A triangle is dilated with the center of dilation at point U. Point E is a vertex of the triangle and point E ’ is the corresponding vertex of the image. If UE = 2 centimeters and UE ’ = 10 centimeters, what is the scale factor?
Answers
A triangle is dilated with the center of dilation at point U. Point E is a vertex of the triangle and point E ’ is the corresponding vertex of the image. If UE = 2 centimeters and UE ’ = 10 centimeters, the scale factor is 5 cm
Scale Factor Definition
A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
By definition, a Dilation is a transformation in which the image has the same shape as the pre-image but size changes.
The center of dilation is a fixed point in the plane, and the scale factor is the ratio of the corresponding sides of the image to the pre-image.
Scale Factor In Geometry
Scale is used in geometry to make accurate reproductions of figures; they are different sizes, but same proportions. Figures are similar but to scale.
Based on the information provided in the exercise, you know that:
UE = 2 centimeters
UE ’ = 10 centimeters
Therefore, you can determine that the scale factor is:
The scale factor for scaling up is a ratio greater than 1
The scale factor for scaling down is a ratio of less than 1
.
Scale factor : 10/2 = 5
Scale factor = 5 cm
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The center of dilation for a triangle is located at point U. The image's point E' corresponds to point E, which is the vertex of the triangle. The scale factor is 5 cm if UE = 2 centimeters and UE'= 10 centimeters.
Define Scale Factor
The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller.
A dilation is, by definition, a transformation in which the size of the image changes but the shape remains the same as the pre-image.
The scale factor is the ratio of the corresponding sides of the image to the pre-image, and the center of dilatation is a fixed point in the plane.
Considering Scale in Geometry
In geometry, scale is utilized to create correct figures that have varying sizes but the same proportions. Similar but scaled figures are shown.
You are aware of the following thanks to the material in the exercise:
2 centimeters equals UE.
10 centimeters equals UE'.
Therefore, you can determine that the scale factor is:
The scale factor for scaling up is a ratio greater than 1
The scale factor for scaling down is a ratio of less than 1
Scale factor : 10/2 = 5
Scale factor = 5 cm
Related Questions
Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
Answers
When using the distributive property, if the term outside the parentheses is negative, then the sign of each term inside the parentheses will change: Always TRUE
What do we mean by distributive property?The distributive property of binary numbers in mathematics generalizes the distributive law, which states that equality is always true in elementary algebra. In elementary arithmetic, for example, one has According to one, multiplication distributes over addition.If the term outside the parenthesis is negative when using the distributive property, the sign of each term inside the parentheses will always change.Example can be: -1(27 - 55) = -27 + 55
It is because of the following reason that when we multiply two numbers:
(positive number (+)) × (positive number (+)) = (positive number (+))(positive number (+)) × (negative number (-)) = (negative number (-))(negative number (-)) × (positive number (+)) = (negative number (-))(negative number (-)) × (negative number (-)) = (positive number (+))Therefore, the statement "when using the distributive property, if the term outside the parentheses is negative, then the sign of each term inside the parentheses will change" is Always TRUE.
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The complete question is given below;
Determine whether the following statement is always, sometimes, or never true. Explain your reasoning. When using the distributive property, if the term outside the parentheses is negative, then the sign of each term inside the parentheses will change.
Jonathan earns $250 plus $40 for every house he paints
Answers
Answer:
250 + 40x
Step-by-step explanation:
x = every house he paints .
im not sure what you want but in case its an equation , here you go .
Answer:
250 + 40x
Step-by-step explanation:
literally what the dude above me said heh
Write a coordinate proof to prove that Δ A B C is an isosceles triangle if the vertices are A(0,0), B(a, b) , and C(2 a, 0) .
Answers
An isosceles triangle is one with two equal-length sides. ΔABC is an isosceles triangle.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²] units.
Given that the coordinates of the vertices of the triangle are A(0,0), B(a, b), and C(2a, 0). Now, to prove that the given triangle is an isosceles triangle we need to find the length of each side of the triangle.
AB = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(a - 0)² + (b - 0)²]
= √(a² + b²)
BC = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(2a - a)² + (0 - b)²]
= √(a² + b²)
AC = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(2a - 0)² + (0 - 0)²]
= √4a²
= 2a
Since the length AB and BC are the same, while the length of AC is different, therefore, ΔABC is an isosceles triangle.
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Suppose two boxes of cereal contain the same amount of ounces but cost different amounts. Without computing, how can you determine which Siri will cost more per ounce of cereal? Explain.
Answers
Answer:
The one that costs more.
Step-by-step explanation:
Because you already know that they have the same volume (amount of ounces) and they are different prices, whichever one is more expensive has the higher cost per ounce. {You don't need to solve for a ratio or anything because they have the same number of ounces!!!}
Answer: If the number of ounces are the same, then the box that costs more will also cost more per ounce.
Use the fact that a/b / c/d = a/b ÷ c/d to simplify each rational expression. State any restrictions on the variables.
9m + 6n / m² n² / 12m + 8n/5 m²
Answers
What can you say about and based on the sum of their angles? How are the angles related?
Answers
Answer: Do you have a picture of the problem so it will be more sense?
Step-by-step explanation:
State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
Determining the arrangement of people around a circular table would require circular permutation.
Answers
True, Determining the arrangement of people around a circular table would require circular permutation.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.True, Determining the arrangement of people around a circular table would require circular permutation.
It happens that there are only two ways we can seat three people in a circle, relative to each other's positions.
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The table shows the elevation above sea level of the lowest and highest points in the United States.
Location
Death Valley
Mount McKinley/Denali
Elevation Above Sea Level (feet)
-282
20,310
Choose three correct statements.
A. Death Valley is -282 feet below sea level.
B. Death Valley is 1-2821 feet below sea level.
C. Death Valley is 1-2821 feet above sea level.
D. Mount McKinley/Denali is 120, 310| feet below sea level.
E. Mount McKinley/Denall is-120, 3101 feet below sea level.
F. Mount McKinley/Denali is 1-20, 3101 feet above sea level.
Answers
Location Death Valley, Mount McKinley/Denali Elevation Above Sea Level (feet), then the statement B , statement E , statement F are correct.
Death Valley is |-282| feet below sea level. Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.These three statements are correct.
The table shows the elevation above sea level of the lowest and highest points in the United States.
Location Death Valley
Mount McKinley/Denali
Elevation Above Sea Level (feet)
So, we can write,
Death Valley is |-282| feet below sea level.Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.You are subtracting the two numbers. Note however, that 282 feet below the sea level = -282
Subtract.
⇒ 20310 - (-282)
Note that two negatives = one positive
⇒ 20310 + 282
⇒ 20592 feet
Therefore, The statement B , statement E , statement F are correct.
Hence,
Death Valley is |-282| feet below sea level. Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.These three statements are correct.
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Simplify.
2 + 8 - 2 [32 + 5 (1 + 2)]}
Answers
Your answer should be - 84.
Explanation:
Starting equation: [tex]2\:+\:8\:-\:2\:\left[32\:+\:5\:\left(1\:+\:2\right)\right][/tex]
-Calculate within parentheses [32 + 5 (1+2)] = 47.
Remaining equation: 2 + 8 - 2 x 47
-Multiply and divide (left to right) 2 x 47 = 94
Remaining equation: 2 + 8 - 94
-Add and subtract (left to right) 2 + 8 - 94 = -84
Your final answer is -84
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Hope this helps!
Have a great day and God bless! :)
What sets (types or categories) of numbers do we use as the input to functions that represent sequences?
Answers
Answer:
electrical is a good servant but master
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
Suppose line l contains points A, B , and C , If A B=7 inches, A C=32 inches, and point B is between points A and C , what is the length of BC? Express your answer in inches.
Answers
Length of BC is 25 inches.
Here,
Line l contains points A, B and C.
A B =7 inches, A C = 32 inches, and point B is between points A and C.
We have to find the length of BC in inches.
What are Collinear points?
If two or more points are lie on a straight line then points are called Collinear points.
Now,
Line l contains points A, B and C.
Point B is between points A and C.
Length of A B = 7 inches and A C = 32 inches
Hence, Length of BC = Length of AC - Length of A B
= 32 - 7 = 25 inches.
Therefore, Length of BC is 25 inches.
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The maximum outstanding balance you should have on a credit card with a $2,000 limit is _____.
Answers
Solve. Find the area of a pantry shelf that measures 3 yards by 3/7 yard.
Answers
Answer:
The answer is 9/7 yards.
identify the inequalities A, B , and C for which the given ordered pair is a solution.
A. x+y ≤ 2
B. y ≤ (3/2)x-1
C. y>-(1/3)x-2
(-8,-11)
Answers
The inequality y ≤ (3/2)x-1 satisfies the point (-8, -11) option (B) y ≤ (3/2)x-1 is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The point is (-8, -11)
As we have inequalities shown in the option:
After plotting the inequality in the graph:
From the graph, the point lies in the solution region of the inequality y ≤ (3/2)x-1 which means the point (-8, -11) satisfies the inequality.
Thus, the inequality y ≤ (3/2)x-1 satisfies the point (-8, -11) option (B) y ≤ (3/2)x-1 is correct.
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Two different tests to write k/4 +16
Answers
Step-by-step explanation:
\begin{gathered}6x - 2y = 6 \\ 6x = 6 + 2y \\ x = \frac{6 + 2y}{6} \end{gathered}
6x−2y=6
6x=6+2y
x=
6
6+2y
y varies directly as x. Describe how the value of y
changes when the value of x is tripled.
Answers
Answer: When x is tripled, y will be tripled.
Step-by-step explanation:
Since y varies directly as x, whatever happens to x will happen to y. This means that if x is tripled, y will also be tripled.
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The arithmetic mean of two terms in an arithmetic sequence is -6 . One term is -20 . Find the other term.
Answers
The other term is +8.
How to find the other term?A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formules:
1. The initial term in the series.
2. The general rule for determining any term from its preceding term.
Formula for the Arithmetic Mean
The ratio of the sum of the items to the total number of items is the arithmetic mean, which is the simplest way to measure central tendency.It is regarded as the most accurate way to measure central tendency. The distribution of the data and the intended use of the data both influence the average that is chosen.
[tex]arithmetic \: mean = \frac{a1 + a2 + a3 + a4 + a5 + .........an}{n} [/tex]
given that
The arithmetic mean of two terms in an arithmetic sequence is -6.One term is -20 .
now, find the other term
[tex]arithmetic \: mean = \frac{a + b}{ 2} [/tex]
[tex] - 6 = \frac{( - 20) + b}{2} [/tex]
[tex]2 \times - 6 = - 20 + b[/tex]
[tex] - 12 + 20 = b[/tex]
[tex]b = 8[/tex]
Hence,the other term is +8.
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Which set of numbers are imaginary numbers?
Answers
Answer:
the third option contains imaginary numbers
Step-by-step explanation:
Imaginary numbers are the numbers when squared it gives the negative result. In other words, imaginary numbers are defined as the square root of the negative numbers where it does not have a definite value. It is mostly written in the form of real numbers multiplied by the imaginary unit called “i”. so we can express them as follows; √-2 = √-1 × √2 = √2 i.... √-1 = i
√-9 = √-1 × √9 = 3i
Claire mowed 5 lawns last week. She mowed each lawn in seven eighteenths hour. She mowed the same lawns this week in five eighteenths hour each using her new lawn mower. How many times longer was Claire’s time to mow all the lawns
Answers
help I'll mark brainliest
Answers
Answer:
2 + (-7) = -5
Step-by-step explanation:
The arrow pointing down is telling you to add a negative. You cannot add positive numbers and get a negative number as your answer.
Taking away -7 from 2 gives you -5
If $9237.05 is put into an account paying %8.82/ a compounding yearly, how much interest will be earned after 16.7 years?
Answers
Answer:
$28,656.82
Step-by-step explanation:
I used the compound interest calculator
A = P(1 + r/100)ⁿ
where A = amount accrued, P = investment amount r = rate% and n = number of years
r = 8.82% = 8.82/100 = 0.082 so 1 + r/100 = 1.0882
[tex]\\A = P(1.0882)^{16.7} = \$37,893.87\\\\\mathrm {Interest} = \$37,893.87 - \$9237.05 = \$28,656.82[/tex]
Answer:
$28,656.82
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf I=P\left(1+r\right)^{t} -P$}[/tex]
where:
I = Total interest earned.P = Principal amount invested.r = Interest rate (in decimal form).t = Time (in years).Given:
P = $9237.05r = 8.82% = 0.0882t = 16.7 yearsSubstitute the given values into the formula and solve for I:
[tex]\implies \sf I=9237.05(1+0.0882)^{16.7}-9237.05[/tex]
[tex]\implies \sf I=9237.05(1.0882)^{16.7}-9237.05[/tex]
[tex]\implies \sf I=9237.05(4.1023777...)-9237.05[/tex]
[tex]\implies \sf I=37893.8685...-9237.05[/tex]
[tex]\implies \sf I=28656.8185...[/tex]
Therefore, the amount of interest that will be earned after 16.7 years is $28,656.82 (nearest cent).
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how do i subtract inteargers
Answers
Answer:
You remove the difference between the two numbers from each other. E.g., 5-2=3, and 6-4=2.
Step-by-step explanation:
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Answers
To solve problems, construct one-variable equations and inequalities.
How to use them to solve problems?As opposed to an inequality, which links two different values, an equation declares that two expressions are equal.
Create one-variable equations and inequalities, then utilize them to solve issues.
Include simple rational and exponential equations as well as those resulting from linear and quadratic functions.
In order to answer word problems, students should be able to decipher them and create equations and inequalities.
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3x3 what is the sum to this..?
Answers
Answer:
9
Step-by-step explanation:
3x3=9
Answer:
the sum is 9
Step-by-step explanation:
3×1=3
3×2=6
3×3=9
Multiply Which equation is the best choice
Answers
Answer:
second option
Step-by-step explanation:
(2 [tex]\frac{4}{5}[/tex] )( - 5 [tex]\frac{2}{3}[/tex] ) ← convert mixed numbers to improper fractions
= [tex]\frac{14}{5}[/tex] × - [tex]\frac{17}{3}[/tex]
= - [tex]\frac{14(17)}{5(3)}[/tex]
= - [tex]\frac{238}{15}[/tex]
= - 15 [tex]\frac{13}{15}[/tex]
96240 is divisible by 2,3,5,10 true or false
Answers
True
It's true, 96240 is divisible by 2,3,5,10
Hope this helps!
Write a relationship for a function whose hx values are 6 less than the cube of x
Answers
The mathematical expression from the algebraic expression is a x^3 - 6.
According to the statement
We have to find that the expression of the statement in the mathematical form.
So, For this purpose, we know that the
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
From the given information:
The hx values are 6 less than the cube of x
Then
To convert into the mathematical form:
The cube of the x is in the mathematical form is a x^3
Then
And the 6 less than the cube
And in the mathematical form it becomes the
x^3 - 6.
So, The mathematical expression from the algebraic expression is a x^3 - 6.
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Square root of 9 =3=3=3 and 1 half + 1 half
Answers
Using the Factor Theorem, which of the following is a factor of the polynomial function f (x) = 5x3 + 5x2 – 60x?
x – 4
x + 4
x – 5
x + 3
Answers
The factors of the given polynomial function are 5x(x+4)(x-3). Therefore, option B is the correct answer.
The given polynomial function is f (x) = 5x³ + 5x² – 60x.
What is the Factor Theorem?The factor theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f(x) if f(a) = 0. In other words, we can say that (x - a) is a factor of f(x) if f(a) = 0.
Using factor theorem 5x³ + 5x² – 60x=0
⇒ 5x(x²+x-12)=0
⇒ (x²+x-12)=0
Using the splitting middle method we can factorise x²+x-12=0
That is, x²+4x-3x-12=0
⇒ x(x+4)-3(x+4)=0
⇒ (x+4)(x-3)
The factors of the given polynomial function are 5x(x+4)(x-3). Therefore, option B is the correct answer.
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Answer:
(x-4)
Step-by-step explanation:
what is the answear for 4a+6b+3a+8b
Answers
Step-by-step explanation:
4a+3a+6b+8b
7a+14b ......
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[tex]4a+6b+3a+8b\\4a+3a+6b+8b\\7a+14b[/tex]<---- SOLUTION================================================
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[tex]\textcopyright ELIZA[/tex]
