Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.
Answers
The scale factor used for the dilation is 3.
What is scaling factor?Scaling factοr, alsο knοwn as dilatiοn factοr, is a ratiο that describes hοw much a figure is enlarged οr reduced. It is used in geοmetry tο describe the relatiοnship between cοrrespοnding lengths in similar figures.
Now,
To find the scale factor used for the dilation, we need to find the ratio of the corresponding side lengths of the two triangles.
Let's start by finding the side lengths of triangle ABC:
AB = √[(3 - (-3))² + (3 - (-3))²] = √[6² + 6²] = √[72] = 6√(2)
BC = √[(0 - 3)² + (3 - 3)²] = √[9] = 3
AC = √[(0 - (-3))² + (3 - (-3))²] = √[6² + 6²] = √[72] = 6√(2)
Now, let's find the side lengths of triangle A'B'C':
A'B' = √[(9 - (-9))² + (9 - (-9))²] = √[18² + 18²] = 18√(2)
B'C' = √[(0 - 9)² + (9 - 9)²] = √[81] = 9
A'C' = √[(0 - (-9))² + (9 - (-9)²] = √[18² + 18²] = 18√(2)
The ratio of the corresponding side lengths of the two triangles is:
A'B' / AB = (18√(2)) / (6√(2)) = 3
B'C' / BC = 9 / 3 = 3
A'C' / AC = (18√(2)) / (6√(2)) = 3
Therefore, the scale factor used for the dilation is 3.
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Related Questions
if you wanted to examine whether the degree of parental involvement differs based on students’ grade in school (i.e., first, second, third, etc.), what is the dependent variable of interest?
Answers
The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.
In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.
The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.
By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.
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Need help???!!!! Please
Answers
This is because
3*2 = 6 up top3+2 = 5 down belowThis is found through trial and error.
This is for problem 1 only. Problems 2 through 6 will follow a similar structure.
If I have $20 to buy snacks for myself and 4 friends if I buy a bag of chips for each person and end up with $13.75 left how much did I spend on each chip bag?
Answers
Answer:
20 - 5x = 13.75
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Diego put $15,000 into a savings account 6 years ago.
- The account earned 3.25% simple annual interest.
He made no additional deposits or withdrawals.
Based on this information, what is the balance in dollars and cents in Diego's savings account at the end of these 6 year
$18.173.21
B $2,925.00
$17,925.00
D $3,173.21
Answers
Answer: The answer is option C: $17,925.00.
Step-by-step explanation: Using the simple interest formula:
I = Prt
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
We can find the interest earned over the 6 years:
I = P * r * t = $15,000 * 0.0325 * 6 = $2,925
Adding the interest to the principal, we get the balance at the end of the 6 years:
Balance = Principal + Interest = $15,000 + $2,925 = $17,925
Therefore, the answer is option C: $17,925.00.
CHICKEN EXPERTS HELP PLEASE One of my chicks wont stop chirping and has half of its body (the bum) with dry feathers. Is it sick? Its been with other chicks and chickens and was doing perfectly fine until today. If so, is it contagious and how long do you think it takes to spread? If I clean myself will it decrease risks?
Answers
The function N(X) = 90(0.86)* + 69 can be used to predict the temperature of a
cup of hot chocolate in degrees Fahrenheit after x minutes. What is the
approximate average rate of change of the temperature of the hot chocolate, in
degrees per minute, over the interval [0, 6]?
1.
-8.93
2.
-0.11
3.
0.11
4.
8.93
Answers
Answer: -8.93
Step-by-step explanation:
Given the function:
N(X) = 90(0.86)^x+ 69
X in the interval [0, 6]
For X = 0
N(0) = 90(0.86)^0 + 69
90 + 69 = 159
For X = 6
N(6) = 90(0.86)^6 + 69
90(0.404567235136) + 69
= 105.41105116224
Therefore, average change of change in temperature ;
(temp 2 - temp 1) / ( time 2 - time)
(105.41105116224 - 159) / (6 - 0)
= - 53.58894883776 / 6
= - 8.93149147296
= - 8.93
The approximate average rate of change of the temperature of the hot chocolate, in degrees per minute, over the interval [0, 6] is;
Option 1; -8.93
We are given the function;
N(x) = 90(0.86)ˣ + 69
We want to find the average rate of change over the interval (0, 6).
Thus;
N(0) = 90(0.86)⁰ + 69
N(0) = 90 + 69
N(0) = 159°
N(6) = 90(0.86)⁶ + 69
N(6) = 105.411°
Formula for rate of change is;
Rate of change = Δy/Δx
Thus; Rate of change = (159 - 105.411)/(0 - 6)
Rate of change = -8.93
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what is the quotient of the expression
\( \frac{21a {}^{3} b - 14ab {}^{2} + 7ab}{7ab} \)
Answers
solve the question.
Answers
Answer: 1
\((\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1\)
Step-by-step explanation:
You have made 160 duct tape wallets to sell. If you sell 3 each day, write a function that represents this situation.
Answers
A function that represents this situation of selling 3 duct tape wallet per day out of of 160 duct tapes wallets produced is
y = 160 - 3xHow to write the expression of the situationInformation from the problem
You have made 160 duct tape wallets to sell
If you sell 3 each day
From the information we can deduce that
assuming amount left is y and the number of days x the we have
y = 160 - 3x
Therefore we can say that the expression to represent the situation of selling 3 duct tape wallet per day is y = 160 - 3x
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Maria gathered the data in the table. She finds the line of best fit to be y = 2.78x – 4.4. A 2-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled y with entries negative 2, 1.3, 4.2, 7.3, 8.9. What is the residual value when x = 4?
Answers
Answer:
The residual value when x = 4 is 0.58
Step-by-step explanation:
The residual value of a fitted function is the difference between the actual value of the data for a given input and the result of the fitted function. On this problem for the actual values, when \(x = 4\) we have \(y_{data} = 7.3\) , although, for the fitted function on the same value of "x", we have a different value, which is calculated below:
\(y(4) = 2.78*4 - 4.4 = 6.72\)
The residual value is:
\(\text{residual value} = y_{data} - y_{function} = 7.3 - 6.72 = 0.58\)
The residual value when x = 4 is 0.58
Functions are written in terms of variables. The residual value when the value of x is 4 is 0.58
Table and valuesFunctions are written in terms of variables. Given the following function that represent the data in the table
y = 2.78x – 4.4
If the value of x is 4, the corresponding value of y is expressed as:
y = 2.78(4) – 4.4
y = 11.12 - 4.4
y = 6.72
Determine the residual value
Residual value = 7.3 - 6.72
Residual value = 0.58
Hence the residual value when the value of x is 4 is 0.58
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If A is the set of all integers, choose the set B that will make the following statement false. B ⊆ A
Answers
B = {2.5, 3.5, 4.5} will make the statement false.
Option B is the correct answer.
We have,
A is the set of all integers.
And,
B ⊆ A
This means,
B is a subset of A where all elements in B is in A.
Now,
B = {1, 2, 3}.
This is true.
B = {2.5, 3.5, 4.5}
This is not true.
2.5, 3.5, and 4.5 are not integers.
They are real numbers.
B = {0}
This is true.
B = {-4, -1, 0, 5, 10}
This is true.
Thus,
B = {2.5, 3.5, 4.5} will make the statement false.
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Which values of a, b, and c represent the answer in simplest form?
5 3
88
=a
a= 1,b=3,C= 2
a=1,b=40, C = 24
a= 1,b= 16,C= 24
a=1; b=2, c=3
Answers
Answer:
1 16/24 1 2/3 answer is D
Step-by-step explanation:
y= 1/2x - 1
what's the slope and intercept.
Answers
Answer:
The slope is 1/2. The x-intercept is (2,0). The y-intercept is (0,-1)
Answer:
The slope is 1/2x and -1 is the (y) intercept
Step-by-step explanation:
Since y= 1/2x - 1 is already a linear equation (y=mx+b) you can use y=mx+b to find the slope and (y) intercept.m is the slope and b is the intercept
Help needed
a hunid points :)
Answers
Answer:
the answer is C, 5a^6b
Step-by-step explanation:
1. In my fruit basket, there are 13 pieces of fruit, 5 of which are apples. How can we express the number of apples as a fraction?
Answers
Answer:
5/13
Step-by-step explanation:
hope that helps
Answer:
the answer to your question is 5/13 im pretty sure!
Step-by-step explanation:
it is impossible to construct a frame for a(n) . a. sampled population b. finite population c. target population
Answers
It is not impossible to construct a frame for a finite population or a target population, but it is impossible to construct a frame for a sampled population.
A frame is a list or map of all the units in a population, which is used to select a sample for a survey or study. If a population is finite, it is possible to list all the units in the population and create a frame. Similarly, if the target population is well-defined and can be identified, a frame can be constructed.
However, if the population is sampled, the frame cannot be constructed because the population is unknown and constantly changing. Therefore, it is impossible to construct a frame for a sampled population.
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The complete question is :
Is it impossible to construct a frame for a sampled population, a finite population, or a target population?
Container A and container B have leaks. Container A has 800 mL of water, and is leaking 6mL per minute. Container B has 1000 mL, and is leaking 10mL per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Answers
Answer:
x = 50 minutes
Step-by-step explanation:
GIven:
Container A contain = 800 mL
Container B contain = 1,000 mL
Container A leak = 6 mL per min
Container B leak = 10 mL per min
Computation:
Assume; in x minute
So,
800 - 6x = 1,000 - 10x
4x = 200
x = 50 minutes
A car travels for 3 hours 15 minutes.Its average speed is 80km/h. Work out the total distance the car travels.
Answers
Answer:
1 hour=60 minutes].
Step-by-step explanation:
Answer:
speed×time
80×3hours and 15min
(3hours)
15÷60=0.25hours
3.25h
80×3.25=260
What is 214 grams in kilograms?
Answers
Answer:
0.214 Kilograms
Step-by-step explanation:
Answer:
0.214 Kilograms
Step-by-step explanation:
I don't have no questions
Answers
Answer: I have no Answer.
Explanation: There is no question to answer but ill take the 5 points.
The Pines Golf Course is offering free ice cream cones to golfers who hit their tee shot on the green at the
7
7th hole.
The following bar graph summarizes the tee shots from this morning.
Based on this data, what is the probability that a tee shot ends up on the green?
Probability
=
=
.16
Note: Write your answer as a decimal rounded to the nearest hundredth.
Answers
The probability that a golfer will get a free ice cream cone by hitting the green on the 7th hole is approximately 0.16 or 16%.
To find the probability that a tee shot ends up on the green, we need to determine the fraction of all tee shots that landed on the green.
Looking at the bar graph, we see that out of the total 125 tee shots, 20 of them landed on the green. Therefore, the probability of a tee shot ending up on the green is:
Probability = (Number of tee shots on green) / (Total number of tee shots) = 20/125 ≈ 0.16
Rounding to the nearest hundredth, we get Probability ≈ 0.16.
Therefore, the probability that a golfer will get a free ice cream cone by hitting the green on the 7th hole is approximately 0.16 or 16%.
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For her daughter’s birthday party, Mrs. Tanner paid $75.00 for 15 movie tickets.
Which unit rate describes the price of each ticket?
A. $1.00 per ticket
B. $3.00 per ticket
C. $5.00 per ticket
D. $7.50 per ticket
Answers
Answer:
C-$5.00 per ticket
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
$75.00 / 15 = $5
Each ticket costs $5
04.03 MC)
What is the slope of the line joining (8, 1) and (24, 9)? (5 points)
a
negative one over two
b
start fraction one over 23 end fraction
c
start fraction one over two end fraction
d
2
Answers
Answer:
A
Step-by-step explanation:
hopes this helps
(x2 + x - 1) = (x - 1)
Answers
Answer:
x=0
Step-by-step explanation:
how can i find the midpoint of a line segment ?
Answers
Answer:
add both x coordinates and divide them by 2.
add both y coordinates and divide them by 2.
Now final product should be (x,y)
Step-by-step explanation:
Example.
let's take 2 points:
(2,5) and (7, 9)
let's add both x coordinates.
2+7 = 9
now add both y coordinates.
5+9 = 14
Now divide both by 2.
Final answer should be (4.5, 7) = this is your midpoint
How to graph y= 2/3x-4
Answers
Answer:
3x-4/2
3x-2 I think it is a right answers
What is the shape of the distribution for the following set of data?Scores: 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6A)SymmetricalB)Positively skewedC)Negatively skewedD)Normal
Answers
The answer is (B) Positively skewed.
A histogram or a frequency polygon can be used to determine the shape of the distribution for a given set of data. However, because the data set is small, we can also visualise the distribution by directly examining its shape.
There are 12 values in the data set, ranging from 1 to 6. The most common values are 4 and 5, which appear 3 and 4 times, respectively, while 1 and 2 appear only once. The numbers 3 and 6 appear twice.
The distribution appears to be skewed towards the right. This is because the distribution's tail is longer on the right side, and the mean is greater than the median. The values on the left side of the distribution are closer together than those on the right, which are more dispersed.
As a result, the correct answer is (B) Positively skewed.
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Which prefix means 10?
deci
centi
Deca
Milli
Answers
For the number 10, the prefix used is 10. The correct option is A.
What is a numeral prefix?Prefixes derived from numerals or other numbers are known as numeral or number prefixes. They are used to coin numerous series of words in English and many other languages.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given number is 10. The prefix used for the number 10 is deci.
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Are they parallel? Please answer like the one on the top, I’m trying to get my geography hw in Bc it’s missing
Answers
Answer:yes they are
Step-by-step explanation:
Lei presold 323232 carnations for a fundraiser, then she sold ccc more carnations on the day of the fundraiser. She earned 0.250.250, point, 25 dollars for each carnation she sold.
The expression 8+ 0.25c8+0.25c8, plus, 0, point, 25, c describes how much money Lei earned for the fundraiser. We can also use the expression 0.25(32+c)0.25(32+c)0, point, 25, left parenthesis, 32, plus, c, right parenthesis to represent the same quantity.
Match each amount in the situation with the expression that represents it.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Sale before fundraiser = 32
Sale on the day of fundraiser = c
Cost of each carnation sold = 0.25
(Cost * sale before fundraiser) + cost * sale on day of fundraiser
(0.25 * 32) + 0.25 * c
8 + 0.25c
Or
Total carnation sold * cost per carnation
(sale before fundraiser + sale on day of fundraiser) * cost per carnation
(32 + c) * 0.25