The translations, reflections, and rotations are types of transformations that change an original object to form a new image, each with its own specific rule and properties. They are used in a variety of real-world applications to change the position or orientation of objects.
There are 3 types of Transformations :
(i) Translation: A translation involves moving an object from one place to another without changing its size or orientation.
The algebraic rule for a translation is to add the same constant to each coordinate of each point
The Translations preserve congruence, meaning that corresponding parts of congruent figures will still be congruent after a translation.
An example of a real-world application of translation is moving a store to a new location.
(ii) Reflection: A reflection involves flipping an object over a line or point, creating a mirror image.
The algebraic rule for a reflection is to negate the value of one of the coordinates.
Reflections preserve orientation, meaning that the orientation of the reflected image is opposite that of the original object.
An example of a real-world application of reflection is looking at your reflection in a mirror.
(iii) Rotation: A rotation involves turning an object about a fixed point, called the center of rotation, through a certain angle.
The algebraic rule for a rotation is to multiply each coordinate by a rotation matrix.
Rotations preserve distance and angle measures, meaning that the lengths of corresponding parts and the angles between them are equal in the original and rotated images.
An example of a real-world application of rotation is turning a steering wheel to change the direction of a car.
The given question is incomplete , the complete question is
Compare and contrast the three types of transformations: translations, reflections, and rotations.
Include the algebraic rules, whether each transformation preserves congruence and any examples of real-world application.
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The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries negative 2, 0, 2, 4. The second column is labeled cost (c) with entries negative 7, 0, 7, 14.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 0.5, 1, 1.5. The second column is labeled cost (c) with entries 0, 1.75, 3.5, 5.25.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 3, 6, 9. The second column is labeled cost (c) with entries 0, 10.5, 21, 31.5.
The table which matches the equation and includes only viable solutions is the third table.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
Given that equation is,
c = 3.5b
Here b is the number of loaves of bread and c is the total cost of the bread.
All the table values matches the equation when we substitute the value of b and c in the equation.
But number of loaves of bread cannot be fractions or negative numbers.
So the most viable solution is the third table consisting of values of b as 0, 3, 6, 9 and corresponding value of c as 0, 10.5, 21, 31.5.
Hence the 2-column table with the first column labeled loaves (b) with entries 0, 3, 6, 9 and the second column labeled cost (c) with entries 0, 10.5, 21, 31.5 is the correct one.
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Answer:
The third one
Step-by-step explanation:
Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.
Answer:
AAA similarity
Step-by-step explanation:
Similar triangles:In ΔECD,
∠E + ∠D + ∠ECD = 180° {Angle sum property}
∠E + 36 + 123 = 180°
∠E + 159 = 180
∠E = 180 - 159
∠E = 21°
In ΔACB,
∠A + ∠B + ∠ACB = 180° {Angle sum property}
∠ACB + 36 + 21 = 180°
∠ACB + 57 = 180
∠ACB = 180 - 57
∠ACB= 123°
In ΔECD & ΔBCA,
∠A ≅ ∠D
∠B ≅ ∠A
∠BCA ≅ ∠ECA
ΔECD ~ ΔBCA by Angle Angle Angle similarity.
4 painters that have completed 12 rooms in 8 hours. assuming they are working at the same efficiency, how many hours does it take 7 painters to paint 21 rooms?
Answer: We can use the concept of rates to solve this problem.
A rate is a ratio of the amount of work done to the amount of time it takes to do the work. We can find the rate of work for the 4 painters by dividing the number of rooms they painted by the number of hours it took them:
Rate = Rooms painted / Hours
Rate = 12 rooms / 8 hours = 1.5 rooms per hour
Now we can use this rate to find out how long it will take 7 painters to paint 21 rooms. To do this, we'll use the formula:
Time = Rooms / Rate
Time = 21 rooms / 1.5 rooms per hour = 14 hours
So it would take 7 painters working at the same efficiency as the 4 painters 14 hours to paint 21 rooms.
Step-by-step explanation:
How do you find the value of x and y?
Check the picture below.
[tex]5x+70=24x-25\implies 70=19x-25\implies 95=19x \\\\\\ \cfrac{95}{19}=x\implies \boxed{5=x} \\\\[-0.35em] ~\dotfill\\\\ 4y+2=x+y\implies 4y+2=5+y\implies 3y+2=5 \\\\\\ 3y=3\implies y=\cfrac{3}{3}\implies \boxed{y=1} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{5(5)+70}{\measuredangle R=95^o}\hspace{5em}\stackrel{24(5)-25}{\measuredangle C=95^o}\hspace{5em}\stackrel{4(1)+2}{QR=6}\hspace{5em}\stackrel{5+1}{BC=6}[/tex]
The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answer(s). (4 points)
x –3 –2 –1 0 1 2
f(x) 0.4 4.5 7 11.3 15 16.2
g(x) 4 8 10 11.3 15 17
The solutions to the system of equations f(x) = g(x) are given as follows:
x = 0 and x = 1.
The reason for these solutions is that f(x) and g(x) have the same numeric value at x = 0 and at x = 1.
How to interpret the solution of a system of equations?A system of equations is composed by multiple equations.
The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.
The x-values for which the numeric values of f(x) and g(x) are the same are given as follows:
x = 0 and x = 1.
Which are the solutions to the system of equations.
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Consider the following number pattern: -7; 0; 9; 20; ... Show that the general term of this quadratic number pattern is given by T₁ = n² +4n-12. 2.1
Hence the general term of the given quadratic number pattern is given by Tn = n²+4n-12 is verified.
The number pattern = -7,0,9,20
What is the formula for quadratic equation?Let the general term of the given quadratic number pattern is given by
Tn = an²+bn + c
When T = -7; n = 1
⇒ -7 = a(1)² +b (1) +6
⇒ a + b + c=-7 -----------1
At n=2, T₂ = 0
⇒ 0 = a(2)²+b(2)+c
4a+2b+c=0 ---------------2
At n=3, T = 9
⇒ 9 = a(3)²+b(3) +c
⇒ 9a+3b+c= 9 ---------3
Subtracting 3 from 2
⇒-5a-b = -9 --------4
Subtracting 2 from 1
-3a-b = -7 -----------5
Subtracting 5 from 4
2a = 2
⇒ a=1
Using eq 5, we get
-3(1) - b = -7
-b = -7 + 3
b = 4
From eq 1, a + b + c=-7 we get the value of c,
1 + 4 + c = -7
c = -7 -5
c = -12
substitute the values of a, b, and c in Tn = an²+bn + c
Tn = n² + 4n - 12
Hence the general term of the given quadratic number pattern is given by Tn = n²+4n-12.
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I need help on part b
Answer:
a) The pattern 6 has 26 sticks,b) The pattern number n has 4n + 2 sticks.--------------------------
If we put the number of sticks in a sequence we get:
6, 10, 14, ...As we see the difference of the terms is common and is 4, and the first term is 6. It is therefore an arithmetic progression with:
a = 6 and d = 4Use the nth term equation:
a(n) = a + (n - 1)dPart a)Substitute n = 6 to find the number of sticks of the 6th term:
a(6) = 6 + (6 - 1)*4 = 6 + 5*4 = 6 + 20 = 26Part b)Find the nth term:
a(n) = 6 + (n - 1)*4 = 6 + 4n - 4 = 4n + 2parallelogram has sides of lengths 35 inches and 75 inches. One angle has measure of140°. Find the length of each diagonal.
The length of diagonal of a parallelogram is 2546 inches.
What is a parallelogram?A quadrilateral with equal pairs of opposing sides and angles is referred to as a parallelogram. It has a pair of opposing sides that are parallel to one another. The inner angles are supplementary in nature, meaning that the sum of them equals 180 degrees. A parallelogram's diagonals are bisected by one another, or divided into two equal portions. A parallelogram's internal angles add up to 360 degrees.
The diagonals of parallelogram are given by:
x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)
Given the two sides are 35 and 75 inches.
We also know that the adjacent angles of parallelogram are supplementary:
∠A + ∠B = 180
140 + ∠B = 180
∠B = 40
Substitute the value of sides and angle in the equation:
x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)
x = √((35)^2 + (72)^2 + 2(35)(72) cos 140)
x = 1225 + 5184 + (5040)(-0.766)
x = 1225 + 5184 - 3860
x = 2546 inches
Hence, the length of diagonal is 2546 inches.
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If the two triangles in the map below are similar, what is the distance from Arrow Road to the end of the forest (x)?
We can write the measurements as -
a = 7.8
b = 9.24
(B) = 50°
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that two triangles in the map below are similar.
We can write -
{ 1 } -
sin (A) = a/c
a = c sin(A)
a = 12 sin(40°)
a = 12 x 0.65
a = 7.8
{ 2 } -
cos (A) = b/c
b = c cos(A)
b = c cos(40°)
b = 12 x 0.77
b = 9.24
{ 3 } -
tan (B) = b/a
tan (B) = 9.24/7.8
tan (B) = 1.19
(B) = 50°
Therefore, we can write the measurements as -
a = 7.8
b = 9.24
(B) = 50°
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Lilyana runs a cake decorating business, for which 10% of her orders come over the telephone. Let C be the
number of cake orders Lilyana receives in a month until she first gets an order over the telephone. Assume the
method of placing each cake order is independent.
Find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
You may round your answer to the nearest hundredth.
PC <5) =
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If Lilyana runs a cake decorating business for which 10% of her orders come over telephone , then probability that it takes fewer than 5 orders for Lilyana to get her first telephone is 0.3439 .
The geometric distribution is used to calculate the required probability ,
In this case, the success is a telephone order, and
the failure is an order placed in some other way.
Let probability of success is ⇒ p , and
let the number of orders needed to get the first telephone order be = x . Then, X follows a geometric distribution with parameter p, so we have:
Probability of P(X = k) is = (1-p)^(k-1) × p ;
where k is the number of orders needed.
the probability of success (p) is = 10% = 0.1
we have to find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
that means : P(X<5) = P(X=1) + P(X=2) + P(X=3) + P(X=4)
Substituting the values of p = 0.1 ,
we get ;
= (1-0.1)⁰ × 0.1 + (1-0.1)¹ × 0.1 + (1-0.1)² × 0.1 + (1-0.1)³ × 0.1
Simplifying further ,
we get ;
= 0.1 + 0.09 + 0.081 + 0.0729
Adding all the terms ,
we have ;
= 0.3439
Therefore , the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month is 0.3439.
The given question is incomplete , the complete question is
Lilyana runs a cake decorating business, for which 10% of her orders come over the telephone. Let C be the number of cake orders Lilyana receives in a month until she first gets an order over the telephone. Assume the method of placing each cake order is independent.
Find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
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In a lab experiment, 40 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 23 hours. How long would it be, to the nearest tenth of an hour, until there are 82 bacteria present?
The time needed until there are 82 bacteria is given as follows:
23.8 hours.
How to use the exponential function to find the time?An exponential function is defined as follows:
[tex]y = a(b)^{\frac{x}{n}}[/tex]
In which:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.The parameters for this problem are given as follows:
a = 40, b = 2, n = 23.
Hence the function is:
[tex]y = 40(2)^{\frac{x}{23}}[/tex]
There will be 82 bacteria at a time x when y = 82, hence:
[tex]82 = 40(2)^{\frac{x}{23}}[/tex]
[tex](2)^{\frac{x}{23}} = 2.05[/tex]
Applying the logarithm of base 2 to each side, we have that:
x/23 = log2(2.05)
x = 23 x log2(2.05)
x = 23.8 hours.
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I need help in this problem
Answer:
b
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180°
sum the 3 angles and equate to 180
2x + 1 + 5x + 5 + 90 = 180
7x + 96 = 180 ( subtract 96 from both sides )
7x = 84 ( divide both sides by 7 )
x = 12
The side length of a square is 5x - 7. Find x if the perimeter is 125.
The numerical value of x in the expression 5x - 7 is 7.65.
What is the numerical value of x?A square is simply a 2-dimentional plane figure with four equal sides and four right (90°) angles.
The perimeter of the square is the sum of the length of all four sides of the square.
P = 4l
Given the data in the question
Side length of square l = 5x - 7Perimeter P = 125Value of x = ?To find the value of x, plug the given values into the above equation and simplify.
P = 4l
125 = 4( 5x - 7 )
125 = 20x - 28
125 + 28 = 20x
153 = 20x
20x = 153
x = 153/20
x = 7.65
Therefore, the value of x is 7.65.
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King Neptune, a 34-foot tall statue that
welcomes visitors to Virginia Beach, casts a
3 13
5 -foot shadow. If Jane is 5’9" tall and is
standing nearby, find the length of her
shadow
The length of Jane's shadow is approximately 2.85 feet
To find the length of Jane's shadow, we can use the principle of similar triangles.
The ratio of the shadow length to the object height is the same for both King Neptune and Jane, then we can set up a proportion:
(shadow length of King Neptune) / (height of King Neptune) = (shadow length of Jane) / (height of Jane)
Given that King Neptune's shadow is 3 13 5 feet and the statue is 34 feet tall.
By substituting these values into the proportion:
(3 13 5 feet) / (34 feet) = (shadow length of Jane) / (5' 9")
To find the shadow length of Jane, we can cross-multiply and solve for the shadow length:
(3 13 5 feet) * (5' 9") = (shadow length of Jane) * (34 feet)
Converting Jane's height into feet: 5'9" = 5*12 +9 = 69 inches = 5.75 ft
(3 13 5 feet) * (5.75 ft) = (shadow length of Jane) * (34 feet)
shadow length of Jane = (313.5*5.75) / 34 = 2.85 ft
So, The length of Jane's shadow is approximately 2.85 feet.
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researchers wanted to see which species of lizard (a, b, or c) is most likely to survive a bacterial infection. so they infected a total of 38 lizards and recorded how many survived after 48 hours. of the 15 species b lizards, 40% survived. for those that were species c, one more survived than died. and of the 24 lizards that died, one-third of them were species a. a. create a contingency table to display this data. (3pt) b. what proportion of the lizards in this study were either species b or c? (1pt) c. what is the probability that a species b lizard in this study did not survive? (1pt) d. are survival and being species c independent events for these lizards? justify your answer. (3pt)
a. The contingency table for the given data is attached file below.
b. The proportion of lizards that were either species A or B is 0.605.
c. The probability that a species C lizard in this study did not survive is 0.4667.
a.
The contingency table for the given data is attached file below.
b.
The proportion of lizards that were either species A or B can be calculated as:
P(A or B) = (15+8)/(15+8+6+9+4)
P(A or B) = 23/38
P(A or B) = 0.605
c.
The probability that a species C lizard in this study did not survive can be calculated as:
P(Not survive| C) = 7/15
= 0.4667
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01. De 200 melones, 80 resultaron en mal estado.
¿Qué porcentaje de los 200 están buenos para la venta?
200 melons are good in 60% of the cases.
Qué es bueno para la buena venta?Create a favourable first impression. Offers customers problems-solutions and a positive experience. Make good use of the newest technologies. clear language for business transactions. Maintain open communication.
The Most Important Characteristic for Sales. No matter what kind of sale it is, or what industry it is in, the most crucial factor that influences someone's decision to buy is always the price. And making oneself increasingly valuable is the key to selling and selling oneself.
200 equates to 100%.
Are good = 200 - 80 = 120
200me = 100%
120me = 100%/200me x = 120000%/200me x = 60%
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Caroline has a discount card that gives her 4% off the purchase of each pizza. If p is the cost of a regular pizza, how much does Caroline pay for her pizza?
Find the balance in the account after the given period. $2,600 deposit earning 4.2% compounded monthly, after 3 years. The balance after 3 years will be $ (Round to the nearest cent as needed.)
To find the balance of the account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial principal is $2,600, the interest rate is 4.2% (expressed as a decimal), the number of times the interest is compounded per year is 12 (monthly), and the number of years is 3.
So, we can plug these values into the formula:
A = 2600(1 + 0.042/12)^(12*3)
A = 2600(1.0035)^36
A = 2600 * 3.876
A = 10,049.6
The balance of the account after 3 years is $10,049.6.
What is the solution for this inequality?
Answer:
r > -3
Step-by-step explanation:
dwbi jus know that's the answer lil one
Gabriela has an average daily balance of $232. 94 on her credit card. Her card charges 9. 25% annual interest. What will her monthly finance charge be?
Her monthly finance charge will be: $1.80
Now, According to the question:
Gabriela has an average daily balance of $232. 94 on her credit card.
and, Her card charges 9. 25% annual interest.
Based on the given condition:
$232.94 × 9.25%
232.94 × 9.25/100
Calculate the product or quotient:
232.94 × 9.25/100 = 21.54694
21.54694 rounds up to 21.55
Her monthly finance charge will be:
21.55/12 = 1.7958333333
1.7958333333 round up 1.80
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Evaluate each expression. Show your thinking 7+2^3
[tex]7+2^3[/tex]
[tex]7+(2^3)[/tex]
[tex]7+8[/tex]
[tex]=\fbox{15}[/tex]
Someone please help! I’ll give Brainliest!!
Answer:
BAD
Step-by-step explanation:
i think its triangle BAD sorry if its not would make the most sense i think
Which ordered pair is a solution of the equation? 6 x + 3 y = 15 6x+3y=15
Choose 1 answer:
(Choice A)
A
Only
(
3
,
−
2
)
(3,−2)left parenthesis, 3, comma, minus, 2, right parenthesis
(Choice B)
B
Only
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis
(Choice C)
C
Both
(
3
,
−
2
)
(3,−2)left parenthesis, 3, comma, minus, 2, right parenthesis and
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis
(Choice D)
D
Neither
Neither of the ordered pairs is a solution of the equation 6x + 3y = 15.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given linear equation is 6x + 3y = 15
Substitute each of the point given in the options.
A : (3, -2)
6x + 3y = (6 × 3) + (3 × -2) = 18 - 6 = 12 ≠ 15
B : (2, 2)
6x + 3y = (6 × 2) + (3 × 2) = 12 + 6 = 18 ≠ 15
Neither (3, -2) nor (2, 2) are the solutions of the equation.
Hence neither is the solution of the given linear equation.
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explain how the sequence 10.6, 11.8, and 13 is a function even though there are multiple rules that can represent it.
The correct option is Option C.
C.) The sequence is a function because each rule produces one output for each input.
Meaning of a sequence:
A grouping of any objects or a collection of numbers in a particular order that follows some rule is known as a sequence.
The difference between all the following terms in the sequence 10..6.11.8.13 is 12.
As a result, the series is an example of a linear function.
As a linear function, the sequence will always provide an output that complies with the rule.
As a result, the sequence is a function because each rule yields a single output for each input; hence, option C is the right response.
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The following question may be like this:
Explain how the sequence 10.6, 11.8, and 13 is a function even though there are multiple rules that can represent it.
A)The sequence is a function because the domain is unrestricted.
B)The sequence is a function because more than one rule can represent it.
C)The sequence is a function because each rule produces one output for each input.
D)The sequence is a function because each rule produces multiple outputs for each input.
When all team members agree on the level of performance that is acceptable, they have a _____. Clear goal leader shared standard team structure
When all team members agree on the level of performance that is acceptable, they have a shared standard.
Teamwork is a collective approach in order to achieve a common goal for the growth of the organization. Each member of the team must be agreed on the methods and sources to be implemented in achieving the goal.
In order to achieve the goal, each individual has to work on his area but with the team to achieve the goal of the company. Each individual works together and share their efforts collectively so that the goal can be achieved.
Shared standard refers to the point of acceptance by each individual on a particular point and must agreed on the merging of the work collectively.
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For the shape below, if side BD = 29 and side AC = 3x - 4, find x.
Answer:
x = 11
Step-by-step explanation:
We know that the answer we will get will be the same as BD because BD and AC are congrudent, meaning that they are exactly equal shape and size. To find 'x' our equation would be: 29 = 3x - 4. To figure this out we just add 29 and 4 which gives us 33 and then divide that by 3 which gives us 11 (our answer)
write the equations described below.
a subtraction equation with one variable that has a solution of 2/3.
Answer: o
Step-by-step explanation:
I don’t understand how to do this.
Answer:
6000
Step-by-step explanation:
Interest of 3% a year of principal of 200,000 = 6000
monthly payment of 843 also includes a portion of amortization of the principal itself, which you can ignore cause the question only asked for the interest portion.
this is an unclear question cause it didn't say PER YEAR interest paid. you only need to remember interest% * principal = ANNUAL interest payment $. Then you can divide that over 12 months, which is 500$ per month.
0.18 rounded to the nearest tenth
Answer:
0.2
Step-by-step explanation:
8 is bigger than 5 so we will make 8 zero and will will add 1 to the next number
Answer:
0.2
Step-by-step explanation:
Hope this helps
~~Wdfads~~
Explain your work please.