The correct transformation that preserves the size and shape of an object, resulting in congruent images, is an isometric transformation. Examples include translation, rotation, and reflection, all of which maintain the object's proportions and dimensions.
A transformation that preserves the size and shape of an object's original image, such that the image is congruent to the pre-image, is known as an isometric transformation. This transformation includes operations like translation (a shift from one place to another), rotation (turning around a center), and reflection (flipping over a line). All these transformations keep the object's dimensions and proportions unchanged. The key property of isometric transformations is that they maintain congruency and preserve distances and angles.
An example of an isometric transformation is when a square is rotated 90 degrees around its center. The square's shape and size remain the same, even though its orientation has changed. This contrasts with dilation, which changes the size of the object, and affine transformations, which can alter both shape and size, such as through stretching or skewing. The correct answer to the student's question is B. isometric.
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In isosceles ∆DEK with base DK, EF is the angle bisector of ∠E, m∠DEF = 43°, and DK = 16cm. Find: KF, m∠DEK, m∠EFD.
The acceleration of an object varies directly with the force acting on it. If a force of 70 newtons causes an acceleration of 6.5 m/s2, what force will cause ann acceleration of 8m/s2? round your answer the hundredths place
Using Newton's Second Law of Motion, and the principle that acceleration is directly proportional to the applied force, a force of approximately 86.15 newtons will cause an acceleration of 8 m/s².
Explanation:The question relates to the principle stated in Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, we can assume the mass of the object remains unchanged.
To find the force that will cause an acceleration of 8 m/s², we can set up a direct proportion based on the given data (70 N correlates with 6.5 m/s²):
70 N / 6.5 m/s² = X N / 8 m/s²
Solving this for X gives X = (70 N * 8 m/s²) / 6.5 m/s². Round your answer to the nearest hundredth, you get approximately 86.15 N.
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Use laws of sine to answer
The temperature fell from 0 degrees to 6 3/5 degrees below 0 in 2 1/5 hours. what was the temperature change per hour?
divide 6 3/5 by 2 1/5
6 3/5 = 33/5
2 1/5 = 11/5
33/5 / 11/5 = 3
the temperature dropped 3 degrees per hour
Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain.
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The coordinates of the vertices of quadrilateral ABCD are A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2) . Drag and drop the choices into each box to correctly complete the sentences.
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A savings account balance can be modeled by the graph of the linear function shown on the grid.
What is the rate of change of the balance with respect to the number of deposits?
A) $100 per deposit
B) $50 per deposit
C) $0.50 per deposit
D) $2 per deposit
Answer:
Hey I am also taking the k12 interim right now and I also think the answer is a.
Step-by-step explanation:
The starting balance was at $50 then it gradually started to increase by $100 with each deposit. So you're answer is a.
Check it out yourself and see that the balance is increasing by $100 dollars with each deposit.
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Create an expression, to equal 13, using any grouping of addition, subtraction, multiplication, and division. You must use all the basic operations at least once (addition, subtraction, multiplication, and division) and you must use at least one set of parentheses.
Answer:
Step-by-step explanation:
(5x2)+3
=13
This how you work the problem:
(5x2)+3 (5x2=10) 10+3=13. :)
Mt.Whitney in California is 14,492 feet tall. Mt. McKinley in Alaska is 5,826 feet taller than Mt.Whitney. How tall is Mt.Mckinley
Final answer:
Mt. McKinley is 20,318 feet tall. This is found by adding Mt. Whitney's height of 14,492 feet to the additional 5,826 feet that Mt. McKinley is taller by.
Explanation:
The question asks how tall Mt. McKinley is. First, we know Mt. Whitney has a height of 14,492 feet. According to the question, Mt. McKinley is 5,826 feet taller than Mt. Whitney. To find the height of Mt. McKinley, we need to add these two measurements together.
Step 1: Write down the height of Mt. Whitney: 14,492 feet.
Step 2: Add the additional height of Mt. McKinley to Mt. Whitney's height: 14,492 feet + 5,826 feet.
Step 3: Perform the addition: 14,492 + 5,826 = 20,318 feet.
Therefore, Mt. McKinley is 20,318 feet tall.
Use long division to determine the quotient of the polynomials. (x3 – 7x – 6) ÷ (x – 4) Which of the following options best describes the relationship between the polynomial division and the remainder? The quotient has a remainder of zero. Therefore, the divisor is a factor of the dividend. The quotient has a remainder of 9. Therefore, the divisor is not a factor of the dividend. The quotient has a remainder of 30. Therefore, the divisor is not factor of the dividend. The quotient has a remainder of 36. Therefore, the divisor is a factor of the dividend.
Using long division of polynomials, when we divide (x³ - 7x - 6) by (x - 4), the quotient is x² + 4x + 16 with a remainder of -70. This implies that the divisor (x - 4) is not a factor of the dividend (x³ - 7x - 6), since a non-zero remainder exists.
Explanation:To perform the task, we first note down the dividend (x³ - 7x - 6) and divisor (x - 4). We divide the first term of the dividend by the first term of the divisor to find the first term of the quotient and continue this process as required in polynomial division. Solving this using long division of polynomials, we get:
Dividend: x³ - 7x - 6
Divisor: x - 4
The quotient after performing long division is x² + 4x + 16 and the remainder is -70. This shows that the divisor (x - 4) is not a factor of the dividend (x³ - 7x - 6), since a remainder exists after the division is performed.
So, the correct option is: The quotient has a remainder of -70. Therefore, the divisor is not a factor of the dividend.
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Which of the following is a radical equation?
Answer:
C. [tex]\sqrt{x}+3=13[/tex]
Step-by-step explanation:
We know that,
A radical equation is the equation in which the variable is under the radical.
According to the options, we see that,
In the equation [tex]\sqrt{x}+3=13[/tex], the variable is under the radical.
All other equations have constant number under the radical.
Thus, we get,
Equation C i.e. [tex]\sqrt{x}+3=13[/tex] is a radical equation.
[tex]\fbox{\text{Option C}}[/tex] is correct as [tex]\sqrt x+3 = 13[/tex] is radical equation because the variable is under the radical and the radicand is [tex]x[/tex].
Further explanation:
Radical can be describing as a square root, a cube root, a fourth root or higher root.
Radical equation can be defined as any equation that contains a radical on the variable is known as the radical equation.
The term under the radical symbol is known as radicand.
Option A is not correct.
Here, [tex]x\sqrt 3= 13[/tex] is not radical equation because the radical is on a constant term 3 not on the variable.
Option B is not correct.
Here, [tex]x+\sqrt 3=13[/tex] is not radical equation because the radical is on a constant term 3 not on the variable.
Option C is correct.
Here, [tex]\sqrt x+3=13[/tex] is radical equation because the variable is under the radical and the radicand is .
Option D is not correct.
Here, [tex]x+3 =\sqrt {13}[/tex] is not radical equation because the variable is not under the radical.
The equation [tex]\sqrt x+3=13[/tex] is a radical equation. Therefore [tex]\fbox{\text{Option C}}[/tex] is correct.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: functions, equation, radical equation, radical, square root, cube root, fourth root, variable, radicand, term, under, contains describe.
A card is dealt from a 52-card deck. find the probability that it is not a 77. express the probability as a simplified fraction
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Cafe A offers 2 free bottled waters or juices for every 20 purchased.Cafe B offers 3 bottled waters or juices for every 25 purchased. A) What is Cafe A's ratio of free drinks to purchased drinks? B) What is Cafe B's ratio of free drinks to purchased drinks? C) If you purchased 50 drinks at each cafe how many free drinks would you get?
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What are the domain restrictions of the expression h^2+3h−10/h^2−12h+20 ?
Select each correct answer.
h≠10
h≠5
h≠2
h≠−5
h≠−10
h≠−2
The domain restrictions of the expression (h² + 3h −10) / (h² − 12h + 20) are h≠2 and h≠10. which are the correct answers would be options (A) and (C).
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The expression is given in the question as
(h² + 3h −10) / (h² − 12h + 20)
(h² + 5h - 2h−10) / (h² − 10h - 2h + 20)
(h(h + 5) - 2(h+5)) / (h(h − 10) - 2(h - 10))
(h + 5)(h - 2) / (h − 10)(h - 2)
We know that the denominator cannot be zero
Here (h-2)(h-10)=0
h= 2 or h = 10
Therefore, h cannot be 2 or 10 i.e. in the notation h≠2 and h≠10.
The domain restrictions of the expression (h² + 3h −10) / (h² − 12h + 20) are
h≠2 and h≠10.
Hence, the correct answers would be options (A) and (C).
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True or false.The GCF of any two odd numbers is always odd
3 1/3 lb of turkey for 10.50
True false to find the midpoint of a segment, first mark a point not on the segment and then fold the paper so that the point you marked and a point on the line are included in the fold
What is the expression in radical form?
(3p^3q)^3/4
The Expression [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]
What is Expression?An expression is a combination of numbers, operator and variables.
The given expression is [tex](3p^{3} q)^{\frac{3}{4} }[/tex]
We know that
[tex]a^{\frac{p}{q} } =\sqrt[q]{a^{p} }[/tex]
So let us use same form to solve the given expression to radical form.
[tex](3p^{3} q)^{\frac{3}{4} }[/tex]=[tex]\sqrt[4]{(3p^{3} q)^{3} }[/tex]
Simplify the terms in root,
=[tex]\sqrt[4]{(3^{3}p^{3.3}q^{3} }[/tex]
=[tex]\sqrt[4]{27p^{9}q^{3} }[/tex]
[tex]\sqrt[4]{27p^{4}p^{4}pq^{3} }[/tex]
=[tex]p.p\sqrt[4]{27pq^{3} }[/tex]
=[tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]
Hence the Expression [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]
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What is the equation of a line that passes through the points (3,6) and (8,4)
) the admission fee at a small fair is $1.50 for children and $4 for adults. on a certain day 2,200 people enter the fair and $5,050 is collected. how many children and how many adults attended?
find the roots of the quadratic function x^2=100
Jordan is three years older than four times Lily's age. The sum of their age is 68. How old is Jordan?
Why do you flip the inequality sign when dividing by a negative number?
What is the inverse of the function f(x) = 2x - 10?
Answer:
[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]
Step-by-step explanation:
We ate asked to find the inverse of the given function [tex]f(x)=2x-10[/tex].
To find the inverse of function, first of all we will replace [tex]f(x)=y[/tex] and then interchange x and y values as shown below:
[tex]y=2x-10[/tex]
Inter-change x and y variables:
[tex]x=2y-10[/tex]
Solve for y using opposite operations:
[tex]x+10=2y-10+10[/tex]
[tex]x+10=2y[/tex]
Switch sides:
[tex]2y=x+10[/tex]
Divide both sides by 2:
[tex]\frac{2y}{2}=\frac{x+10}{2}[/tex]
[tex]y=\frac{x+10}{2}[/tex]
We will inverse function notation [tex]f^{-1}(x)[/tex] to write the inverse function as:
[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]
Therefore, our required inverse function would be [tex]f^{-1}(x)=\frac{x+10}{2}[/tex].
Find the time in hours and minutes from 09.40 to 13.25
You're at a halloween fair with a big ferris wheel. the wheel has ten chairs and people are seated two per chair. every minute a chair passes the exit platorm. the wheel opens at 11 am for thirty minutes -- how many people took a ride in that time?
The number of persons who have taken the ride is 60.
According to the question, a halloween fair with a big ferris wheel. The wheel has 10 chairs and people are seated [tex]2/chair[/tex].
Also, every minute a chair passes the exit platform and the wheel opens at 11 am for thirty minutes so, the rate at which the chair passes the exit platform is [tex]1\;chair\;per\;minute[/tex].
Now, number of persons who have taken the ride is calculated as-
[tex]n= minutes \times (1\;chair\;per\;minute)\times (2\;persons\;per\;chair)\\n=30\times 2\times 1\\n=60[/tex]
Hence, the number of persons who have taken the ride is 60.
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The temperature dropped 6c every hour for 7 hours. What was the total number of degrees the temperature changed in the 7 hours
Ind the perimeter and area of the sandbox. Make sure your answers have the correct number of significant digits. A children's sandbox measures 7.8 feet by 5.23 feet.
What's the relationship between compound interest and exponential growth?
Final answer:
Compound interest and exponential growth both involve the concept of compounding, where growth is based on previous amounts. Compound interest refers to interest earned on past interest, causing savings to grow over time. Similarly, compound growth rates result in exponential growth.
Explanation:
The relationship between compound interest and exponential growth is that they both involve the concept of compounding, where the growth or increase is based on previous amounts. Compound interest refers to the interest earned on past interest, causing the total amount of financial savings to grow over time. Similarly, compound growth rates mean that the rate of growth is multiplied by a base that includes past growth, resulting in an exponential growth curve.
For example, if you have $1,000 in a bank account with a compound interest rate of 5% per year, the interest earned each year is added to the principal amount and becomes part of the new base for calculating future interest. As a result, the amount of money in the account grows exponentially over time. This relationship can also be seen in other areas, such as population growth or economic growth rates.