be damaged by virus 1) x P(system will not be damaged by virus 2) x P(system will not be damaged by virus 3)

P(the system will be damaged) = 1 - 0.9x0.5x0.7

P(the system will be damaged) = 0.685

To learn more about probability link is here

brainly.com/question/30034780

#SPJ4

The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

Learn more about fraction here:

https://brainly.com/question/28699958

#SPJ1

Answer:

D: 39

Step-by-step explanation: Using the steps of the Pythagorean theorem.

The total number (n) of distinct solutions of the equation (x + y + z = 15) with the assumption that x, y and z are all nonnegative integers is 153.

The generating function for the number of solutions of the equation (x + y + z = n) is given by the binomial coefficient (n+2)C2, where C2 is the number of ways to choose 2 objects from a set of n+2 objects.

The number of solutions for the given equation (x + y + z = 15) is then given by:

(15+2)C2 = (17C2)

We can also use the formula for binomial coefficient: nCr = n! / (r! (n-r)!)

17C2 = (17!) / (2! * 15!) = 153

So the total number of distinct solutions of the equation (x + y + z = 15) with x, y, z non-negative integers is 153.

"

Complete question

what is the total number n of distinct solutions  the equation (x + y + z = 15) after we impose that x, y and z are all nonnegative integers?

"

You can learn more about distinct solutions of equation at

https://brainly.com/question/28471746

#SPJ4

Answer: 5.4h -13 -1.9d

Step-by-step explanation:

combine the like terms together.

Answer:

By definition, if two angles are complementary, they both will add up to 90 degrees. Knowing this add 18 and (6d-6) together to equal 90.

18+(6d-6)=90

Subtract 18 from both sides, then add 6. This leaves you with 6d equal to 78. Divide by 6 to get 13.

(6d-6)=72

6d=78

d=13 degrees

Make sure of your answer. You know that d is 13, so plug it back into the equation to see if it equals 90 degrees.

18+6(13)-6=90

18+78-6=90

90=90

Answer: To find the rotation in revolutions per minute (RPM) given the angular speed and the radius, we can use the formula:

RPM = (Angular Speed (rad/s)) / (2 * pi)

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (m/s) / Radius (m)

Angular Speed = 82.3 m/s / 0.131 m = 630 rad/s

RPM = (630 rad/s) / (2 * pi) = 131 rev/min

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (ft/min) / (Radius (ft) * 12)

Angular Speed = 144.2 ft/min / (10.9 ft * 12) = 10.9 rad/s

RPM = (10.9 rad/s) / (2 * pi) = 10.9 rev/min

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (in/h) / (Radius (in) * 3600)

Angular Speed = 553 in/h / (553 in * 3600) = 0.09 rad/s

RPM = (0.09 rad/s) / (2 * pi) = 0.09 rev/min

Step-by-step explanation:

Answer: -25

Step-by-step explanation:

For f(x) functions, all you do is plug in whatever value that is given in the parenthesis into x.

f(5) = -4(5) - 5

= -20 -5

= -25

The domain of the function f(x) - g(x) is given as follows:

[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]

The domain of a function is the set composed by all the input values that the function accepts.

For a square root, the inner term cannot be negative, hence the domain of f(x) is given as follows:

x² - 3 >= 0

|x| >= sqrt(3)

x <= -sqrt(3) or x >= sqrt(3).

For function g(x), the domain is given as follows:

36 - x² >= 0

x² <= 36

|x| <= square root (36)

|x| <= 6.

-6 <= x <= 6.

The domain of the subtraction function is the intersection of the domain of both functions, hence:

[tex][-6, -\sqrt{3}] \cup [\sqrt{3},6][/tex]

More can be learned about the domain of a function at https://brainly.com/question/10687170

#SPJ1

Shop ZYX represents the cheaper plan, with a cost of $2.4 per plum.

To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.

The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.

Hence the cost per plum in each shop is given as follows:

(division of the total cost by the number of plums).

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer: here

Step-by-step explanation:

Divide each term in ma=3xma=3x by aa and simplify.m=3xa

The required value of x to satisfied the given condition is 1/5.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

We have,

3x (1 + 6) = (3 x 1) + ( 6x)​

3x(7) = 3 + 6x

21x = 3 + 6x

15x = 3

x = 1/5

Thus, required value of x is 1/5.

To know more about Equation visit:

brainly.com/question/10413253

#SPJ1

In order to satisfy the requirement, x must be 1/5 of the desired value.

To lean more about Equation refer:

brainly.com/question/10413253

#SPJ1

Price paid for car = $23622, The loss value is $3742 and total distance the car was used for is 18000 kilometres.

Distance is a measurement of how far apart two objects or points are. It is the length of the actual route taken to get from one place to another. In physics, distance is frequently used to refer to a physical length or an estimation based on other criteria, such as "a few kilometres apart" or "some miles away."

However, the distance travelled by an object to move from its initial position to its final position will be the same as the distance travelled to move from its final position to its initial position. As a result, distance is independent of a body's motion.

a. Price paid for car = $23622

Discount = 7%

Sale price = $19880

b. The loss value is $3742

c. Let total distance travelled be d

Fuel consumption=10km per litre

Cost of fuel =1.4 per litre

Cost of fuel per kilometre =1.410= 0.14

Other cost = 938

Cost of usage =0.14*d +938

Total cost including loss = 0.14*d +938+3742

The cost per kilometre has been provided as 0.4

Total cost of the vehicle's use = 0.4*d

B=A0.4*d = 0.14*d +938+37420.26*d = 4680d = 18000

Thus, Total distance the car was used for is 18000 kilometres.

Learn more about distance

https://brainly.com/question/15172156

#SPJ1

Answer: x=-4/3,      y=19/3

Step-by-step explanation:  According to the formula,  

x=(mx2+nx1)/(m+n) ,     y=(my2+ny1)/(m+n)

Here the ratio is 1:5

m=1 ,   n=5

x1 = -4,  x2 = 12

y1 = 5,   y2 = 13

Now put in the formula,

[tex]x=\frac{1*12+5(-4)}{1+5}[/tex] ,     [tex]y=\frac{1*13+5*5}{1+5}[/tex]

x=(12-20)/6 ,      y= (13+25)/6

x=-8/6         ,      y=38/6

x=-4/3          ,     y=19/3

Read more about it:

https://brainly.com/question/23907194

Elizabeth's annual Social Security deduction is $72580, Medicare deduction is $1053.71 per year, biweekly gross pay is $2796.15, total amount withheld for federal tax is $15336.80, amount deducted is $66.50 and annual salary is $79,307.38

a) Social Security deduction is 6.2% of Elizabeth's annual salary, which is $72,580 x 6.2% = $4,486.76 per year.

b) Medicare deduction is 1.45% of Elizabeth's annual salary, which is $72,580 x 1.45% = $1,053.71 per year.

c) Elizabeth is paid every other week, so her bi-weekly gross pay is $72,580 / 26 = $2,796.15.

d) The total amount withheld for federal tax from Elizabeth's annual salary is $72,580 x 21% = $15,336.80.

e) The amount deducted from Elizabeth's salary per paycheck for city tax is ($72,580 x 2.875%) / 26 = $66.50.

f) As of January 1, Elizabeth will receive a 9.1% raise, so her annual salary will be $72,580 x (1 + 0.091) = $79,307.38.

Correct Question :

Elizabeth works for Picasso Paint Supplies. Her annual salary is $72,580.

a) What is Elizabeth's annual Social Security deduction?

b) What is Elizabeth's annual Medicare deduction?

c) Elizabeth is paid every other week. What is her biweekly gross pay?

d) Each pay period, Elizabeth's employer deducts 21% for federal withholding tax. What is the total amount withheld for federal tax from Elizabeth's annual salary?

e) If Elizabeth is taxed at an annual rate of 2.875% for city tax, how much is deducted from her salary per paycheck to withhold that tax?

f) As of January 1, Elizabeth will receive a 9.1% raise. What will Elizabeth's annual salary be?

To learn more about annual salary here:

https://brainly.com/question/13575235

#SPJ4

Answer:

Step-by-step explanation:

  f f

Answer:38.6

Step-by-step explanation:

The expression that represents the number of seconds Jacob has been running is t - 7.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. An expression's structure is as follows: (Math Operator, Number/Variable, Math Operator). The two integers are connected by a mathematical operator.

Since Jacob started running 7 seconds after Alma, the number of seconds Jacob has been running can be represented as t - 7. So the expression that represents the number of seconds Jacob has been running is: t - 7.

To learn more about expression here:

https://brainly.com/question/28980347

#SPJ4

Step-by-step explanation:

First one is good, all you have to do is combine like terms

-28x and +4x are like terms because they both have X

Combining those is -28x+4x=+24x

Making #1 7+24x

Answer:

(Their all down there)

Step-by-step explanation:

Okie dokie so! Your answer for 17 is technically correct but you need to imply it further so it would be [tex]7-24x[/tex]

18. [tex]-2(-6+5k)-1[/tex]

do distributive property

[tex]12-10k-1[/tex]   combine like terms (12 and -1)

[tex]-10k+11[/tex]

19. [tex]6(v-5)+1\\[/tex]

do distributive property

[tex]6v-30+1[/tex]    combine like terms (-30 and 1)

[tex]6v-29\\[/tex]

20. [tex]10(n+5)-5n[/tex]

do distributive property

[tex]10n+50-5n[/tex]  combine like terms (10n and -5n)

[tex]5n+50[/tex]

21. [tex]-7(8+8x)-6x[/tex]

do distributive property

-[tex]56-56x-6x[/tex]   combine like terms (-56x and -6x)

[tex]-56-62x[/tex]

22. [tex]6(x-9)+5[/tex]

do distributive property

[tex]6x-54+5[/tex]  combine like terms (-54 and 5)

[tex]6x-49[/tex]

Answer:

(i) 11 years old

(ii) 30 years old

Step-by-step explanation:

K is x

In four years, he will be x+4 and his mother will therefore be 3(x+4)

Six years ago, he was x-6 and his mother was 7(x-6).

In 10 years his mother went from 7(x-6) to 3(x+4)

so their difference is 10

7x-42+10=3(x+4), since 7x-42 is 10 years less than 3x+12

7x-32=3x+12

4x=44

x=11 age of K now

in 4 years he will be 15 and his mother 45.

Six years ago he was 5 and his mother 35

Therefore, his mother was 30 when he was born.

She is now 41.

Imran is currently 10 years old. His mother's current age is 34 years old and she was 24 years old when Imran was born.

The question involves a system of equations based on the relationship between Imran and his mother's ages. We can define Imran's current age as i and his mother's current age as m. From the problem we have the following two equations:

By solving this system of equations, we can determine that Imran's current age (i) is 10 years old and his mother's current age (m) is 34 years old. To find the age of Imran's mother when he was born, we would subtract Imran's age from his mother's, i.e., 34 - 10, so Imran's mother was 24 years old when Imran was born.

https://brainly.com/question/35467992

#SPJ2

(0, -26) and (0,25 )is the focus of the hyberbola.

Any point in a hyperbola has distances from the two foci that are fixedly different from each other.

Every hyperbola has two foci (plural for focus). The hyperbola's branches are encircling both of them.

(0,-26) is inside the lower branch (0,-24) is not inside the lower branch (0,25) is inside the upper branch (0,30) is inside the upper branch

Lower branch is our main focus. We must examine the image to determine which of two potential solutions is correct. From the maxima to the focus for the lower branch is one distance. The top branch needs the same, which we must discover. Distances between points (0,30) and (0.25) are 1 and 6, respectively.

(0, -26) and (0,25).

The complete question is,

What is the depicted hyperbola's point of focus? (0, −26) (0, −24) (0, 25) (0, 30) (0, 30) BRAINLIESTT.

To learn more about hyperbola's focus refer to:

https://brainly.com/question/4514506

#SPJ1

Answer: Amber has 50 pennies and 10 dime

Step-by-step explanation:

The number of pennies is represented by x, while the number of dimes is represented by y. This means that the statement, "there are five times as many pennies as dimes" can be written as x = 5.

The sum of the coins is $1.50, which can now be written as

0.01x + 0.1y = 1.50

0.01(5y) + 0.1y = 1.50

0.05y + 0.1y = 1.50

0.15y = 1.50

y = 10

Next up:

x = 5y

x = 5(10)

x = 50

Finally, we can conclude that Amber has 50 pennies and 10 dimes

I hope this helps!

The exponential function that satisfies the given conditions is given as follows:

[tex]f(t) = 4e^{1.099t}[/tex]

The format of the exponential function for this problem is given as follows:

f(t) = 4e^(kt).

In which k is the exponential growth rate.

After five hours, there was 972 bacteria, meaning that when t = 5, f(t) = 972, hence the growth rate is obtained as follows:

[tex]972 = 4e^{5k}[/tex]

[tex]e^{5k} = 243[/tex]

5k = ln(243)

k = ln(243)/5

k = 1.099.

Meaning that the function is defined as follows:

[tex]f(t) = 4e^{1.099t}[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

On the graph:

A  represents the reactants

B represents the activated complex

C represents the products

D represents the activation energy

The path of energy changes that take place in a reaction, as well as the energy content of the reactants and products, are depicted in the energy profile diagram.

The letters shown in the diagram represents the following:

Learn more about energy profile diagram at:

brainly.com/question/10338784

#SPJ1

In a data set, the number of observations will always be the same as the group of answer choices number of variables is the number of elements.

A data set is a collection of data. It is a set that corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.

The data set lists values for each of the variables, such as example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files.

To know more about the data set:

https://brainly.com/question/24326172

#SPJ4

Answer:

(3,2)

Step-by-step explanation:

 2(y = 5x - 13)

-(2y = -5x + 19)

0 = 15x - 45

15x = 45 --> x=3

y = 5(3) - 13

y = 2

The estimated probability that Pedro will eat pizza for lunch every way next week is 1/2

The term called probability in math is known as branch of mathematics that measures the uncertainty of the occurrence of an event using numbers

Here we know that the cafeteria has pizza about 80% of the time.

And here we have also know that Pedro runs a simulation to model this using a random number generator.

The result of the table shows the results of the simulation.

Here we need to estimate the probability that Pedro will eat pizza for lunch every way next week and it can be calculated as,

Here we have know that in each box, here there are 5 digits to represent the 5 days in a week.

And here there’s 10 boxes to represents 10 weeks.

Then in each box there’s a chance out of 5 for Pedro to get pizza.

Then the probability is calculated as,

=> 5/10

=> 1/2

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4