Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation.
How do you know if a dilation is an enlargement or reduction?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation.
A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
An enlargement (imagine stretching) is a dilation that makes a larger image, whereas a reduction (think shrinking) is a dilation that creates a smaller image. A diminution in the image occurs when the scale factor is between 0 and 1. An enlarged version of the image is shown if the scale factor is larger than 1.
A transformation called a dilation (similarity transformation) alters the size of a figure. A center point and a scaling factor, k, are necessary. Which kind of dilation it is—an enlargement or a reduction—depends on the value of k. An enlargement results from a dilatation if |k|>1.
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Lois is saving $11.00 out of her $32.00 allowance each week for a
scooter. She must divide the rest between her savings account, a
charity of her choice, and her college fund. Lois gives $10.00 per week
to a local charity. She puts the same amount in her saings account as
her college fund. How much does Lois put in her college fund each
week?
Answer:
the answer is $5.50
Step-by-step explanation:
32 total
10+11=21
32-21=11
so 11 left for college and saving account
now divide it with 2 so both gets same amount
11/2=5.50
im not sure how to answer thank you
The value of x in the triangle WXY is 27°
What is an equation?An equation shows how two or more numbers and variables are related to each other.
∠VWY + ∠XWY = 180° (sum of angle in straight line)
6x + ∠XWY = 180°
∠XWY = 180 - 6x
∠XYW + ∠ZYW = 180° (sum of angle in straight line)
∠XYW + 4x = 180°
∠XYW = 180 - 4x
∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)
(180 - 6x) + (180 - 4x) + 90 = 180
450 - 10x = 180
10x = 270
x = 27°
The value of x is 27°
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Remember, adjectives in Spanish agree with the gender of the noun they describe.
Por ejemplo: el chico ordenado / la chica artística
Answer:
1) A serious girl - Una chica seria/Una joven seria
2) The talented boy - El chico talentoso/El joven talentoso
3) An outgoing girl - Una chica extrovertida/Una joven extrovertida
4) The tasty ice cream - El helado delicioso/El helado sabroso
5) A funny book - Un libro divertido/Un libro entretenido
Step-by-step explanation:
Now, we present a possible set of solution, as there are solutions as many synonyms exist in Spanish. Then:
1) A serious girl - Una chica seria/Una joven seria
2) The talented boy - El chico talentoso/El joven talentoso
3) An outgoing girl - Una chica extrovertida/Una joven extrovertida
4) The tasty ice cream - El helado delicioso/El helado sabroso
5) A funny book - Un libro divertido/Un libro entretenido
All 210 students in a school went roller skating, to a water park, or both. The number of students who went only to the water park is four times the number of students who went only roller skating. The number of students who went only to the water park is two times the number of students who did both. How many students did both?
60 students out of 210 in a school went both roller skating and water park.
What is algebraic equation ?
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Have given ,
Total students = 210
Let x = The number of students who went only to the roller skating
and y = The number of students who went to the water park and roller skating
x + 4x + y = 210 ⇒ 5x + y = 210 ......(i)
x + y + 2y = 210 ⇒ x + 3y = 210 ⇒ x = 210 - 3y
Put the value of x in equation no. (i),
5(210 - 3y) + y = 210 ⇒ 1050 - 14y = 210 ⇒ 14y = 1050 - 210
14y = 840 ⇒ y = 60
Hence , 60 students out of 210 in a school went both roller skating and water park.
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Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a
30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
0
1
2
W = # of walleye
P(W)
0. 49
0. 42
0. 09
Calculate the mean of W.
walleye
The mean of the walleye 'W' for the given number of walleye and its probability to represent that 30% chances are of walleye is equal to 1.4.
As given in the question,
Let 'W' is the random variable represents the number of walleye.
'P(W)' represents its probability
The values are given as follow:
W : 0 1 2
P(W) : 0.09 0.42 0.49
Mean of the walleye 'W' is given by :
= W₁P(W₁) + W₂P(W₂) + W₃P(W₃)
= ( 0 × 0.09 ) + ( 1 × 0.42 ) + ( 2 × 0.49 )
= 0 + 0.42 + 0.98
= 1.4
Therefore, the mean of the walleye 'W' for the given number of walleye and its probability is given by 1.4.
The above question is incomplete , the complete question is :
Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30% chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets
if she catches 2 fish.
W : 0 1 2
P(W) : 0.09 0.42 0.49
Calculate the mean of W.
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Chapter 3 Lesson 4 Arithmetic Sequence
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
What is Arithmatic Sequence?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence. As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulae for arithmetic sequences.
The equation to determine the nth term in an arithmetic series
The formula for calculating the sum of an arithmetic sequence's first n terms
There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."
Option 1, 4 and 6 are in Arithmatic Sequence as
In 1:
1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)
again in 4 :
37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)
and in 6
-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).
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What is the solution to 3(1-3x)=2(-4x+7)?
Answer:
x = -11
Step-by-step explanation:
3(1 - 3x) = 2(-4x + 7)
Distribute the 3.
(3 - 9x) = 2(-4x + 7)
Distribute the 2.
3 - 9x = -8x + 14
Add 8x to both sides.
3 - x = 14
Subtract 3 from both sides.
-x = 11
Multiply by -1.
x = -11.
Proof:
3(1 - 3x) = 2(-4x + 7)
3(1 - 3(-11)) = 2(-4(-11) + 7)
3(1 + 33) = 2(44 + 7)
3(34) = 2(51)
102 = 102
Find the area of the surface obtained by rotating the circle
x2 + y2 = r 2
about the line
y = r.
The area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
To find the area of the surface obtained by rotating the circle
[tex]x^2 + y^2 = r^2[/tex] about the line y = r, we can use the method of cylindrical shells.
The circle [tex]x^2 + y^2 = r^2[/tex] is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.
When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.
Consider a small strip on the circle at a distance y from the line y = r.
This small strip is at a distance r - y from the y-axis.
The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).
The width of this strip is the change in x, which we can denote as dx.
The area of this small strip is then given by the product of its length and width, which is 2πy dx.
Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):
Total Surface Area = ∫[from -r to r] 2πy dx
Now, we need to express y in terms of x using the equation of the circle [tex]x^2 + y^2 = r^2:\\y^2 = r^2 - x^2[/tex]
y = ±√(r² - x²)
Since we are considering the upper half of the circle, we take the positive square root:
y = √(r² - x²)
Now, we can rewrite the integral with respect to x:
Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx
To solve this integral, we can make a trigonometric substitution:
Let x = r sin(θ), then dx = r cos(θ) dθ.
When x = -r, θ = -π/2, and when x = r, θ = π/2.
Now the integral becomes:
Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ
Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ
Now, we can use the trigonometric identity:
sin²(θ) + cos²(θ) = 1
√(1 - sin²(θ)) = cos(θ)
Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ
Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2
Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ
Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]
Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]
Since sin(π) = 0 and sin(-π) = 0:
Total Surface Area = 2πr² [(π/2 - (-π/2))/4]
Total Surface Area = 2πr² (π/2)
Total Surface Area = π²r²
So, the area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
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look at the screenshot.....
Answer:
the total surface area is 360 cm
Step-by-step explanation:
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:
Step-by-step explanation:
The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:
f(–10) = (–10)^2 – 5(–10) + 12 = 100 – (–50) + 12 = 162
The statement "The graph of the function is a parabola" is true. Because the equation of the function is of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0, the graph of the function is a parabola.
The statement "The graph of the function opens down." is true. The coefficient of x^2 is a positive value, which means the parabola opens down.
So, the true statements are
The graph of the function is a parabola.
The graph of the function opens down.
The graph does not contain the point (20, –8)
When working modulo m, the notation a^-1 is used to denote the residue b for whichab = 1 (mod m), if any exists. For how many integers a satisfying 0 < a < 100 is it true thata(a − 1)−¹ = 4a-¹ (mod 20)?Please hurry up guys!!
There are 10 integers that satisfy 0 < a < 100.
What are integers?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.
Here, we have
Given: When working modulo m, the notation a⁻¹ is used to denote the residue b for which ab = 1 (mod m), if any exists.
We have to find integers that satisfy 0 < a < 100.
a(a − 1)⁻¹ ≡ 4a⁻¹ (mod 20)
a ≡ 4a⁻¹(a − 1)(mod 20)
a² ≡ 4(a-1)(mod 20)
a² - 4a + 4 ≡ 0(mod 20)
(a - 2)² ≡ 0(mod 20)
a = 2 + 10n | for n = (0, 1, 2, 3.....9)
Hence, there are 10 integers that satisfy 0 < a < 100.
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if two lines in a plane intersect then they are not parallel true or false
Answer:
true because parallel means lines that doesnt meet
Answer:true, parallel line never intersect, I hope this helps!!
Cute cat btw<3
1. Are the triangles shown below similar? Explain.
Answer:
Step-by-step explanation:
These are the tests for similar triangles:
AA - if 2 pairs of corresponding angles are equal.
SSS - if corresponding sides have the same ratio.
SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.
This diagram does not indicate any of these relationships exist.
Therefore the triangles are not similar.
The point A (1,1) and the point B(5,-1) lie on the line L. Find the equation of the line L
What is the measure of ZB?
Answer:
m<B=60°
Step-by-step explanation:
an exterior angles equals the sum of its two remote interior angles, so:
m<A+m<B=m<BCG:
3x+4x=10x-45
7x=10x-45
-3x=-45
x=15
to find the measure of <B:
since m<B=4x:
4(15)=60°
so, m<B=60°
Answer:
Step-by-step explanation:
A small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded. The results showed that 150 of the adults who were parents and 40 of the adults who err not parent’s thought the park should be expanded.
Answer: In this exercise we have to calculate the values of the people who voted to expand the parking lot, so we have to:
Yes: parents will be 150 and not parents 40
No; parents will be 40 and not parents 30
As it is about sets, we have to use the data that were:
total: 250 adults
180 of whom were parents a park should be expanded.
40 of the adults who were not parents thought the park should be expanded.
then calculate that:
Step-by-step explanation:
The surveyed parents favor park extension, and two way table is a way or representation of data. and The two-way table is completed as,
yes no
parents 150 | 30
|
not parents 40 | 30
The two-way table shown in the table is attached below.
What is two way table?
Two-way table is a way of representing of data to better understand it.
Given information-
The total number of adults took the survey is 250.
Total number of parents took the survey is 180.
150 of the adults with children and 40 of those without thought the park should be expanded.
Suppose the number of adults who are not the parents and took the survey is .
As the total number of adults took the survey is 250 in which the number of parents took the survey is 180. Thus the number of adults who are not the parents and took the survey is,
Suppose the parents who does not thing that the park should be expanded is .
There is total 180 parents. As 150 of the adults with children thought the park should be expanded. Thus, the parents who does not thing that the park should be expanded is,
Form the 70 adults who are not parents things that park should be expanded is 40, hence the adults who are not parents does not thing the park should be expanded is (70-40) which is 30.
Hence the two way table is completed as,
yes no
parents 150 | 30
|
not parents 40 | 30
the two way
YES NO
30
30
(parents 150
not parents_40
One yard of ribbon is 3.5 dollars. How much should one pay for
5/8 yards
Answer:
38
Step-by-step explanation:
One should pay 2.1875 dollars.
What are arithmetic operations?Addition, subtraction, multiplication, and division are the most fundamental operations in arithmetic. However, arithmetic also includes more complex operations like manipulating percentages, square roots, exponentiation, logarithmic functions, and even trigonometric functions, which are analogous to logarithms. It is necessary to evaluate arithmetic expressions in accordance with the intended order of operations.
Given one yard of ribbon is 3.5 dollars
1y = 3.5
where y = yards
dollar for 5/8 yards is
1y x 5/8 = 3.5 x 5/8
5/8y = 2.1875
Hence one should pay 2.1875 dollars for 5/8 yards.
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ILL BRAINLIEST YOU PLEASE HELP ME
Answer:
x = 71/5 (as an improper fraction)
x = 14 1/5 (as a proper fraction
x = 14.2 (as a decimal)
Step-by-step explanation:
It's a rectangle so the diagonals are equal
7x - 9 = 2x + 62
Subtract 2x from both sides
5x - 9 = 62
Add 9 to both sides
5x = 71
Divide both sides by 5
x = 71/5 (as an improper fraction)
x = 14 1/5 (as a proper fraction
x = 14.2 (as a decimal)
Answer:
x= 14.2
Step-by-step explanation:
BD and and AC are equal so
7x-9 = 2x+62
isolate the variable means x = 14.2
first time I had to take out pencil and paper so I hope it's right
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
Answer:
The area of this parallelogram is 140 square feet.
Step-by-step explanation:
A = bh
A = 14 * 10
A = 140
Hope this helps; have a wonderful day!
What are the solutions of the quadratic equation 2x^2 5x 12 0?
The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.
what is a quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.
where a, b, and c are constant terms and x is the unknown variable.
Here I am using the factoring method to solve a quadratic equation.
Given quadratic equation is
[tex]2x^2 - 5x -12 = 0.[/tex]
By comparing the General form of the quadratic equation we will get
a = 2, b = -5 and c = -12.
2x^2 - (8-3)x - 12 = 0.
2x^2 - 8x + 3x -12 = 0.
2x(x-4) + 3(x-4) = 0
(x - 4) (2x + 3) = 0.
x - 4 = 0 or 2x + 3 = 0
x = 4 or x = -3/2
Given Question is incomplete complete question here:
What are the solutions of the quadratic equation 2x^2-5x-12 = 0?
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What are the 3 linear equations?
The 3 linear equations are
1. y = mx + b
2. ax + by = c
3. x/a + y/b = 1
1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.
2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.
3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.
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The first laptop ever was sold was the Osborne 1. It came onto the market in 1981, and
it had a mass of 11 kg. Suppose that since 1981 the mass of laptops has decreased at an
average rate of 4. 7% per year. What was the approximate weight of a laptop in 2019?
The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.
1981: 11 kg
1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)
1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)
1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)
2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)
The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.
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Find the sum of the first 44 terms of the following series, to the nearest integer.
5,12, 19,...
Answer:6842
Step-by-step explanation:
13684/2
How many square feet of outdoor carpet will
we need for this hole?
Answer:
8
Step-by-step explanation:
Question 2 of 5
Simplify.
(m3)6 +m18
A. m4
B. 1
C. m
D. m-9
SUBMIT
Using the first index law, the solution provided indicates that this has a value of 1.
What is the first index law?X to the power of A multiplied by X to a power of B results in X to the power of A + B, according to the first law of indices. Keep in mind that adding the indices when multiplying terms with them means that the base must remain constant throughout.
What exactly is index theory?A topological invariant of a certain class of differential operations on a manifold is studied in index theory, as well as the invariant's local formula in terms of the manifold's geometry. inspirational cases. operator elliptic The index theorem by Atiyah-Singer.
According to the given information:(m³)⁶/m¹⁸ = m³ˣ⁸/m¹⁸
= m¹⁸/m¹⁸
= 1
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The Paulsens ordered $75.41 worth of Chinese food. They paid 11.5% sales tax and left a
15% tip on $75.41. What was the total cost?
Answer:
$95.39
Step-by-step explanation:
First, find sales tax
75.41×(11.5/100)=8.67
Then, tip
75.41×(15/100)=11.31
Therefore,
75.41+8.67+11.31
is the total cost
Answer:
95.39
Step-by-step explanation:
Ans the question...... very urgent
Answer:
The solution should be log7^3(49)-1/3log7(49)=1/3*2
B-2/3
how to solve -6/ 2/3 (use inverse operations to solve it) please explain!
please help due next hour this is one of my answer I'm struggling with Show WORK please. No links
x/2 = -1
please help I need it
x/2 = -1
=> x = -1 × 2
=> x = -2
The following dotplot shows the centuries during which the 111111 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle. According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?
The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.
We will calculate the interquartile range and us the rule 1.5 .
The formula to calculate interquartile range is to subtract the value of first quartile by the value of second quartile.
IQR = Q3 - Q1
Therefore, interquartile range becomes,
IQR = 17 - 13
IQR = 4
Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first
4 * 1.5 = 6
and then,
17 + 6 = 23
on applying the rue we will get ,
13 - 6 = 7 .
This value means that there is no outlier in the displayed data set.
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