The four types of Transformations - Rotation, Translation, Reflection, Dilation.
What is transformation ?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
When we relocate a picture without making any other changes to it, we say that we have translated it.Rotation is the process of slightly rotating a picture.When we flip an image along a line (the mirror line), it is called reflection.Dilation is the process of enlarging or contracting an image's size without altering its form.Transformations may be divided into four categories: translation, rotation, reflection, and expansion. You must be able to carry out each change and recognize which ones have already been done.
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Translation, rotation, reflection, and dilation are the four basic forms of transformations.
What is Transformation?By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made. A fresh viewpoint on geometry known as transformational geometry was put forth by Felix Klein in the 19th century.
The transformation is f: X X, which stands for a function, f, that maps to itself. The transformation causes the pre-image X to change into the picture X. Translation, rotation, reflection, and dilation are only a few examples of the transformations that can be used alone or in combination. A function is translated when it is moved in one direction, rotated when it is spun around a point, reflected when it is turned into the opposite of itself, and dilated when it is scaled. Two-dimensional geometrical figures can move about a coordinate plane via mathematical transformations.
Hence, Translation, rotation, reflection, and dilation are the four basic forms of transformations.
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The product of two consecutive positive integers is 1,332. Explain how you can write and solve a quadratic equation to find the value of the larger integer.
Answer:
The numbers can be written as x and x + 1. Set the product of the numbers equal to 1,332 to get x(x + 1) = 1,332. You can solve the quadratic equation by using the quadratic formula, completing the square, or factoring. When you solve the quadratic equation, you find that x = –37 and 36. Since the question asked for positive integers, the only viable solution is x = 36. To solve for the larger integer, you add 1 to 36 to get an answer of 37.
Step-by-step explanation:
sample response
The first consecutive number is 36 and the second consecutive number is 37.
What are the consecutive numbers?Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.
Let the first consecutive number be x and the second consecutive number be (x+1).
The product of two consecutive positive integers is 1,332.
[tex]\rm x\times (x+1)=1332\\\\x^2+x=1332\\\\x^2+x-1332=0\\\\x^2+37x-36x-1332=0\\\\x(x+37)-36(x+37x)=0\\\\(x+37)(x-36)=0\\\\x+37=0, \ x=-37\\\\x-36=0, \ x=36[/tex]
(Ignoring the negative value of x).
The first consecutive number = x = 36
The second consecutive number = x+1 = 36 + 1 = 37
Hence, the first consecutive number is 36 and the second consecutive number is 37.
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James joins Club one which charges a monthly membership of 19.99 how much will James spend in all if he continues his membership for six months
12-6.5 also i need help with a scenario and with a word problem the scenario is the photo i put and with two word problems ramona sees that her cat hasn"t been eating and wants him to gain more weight. If the cat weighs 6.78 pounds and the goal weight is 10.5 lbs, how much weight does Ramona want her cat to gain? these are two separate problems. Jessica is running a 5k which is about 3.1 miles at a charity event. She starts slowing down around 1.75 miles into the race. How much farther does Jessica have before reaching the finish line?
Answer:
The cat needs to earn 3.72 pounds
Jessica has 1.35 miles to earn in the race.
Step-by-step explanation:
Rewrite the following without an exponent. (9/5^-2)
Answer:
225
Step-by-step explanation:
5^-2 can be rewritten as 1/25.
Then we can divide 1/25 by 9. 9/(1/25)= 225
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the polynomial y = x^{5} + x^{3} - x^{2} - 1 factors into (x^{2} + 1) (x^{3} - 1). what is the multiplicity of the root (x^{3} - 1)?
Answer:
The multiplicity of the root is 1
Step-by-step explanation:
Firstly, we need to understand what multiplicity is
By multiplicity, we simply refer to the number of times we have the certain root repeating itself
From the factorization, each of the given roots were only repeated once
That indicates that the given multiplicity is 1
You need at least $48,000 in two years. If you earn 4.8% compounded annually, how much principle do you need to invest?
Answer:
488305
Step-by-step explanation:
100 plus 4.8 percent then add 4.8 percent gets you 109.83
then apply 9.83 percent to random numbers in a calculator
in ABC , Ab=7 , BC=9, AND AC=9, What is the smallest angle of the triangle ?
Answer:
Angle C
Step-by-step explanation:
It is an isoceles triangle.
Write a positive or negative integer that represents the situation. You earn $15 raking leaves. The integer represents the situation.
Answer:
+$15
Step-by-step explanation:
Amount earned for raking leaves = $15
Representing the amount earned above. As a positive or negative integer will depend on what the money is used for or stands for.
Amount earned for working adds to one's wealth while expenses will be represented as negative as it decreases the amout one has ;
Hence, integer ; +$15
3 + 2x - y = 0, -3 - 7y = 10x}
Answer:
In point form:
( -1 , 1 )
In equation form:
x = − 1 , y = 1
A television network wanted to estimate the proportion of a one-hour time slot that is made up of commercials. The network took random samples of
10
10 one-hour time slots. The following are the sample proportions the network found in
12
12 samples.
Part A
What is the estimated proportion of commercials in all one-hour time slots? Round your answer to the nearest thousandth.
Answer:
120
Step-by-step explanation:
Remember, always round sample size up, regardless of the decimal part. Answer: To find a 95% CI with a margin of error no more than ±3.5 percentage points, where the true population proportion is around 42%, you must survey at least 764 people. 10×764 = 7640; presumably the electorate is larger than that. So, then 10 × 12 = 120
The price of a watch was increased by 20% to £198.
What was the price before the increase?
Answer:
$165 Hope this helps! May I have brainliest? I need to level up?
Step-by-step explanation:
To find the original price before the increase, divide the new price by 1 + the percent of increase.
198 / 1.20 = 165
The original price was $165
How can you translate words into equations?
Answer:
try to look out for words such as more than, less than, twice as much, half as much, in addition to, took away something, etc
Step-by-step explanation:
hope this helped!
This table represents the monthly fees for checking accounts at two banks.
Which statement is best supported by the information in the table?
Answer options:
a) The fee at Sunset Bank will be less than the fee at Oceanview Bank only when the checking account balance is more than $200.
b) The fee at Sunset Bank will always be less than the fee at Oceanview Bank.
c) The fee at Sunset Bank will always be more than fee at Oceanview Bank.
d) The fee at Sunset Bank will be less than the fee at Oceanview Bank only when the checking account balance is less than $200.
[tex]23 1/5 in to percentAGE
can some give me the anwsers
Answer:
150 -160
Step-by-step explanation:
I not amazing at this but i do know this is kinda hard. sorry if it is wrong
I need help with this question, plsssssssss
Answer: 60 also your welcome
A store had 112 diet sodas. The ratio of diet sodas to regular sodas was 8:4. How many regular sodas were there?
Answer:
56
Step-by-step explanation:
There are two ways the answer to this question can be determined
Method 1 : the fast method
We know that 8 is twice 4
4 x 2 = 8
The ratio of diet soda = 8
the ratio of regular sodas = 4
Diet sodas = 112
the number of regular sodas = 112 / 2 = 56
Method 2 : The long method
I would first determine the total number of diet and regular sodas. Let the total number be represented by d
from the question, the following equation can be derived :
(8/12) x d = 112
divide both sides of the equation by 12/8 to determine the value of d
d = 112 x (12/8) = 168
We can now derive a value for the number of regular soda
regular sodas = ( ratio of regular sodas / total soda) x total number of sodas
(4/12) x 168 = 56
4)
Which set of numbers are equivalent?
A)
5
5%, 0.5, 5/100
100
B)
8
8%, 0.08, 8/10
10
C)
10.
10%, 0.1,
10/100
D)
12%, 0.012,
12/100
Answer:
It’s c
Step-by-step explanation:
.1 can also be written as .10 which when you multiply by 100 is 10 so it’s also written as 10%
01. En una piscigranja el 30% de boquichicos es el 20% del número de carachamas. Si sólo hay boquichicos y carachamas. ¿Qué porcentaje del 80% del total es el número de boquichicos? A) 30% B) 50% c) 40% D) 60% E) 25% 02. Se sabe que un libro de de Psicología es más caro que uno de Inglés; uno de Matemática más caro que uno de Historia, pero más barato que uno de Psicología. ¿Cuál es el más caro? A) Psicología B) Historia C) Matemática D) Inglés E) No se puede determinar 03. Calcular la cantidad total de esferas en el siguiente arreglo triangular. A) 4950 B) 5000 C) 4850 D) 5050 E) 5151 04. Calcular "E" y dar como respuesta la suma de sus cifras. A) 900 B) 1200 c) 1800 D) 2700 E) 9990
Answer:
0.1. B) 50%
0.2 A) Psicología
Step-by-step explanation:
01. Dejemos que 'x' e 'y' representen el porcentaje de boquichicos y carachamas en la piscifactoría, tenemos;
Dado que el 30% de los boquichicos es el 20% del número de carachamas
30% x = 20% y
∴ 0.3 · x = 0.2 · y
Por lo tanto, tenemos;
x / y = 0,2 / 0,3 = 2/3
Por lo tanto, por cada 100% de pescado, tenemos;
x + y = 100%
x = 2/3 · y
2/3 · y + y = 100%
5 · años / 3 = 100
y = 100 × 3/5 = 60%
El porcentaje de carachamas en la finca, y = 60%
∴ x = 100% - y = 100% - 60% = 40%
El porcentaje de boquichicos en la finca, x = 40%
Por lo tanto, tenemos el 80% del pescado en la granja, obtenemos;
Si hay 100 peces en la granja, 80% = 80 peces
Pero el número de los 100 peces que son boquichicos en la granja = 40% × 100 = 40 peces
Por lo tanto, los boquichicos son la mitad del 80% del número de peces o el 50% de los peces en la piscifactoría.
La opción correcta es;
B) 50%
02. Tenemos;
El costo de un libro de psicología> El costo de un libro en inglés
El costo de un libro de matemáticas> El costo de un libro de historia
El costo de un libro de psicología> El costo de un libro de matemáticas
Por lo tanto, tenemos;
El costo de un libro de psicología> El costo de un libro de matemáticas> El costo de un libro de historia
∴ El libro de Psicología es más caro que todos los demás libros y, por tanto, es el libro más caro
La opción correcta es;
A) Psicología
Find the volume of the sphere.
Either enter an exact answer in terms of 7 or use 3.14 for I and round your final answer to the nearest hundredth.
units
Answer:
Volume of the given sphere = 4.19 units³
Step-by-step explanation:
Volume of a sphere is given by the expression,
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
Here, r = radius of the sphere
From the picture attached,
Radius of the sphere 'r' = 1 unit
Volume of the given sphere = [tex]\frac{4}{3}\pi (1)^3[/tex]
= [tex]\frac{4}{3}\pi[/tex]
= [tex]\frac{4}{3}(3.14)[/tex]
= 4.187
≈ 4.19 units³
Solve for m:
598 + 15.75m < 850
Answer:
m < 16
Step-by-step explanation:
598 + 15.75m < 850
15.75m < 850 - 598
15.75m < 252
m < 16
What is the vertex of y = x2 + 4x – 7?
O(-4,-7)
O (2, 5)
0 (-2, -19)
0 (-2, -11)
can I get help please
Answer:
Answer is D
Step-by-step explanation:
help!!
Show that 1 + tan2(x) = sec2(x)
Answer:
tan2(x) + 1 = sin2(x)/cos2(x) + 1 = [sin2(x) + cos2(x)]/cos2(x) = 1/cos2(x) = (1/cos(x))2 = sec2(x). Thus tan2(x) + 1 = sec2(x).
Step-by-step explanation:
Answer: Not an identity
Step-by-step explanation:
Write the equation of the line passing through point (-2 - 2) with a slope of -1
Substitute into y = mx + b and for b
yoo i got a paper due tmrw if anyone could answer this that’d be bomb thank u
x/8- 3/4=5/8 , solve the equation for x
The customer saves $.96 by using a coupon. The coupon takes 30% off the original price of the serial. What is the original price of the box of cereal?
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Trigonometry, NEED HELP ASAP
Answer:
[tex]sin(\theta_1) = \dfrac{\sqrt{357} }{29}[/tex]
Step-by-step explanation:
The parameters of the angle θ₁ are;
The location of θ₁ = Quadrant II
cos(θ₁) = -22/29
We note the following;
1) The sine of an angle in quadrant II is positive
2) The cosine of an angle in quadrant II is negative,
2) The cos of an angle = The adjacent leg length to the reference angle divided by the hypotenuse length of a right triangle
3) With regards to the right triangle for finding cos(θ₁)
The adjacent leg length = -22 (The x-axis is negative in quadrant II)
The hypotenuse length = 29
The negative sign is obtained from the value of cosine in the quadrant
Therefore, by Pythagoras' theorem, for a right triangle, we have;
The opposite leg length to 'θ₁' = √(29² - 22²) = √(357)
[tex]sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]
Therefore, we have;
[tex]sin(\theta_1) = \dfrac{\sqrt{357} }{29}[/tex].