A mysterious flying superhero known as blue sky protects the good citizens of oxford. unknown to these citizens, blue sky is actually mild-mannered trudy, a scientist in a flying suit. before trudy can fly in the suit, she needs to charge its battery. there is a proportional relationship between the number of hours trudy has charged her flying suit, x, and the number of hours she can fly, y. x (hours charged) y (flight hours) 1 1 4 4 7 7 8 8 what is the constant of proportionality? write your answer as a whole number or decimal. flight hours per hour charged
Answers
The ratio of flight hours to hours charged is consistently 1 for all the given data points. Therefore, the constant of proportionality is 1.
To find the constant of proportionality, we can examine the relationship between the number of hours charged (x) and the number of flight hours (y) in the given data points.
Let's calculate the ratio of flight hours to hours charged for each data point:
For the first data point:
y/x = 1/1
= 1
For the second data point:
y/x = 4/4
= 1
For the third data point:
y/x = 7/7
= 1
For the fourth data point:
y/x = 8/8
= 1
As we can see, the ratio of flight hours to hours charged is consistently 1 for all the given data points. Therefore, the constant of proportionality is 1.
This means that for every hour Trudy charges her flying suit, she can fly for an equal number of hours.
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Related Questions
ABCD is a trapezoid. The coordinates are A(-4, -1), B(0,3), C(8,3) and D(8, -1). Find the length of the midsegment of the trapezoid.
Answers
Answer:
the length od the midsegment is 10
Step-by-step explanation:
8+12/2=20/2=10
Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 3; zeros: 9,−8−i The remaining zero(s) of f is(are) (Use a comma to separate answers as needed.)
Answers
The zeros of the given polynomial are: `9`, `-8-i`, and `-8+i`.
We are given a polynomial `f(x)` whose coefficients are real numbers and the degree of the polynomial is 3. To find the remaining zero(s) of `f`.
Now, if `p` is a zero of a polynomial `f(x)` of degree `n`, then the remainder when `f(x)` is divided by `x - p` is equal to `f(x)` evaluated at `p`.This is known as the Remainder Theorem.So, using Remainder Theorem, we have:f(9) = 0 (Since 9 is a zero of `f(x)`).
Similarly, let's find the last zero of `f(x)`:
Let `α` be the remaining zero of `f(x)`. Since the `f(x)` coefficients are real, we know that complex zeros occur in conjugate pairs. Therefore, the complex conjugate of `-8-i` must also be zero of `f(x)`. The complex conjugate of `-8-i` is `-8+i`. Therefore, `-8+i` is also a zero of `f(x)`.
Now, using Remainder Theorem, we have:
f(-8+i) = 0 (Since `-8+i` is a zero of `f(x)`).Now, we can write `f(x)` in factored form using the zeros as:
`f(x) = (x - 9)(x - (-8-i))(x - (-8+i))`.
This is because when we multiply the three factors, we get a polynomial of degree 3 with the given zeros.
Now, we can simplify the factored form of `f(x)` as follows:```
f(x) = (x - 9)(x + 8 + i)(x + 8 - i)
= (x - 9)(x² + 16x + 65)
```Therefore, the remaining zero(s) of `f(x)` are the solutions to `f(x) = 0`. Solving for `f(x) = 0`, we get:
`(x - 9)(x² + 16x + 65) = 0
`Using the zero product property, we can write:
`(x - 9)(x + 8 + i)(x + 8 - i) = 0`
Therefore, the remaining zero(s) of `f(x)` are `x = -8 + i` and `x = -8 - i`.Hence, the remaining zeros of `f(x)` are `-8+i` and `-8-i`.The zeros of the given polynomial are: `9`, `-8-i`, and `-8+i`.
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2e=6.4
What is the solution for e?
Answers
Answer:
3.2
Step-by-step explanation:
2e = 6.4
dividing through by 2 in order to make e the subject of the equation
e = 6.4/2
e =3.2
Determine whether the series is convergent or divergent. 3^(n+1)4^-n If it is convergent, find its sum.
Answers
Geometric series is convergent if the |r|<1 where r is the common ratio.
Let Sn=∑ni=0(−3/4)i then
Sn=(−3/4)n+1−1(−3/4)−1
Now take n→∞ then
Sn→0−1(−3/4)−1=4/7
because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is
lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.
Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).8, 20,50,...Find the 10th term.
Answers
The value of the 10th term of the geometric progression is 30517.578
Based on the information given,
First term = 8
Second term = 20
Common ratio = 20/8 = 2.5
The nth term of a geometric progression is calculated as:
= ar\(n\) - 1
The 10th term will then be:
= 8 × (2.5)\(9\)
= 8 × 3814.6973
= 30517.578
Therefore, the value of the 10th term of the geometric progression is 30517.578.
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The 10th term of the geometric sequence is: 30,715.578.
In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio q.
The equation for the nth term is:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term.In this problem:
The first term is \(a_1 = 8\).The common ratio is:\(q = \frac{50}{20} = \frac{20}{8} = 2.5\)
Thus, the nth term is given by the following equation:
\(a_n = 8(2.5)^{n-1}\)
The 10th term is:
\(a_{10} = 8(2.5)^9 = 30517.578\)
The 10th term of the sequence is 30,715.578.
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What y equals when x= -4 and when x= 6
Answers
Evaluating a function means finding the value of the function that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned.
Evaluating our function at x = -4 and x = 6, we have:
\(\begin{gathered} y(-4)=\frac{1}{4}(-4)^2-2=4-2=2 \\ y(6)=\frac{1}{4}(6)^2-2=\frac{36}{4}-2=9-2=7 \end{gathered}\)and those are our answers.
\(\begin{gathered} x=-4,\:y=2 \\ x=6,\:y=7 \end{gathered}\)The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 920 feet of fencing available, what is the maximum possible area of the pasture
Answers
Answer:
Max Area = 105,800 sq.ft
Step-by-step explanation:
A square will always give us the maximum area.
Thus, one side would be;
920/4 = 230 feet
So, we want a square 230 ft by 230 ft
however, from the question, we are to use the creek as one side. So, we'll take the 230 ft that we don't need because of the creek and then add it to the opposite side to get 230 + 230 = 460 ft.
Thus,we now have a rectangle with dimensions: 230 ft by 460 ft
Area is given by;
area = length × width
Maximum Area = 230 × 460
Max Area = 105,800 sq.ft
Check the functions whose inverses are also functions.
On a coordinate plane, an absolute value function opens down.
On a coordinate plane, an exponential functions increases from quadrant 2 into quadrant 1.
On a coordinate plane, a cubic function has an x-intercept of (0, 0).
Answers
Answer:
b and c
Step-by-step explanation:
Answer:
Hands down c and b
Step-by-step explanation:
What is the value of y in the solution to the system of equations x Y 1 2x 3y 30?
Answers
The value y in of system of equations is 32/5;
What is a System of Equations?
A finite collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.
Finding the values of the variables employed in a system of equations entails solving the set of equations. While keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system.
Given:
Equations are x + y = 1 --- (1)
2x - 3y = -30 --- (2)
Solving the equations by elimination method
Multiply the first equation by 2 so that x will get eliminated and we will get the value of y
So we get = 2x + 2y = 2 --- (3)
Now eq(3) - eq(2)
⇒ 2x + 2y - (2x - 3y) = 2 - (-30)
⇒ 2x + 2y - 2x + 3y = 2 + 30
⇒ 5y = 32
⇒ y = 32/5;
Hence, The value y in of system of equation is 32/5;
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solve for the measure of x in the drawing shown below
Answers
Answer:
50
Step-by-step explanation:
x° = 1/2 * 100°
x° = 50°
x = 50
A first grade teacher is teaching algebraic reasoning through problems which present to the students as if they are puzzles. One way the teacher could do this is to introduce students to a card game in which they must find the missing addend. What could be the teacher's goal with this method?
Answers
The teacher's goal in introducing students to a card game where they must find the missing addend could be to develop and enhance their algebraic reasoning skills.
By presenting the problem as a puzzle or game, the teacher aims to engage the students in a fun and interactive way while fostering their ability to think critically and solve mathematical problems. The game helps students practice identifying the missing addend and applying algebraic thinking to find the solution. Additionally, it promotes the development of problem-solving strategies, logical reasoning, and the ability to generalize mathematical patterns, which are foundational skills in algebraic reasoning.
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One third of a number less than nine equal to seven
Answers
Step-by-step explanation:
Let the number be denoted by x.
Now, we are given a word phrase as follows one-third of a number less than nine is equal to seven.
Now this word phrase could be mathematically expressed as a equation by: one third of x is 1/3 x
And this number less than 9 is given by :
9- 1/3x
Now, this number is equal to 7.
I.e. we finally have:
9- 1/3x = 7
The person who answered is correct
5(2x-1) expanded
Please help
Answers
Answer:
the answer would be 10x-5
Step-by-step explanation:
Because u multiply the 5 by each number within the parentheses.
Find an equation for the line perpendicular to the tangent to the curve y=x3−4x+1 at the point (2,1).
Answers
The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.
To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.
The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.
Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.
Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):
y - 1 = (-1/8)(x - 2)
Simplifying and putting the equation in slope-intercept form:
y = (-1/8)x + 9/8
Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.
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Solve. Write answer in simplest form.
7 - 2/5 =
Answers
Answer:
6 3/5
Step-by-step explanation:
7 - 2/5 = 6 3/5
Sorry I can’t really explain this. It just comes into my head
Answer:
6 3/5
Step-by-step explanation:
simply subtract 2 from 5 and thats 3. you cut into the seven while doing that therefore its 6 3/5
1. y-5/3 = 1 Activity Review
O -2
O 8
O 18
O 6
Answers
Activity Review for the value of y in the equation is 8
Simplify ExpressionSimplify expression is the process of writing an expression in the most efficient and simple form.
y-5/3 = 1
Step 1 : simplify the equation by cross multiply
we have;
y-5= 3 * 1
y-5 = 3
Step 2: Add 5 to both sides
therefore, y-5 +5 =3 + 5
y= 8
Therefore the value of y = 8
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Classify the polynomial as a monomial, binomial, trinomial, or none of these. x2 - 10x + 25
Answers
It is a trinomial because it follows the pattern of x^2 + bx + c. In this case, x^2 - 10x + 25. Also, it only has three numbers and two operation symbols, signifying a trinomial (three = tri).
What does the magnitude of the correlation coefficient indicate about the variables?
Answers
The magnitude of the correlation coefficient indicate the "strength" about the variables.
What is correlation?In the financial and investing industries, correlation is a statistic which indicates the extent that two securities change in relation to one another.
Correlations are employed in advance portfolio management and are calculated as correlation coefficient, that must be between -1.0 and +1.0.
Some key features regrading correlation are-
Within finance, this correlation can be used to compare the movements of a stock to the movement of benchmark index, like the S&P 500.Correlation is inextricably linked to diversification, the idea that some types of risk can be minimized by investing in non-correlated assets.Correlation quantifies relationship but does not reveal whether x affects y or conversely whether the association is due to a third component.A scatterplot may be the best way to identify correlation, especially is if variables get a non-linear but nevertheless substantial connection.To know more about correlation, here
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Solve the inequality 20 – 6x < -10.
Answers
Answer:
x = 5
Step-by-step explanation:
Can someone answer this please?
Answers
Answer:
29.) y = -1.5x - 20
30.) y = 6 - 3x
Step-by-step explanation:
29.) For parallel lines; M1 = M2
put the equation in the form y = mx + c
the equation becomes 2y = 14 - 3x
therefore y = 7 - 1.5x.
For the points, introduce another point; (x,y) and the initial (-6,-11)
(y - - 11) ÷ ( x - - 6) = -1.5
y+11 = -1.5x - 9
y= -1.5x - 20
30.) still following the same procedure, only that M1 × M2 = -1
M1 = 1/3, M2 = -3
(y + 9)/(x - 5) = -3
y + 9 = 15 - 3x
y = 6 - 3x
What is the value of 80 + 57
Answers
have a good day. hope i helped
Answer:
137
Step-by-step explanation:
Add 80 and 57.
let f and g be the functions given by f(x)=1/4+sin(pi x) and g(x)=4^-x
Answers
The function f(x) is a periodic function with oscillations, while g(x) is an exponential function that decreases rapidly.
The function f(x) is a periodic function that oscillates between 1/4 - 1 and 1/4 + 1 with a period of 2.
It starts at 1/4 - 1, reaches a maximum of 1/4 + 1, then returns to 1/4 - 1, and so on. The sine function sin(πx) generates these oscillations, and the constant 1/4 shifts the graph vertically.
The function g(x) is an exponential function with a base of 4 raised to the power of -x. As x increases, the exponent becomes more negative, causing the function to decrease rapidly.
Similarly, as x decreases, the exponent becomes less negative, causing the function to increase rapidly. The function approaches zero as x approaches infinity.
In summary, f(x) is a periodic function with oscillations, while g(x) is an exponential function that decreases rapidly.
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Use the Coordinates panel to view the degrees of freedom of the model. How many degrees of freedom, in total, does the model have
Answers
The degrees of freedom of a model refer to the number of independent pieces of information that are available to estimate the model parameters.
In other words, it represents the number of observations that are free to vary in the analysis. To view the degrees of freedom of the model, we can use the Coordinates panel in the statistical software. The total number of degrees of freedom in a model depends on the number of variables and observations in the data set.
For example, if we have a data set with 100 observations and 5 variables, including an intercept, the total number of degrees of freedom in the model would be 94. This is because the intercept uses one degree of freedom, and each additional variable uses one degree of freedom.
Therefore, the total number of degrees of freedom is equal to the number of observations minus the number of variables used in the model. The Coordinates panel provides a convenient way to view this information and can help us better understand the statistical properties of our model.
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In a high school graduating class of 143 students, 59 are on the honor roll. Of these, 55 are going on to college. Of the 4 students not on the honor roll, 61 are going on to college. A student is selected at random from the class. (a) What is the probability that the student selected is going to college? (b) What is the probability that the student selected is not going to college? (c) What is the probability that the student selected is not going to college and on the honor roll? Find the probability for the experiment of drawing two marbles at random (without replacement) from a bag containing four green, two yellow, and four red marbles. Both marbles are red. Find the probability for the experiment of tossing a six-sided die twice. The sum is odd and no more than 9. x Find the sample space the experiment. (Enter your answer in set notation.) You select two marbles (without replacement) from a bag containing nine red marbles (denote by R), five blue marbles (denote by B), and nine yellow marbles (denote by Y). You record the color of each marble.
Answers
The probability that the student selected is going to college is found out to be 116/143.
(a) To calculate the probability that the student selected is going to college, we need to divide the number of students going to college by the total number of students. Number of students going to college = 55 + 61 = 116. Total number of students = 143. Probability = Number of students going to college / Total number of students. Probability = 116 / 143. Therefore, the probability that the student selected is going to college is 116/143. (b) To calculate the probability that the student selected is not going to college, we can subtract the probability of going to college from 1. Probability = 1 - (116/143), Probability = 27/143. Therefore, the probability that the student selected is not going to college is 27/143.
(c) To calculate the probability that the student selected is not going to college and on the honor roll, we need to find the number of students who are not going to college and on the honor roll, and divide it by the total number of students. Number of students not going to college and on the honor roll = 4. Total number of students = 143. Probability = Number of students not going to college and on the honor roll / Total number of students, Probability = 4 / 143. Therefore, the probability that the student selected is not going to college and on the honor roll is 4/143. Now let's move on to the next part of the problem. Experiment: Drawing two marbles at random (without replacement) from a bag containing four green, two yellow, and four red marbles. We want to find the probability that both marbles are red.
Step 1: Find the total number of marbles in the bag. Total number of marbles = 4 (green) + 2 (yellow) + 4 (red) = 10. Step 2: Find the number of red marbles. Number of red marbles = 4. Step 3: Find the probability of drawing the first red marble. Probability of drawing the first red marble = Number of red marbles / Total number of marbles. Probability of drawing the first red marble = 4 / 10. Step 4: Find the probability of drawing the second red marble (without replacement). Since we are not replacing the first marble, the total number of marbles decreases by 1. Probability of drawing the second red marble = (Number of red marbles - 1) / (Total number of marbles - 1). Probability of drawing the second red marble = (4 - 1) / (10 - 1) = 3 / 9
Step 5: Multiply the probabilities of drawing both red marbles. Probability of drawing two red marbles = Probability of drawing the first red marble * Probability of drawing the second red marble. Probability of drawing two red marbles = (4 / 10) * (3 / 9) = 12 / 90. Therefore, the probability of drawing two red marbles is 12/90, which simplifies to 2/15. Now let's move on to the next part of the problem. Experiment: Tossing a six-sided die twice. We want to find the probability that the sum is odd and no more than 9. Step 1: Determine the sample space for the experiment. The sample space is the set of all possible outcomes when tossing the die twice. It can be represented in set notation as follows: Sample space = {(1, 1), (1, 2), (1, 3), ..., (6, 6)}. Step 2: Identify the outcomes that satisfy the given conditions. The outcomes that satisfy the conditions (sum is odd and no more than 9) are: (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5)
Step 3: Calculate the probability. The probability is the number of outcomes that satisfy the conditions divided by the total number of outcomes in the sample space. Number of outcomes that satisfy the conditions = 18. Total number of outcomes in the sample space = 6 * 6 = 36. Probability = Number of outcomes that satisfy the conditions / Total number of outcomes in the sample space. Probability = 18 / 36, Probability = 1/2. Therefore, the probability that the sum is odd and no more than 9 is 1/2. Lastly, let's move on to the final part of the problem. Experiment: Selecting two marbles (without replacement) from a bag containing nine red marbles (denoted by R), five blue marbles (denoted by B), and nine yellow marbles (denoted by Y). We want to determine the sample space for this experiment. The sample space can be represented in set notation as follows: Sample space = {(R1, R2), (R1, B1), (R1, B2), ..., (Y8, Y9), (Y9, R1), (Y9, R2), ..., (Y9, Y7), (Y9, Y8), (Y9, Y9)} where R1, R2, B1, B2, ..., Y8, Y9 represent individual marbles from the bag. The sample space includes all possible combinations of selecting two marbles from the bag, without replacement.
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Ingrid wants to buy a $17,000 car in 6years. How much money must she deposit at the end of each quarter in an account paying 5.5% compounded quarterly so that she will have enough to pay for her car?
Answers
Ingrid needs to deposit approximately $558.95 at the end of each quarter to have enough money to buy the $17,000 car in 6 years.
To calculate the amount Ingrid needs to deposit at the end of each quarter, we can use the future value of an annuity formula. The future value (FV) of an annuity is given by the formula:
FV = P * ((1 + r/n)(n*t) - 1) / (r/n)
Where:
P is the periodic deposit
r is the annual interest rate (as a decimal)
n is the number of compounding periods per year
t is the number of years
In this case, Ingrid wants to accumulate $17,000 in 6 years, with a quarterly compounding rate of 5.5% (0.055) and 4 compounding periods per year. Plugging these values into the formula:
17,000 = P * ((1 + 0.055/4)²⁴ - 1) / (0.055/4)
By solving this equation, we find that Ingrid needs to deposit approximately $558.95 at the end of each quarter to accumulate enough money to pay for her car.
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Hiiooo! Can someone help me out❤️
Answers
Answer:
Im pretty sure its 6
Step-by-step explanation:
hope this helps :)
Answer:
B.
Step-by-step explanation:
You just take the pythagorean theorem and use the same steps but just plug in the hypotenuse and the one leg you have and solve the problem using the pythagorean theorem.
I have a test an in hour and I need help with what to do
Answers
Suppose that triangles ABC and DFE are similar. Therefore, the ratio between their corresponding sides is constant. Let x and y be
\(\begin{gathered} AB=x \\ BC=y \end{gathered}\)Then,
\(\Rightarrow\frac{x}{5}=\frac{y}{12}=\frac{26}{3}\)Triangle DFE is impossible, the lengths of its sides are impossible to construct in such a manner that the result is a right triangle whose hypotenuse is 3. DFE is an impossible triangle, the hypotenuse of a right triangle is always its largest side.
However, we can algebraically find x and y, although it would not make any sense geometrically speaking.
\(\Rightarrow\frac{x}{5}=\frac{26}{3}\)Solving for x,
\(\begin{gathered} \Rightarrow x=\frac{26\cdot5}{3}=43.333\ldots \\ \Rightarrow AB=43.333\ldots \end{gathered}\)Similarly, solving for y,
\(\begin{gathered} \Rightarrow\frac{y}{12}=\frac{26}{3} \\ \Rightarrow y=26\cdot\frac{12}{3}=104 \\ \Rightarrow BC=104 \end{gathered}\)w=0.75f.
What does 0.75 tell us in this situation?
Answers
Answer:
it should be in the ratio of 3:4
Step-by-step explanation:
100w= 75f
w/f = 75/100
= 3/4
= 3:4
Two boats leave a port traveling on paths that are 48 acant. After some time the boath has gone 52 min and the second boat has gone 79 mi. How far aport are the boats?
Answers
Two boats leave a port traveling on paths that are 48 acant. After some time the boath has gone 52 min and the second boat has gone 79 mi., by using the Pythagorean theorem, we determined that the distance between the two boats is approximately 92.52 miles.
To determine the distance between the two boats, we can consider the paths they have traveled and use the concept of Pythagorean theorem.
Let’s assume that the two boats have traveled along perpendicular paths, forming a right triangle. The first boat has traveled a distance of 48 miles, and the second boat has traveled a distance of 79 miles. We want to find the distance between the boats, which corresponds to the hypotenuse of the triangle.
By applying the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the distance between the boats.
Let’s denote the distance between the boats as d. According to the Pythagorean theorem:
D^2 = (48 miles)^2 + (79 miles)^2
D^2 = 2304 miles^2 + 6241 miles^2
D^2 = 8545 miles^2
Taking the square root of both sides, we find:
D ≈ 92.52 miles
Therefore, the boats are approximately 92.52 miles apart.
In conclusion, by using the Pythagorean theorem, we determined that the distance between the two boats is approximately 92.52 miles.
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In each graphic, the triangle was dilated to create the image triangle. Determine which scale factor was used for each dilation by dragging the correct scale factor to each graph.
pls help i well give brllant
Answers
The scale factor was used for each dilation are-
Part a: For ΔABC - scale factor = 2Part b: For ΔDEF - scale factor = 1/2Part c: For ΔGHJ - scale factor = 1/3Part d: For ΔKML - scale factor = 3Explain about the dilation:A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.
A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.
Part a: For ΔABC
Length AB = 2 units
Length A'B' = 4 units
A'B' = 2 *AB
Thus, For ΔABC - scale factor = 2
Part b: For ΔDEF -
Length DF = 2 units
Length D'F' = 1 units
D'F' = 1/2 DF
Thus, For ΔDEF - scale factor = 1/2
Part c: For ΔGHJ -
Length GH = 3 units
Length G'H' = 1 units
G'H' = 1/3 GH
Thus, For ΔGHJ - scale factor = 1/3
Part d: For ΔKML -
Length KM = 2 units
Length K'M' = 6 units
K'M' = 3*KM
Thus, For ΔKML - scale factor = 3
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