which sequence of rigid transformations will map the preimage ABC onto image A'B'C'?
Answers
The sequence of rigid transformations that will map the preimage ΔABC onto image ΔA'B'C' is Option(a) a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis.
What is the sequence of rigid transformations?There are three basic rigid transformations: reflections, rotations, and translations.Reflections, as the name implies, mirror the given shape over a particular line. Translations slide or shift a shape from one location to another, whereas rotations spin a shape about a predetermined center point.Co-ordinates of the points of ΔABC are,
A = (-4, 2)
B = (-6, 2)
C = (-2, 6)
point (x,-y) is the reflection of the point (x,y) across the x-axis.
So, new co-ordinates are,
A = (-4, -2)
B = (-6, -2)
C = (-2, -6)
point (x+8,y) is the translation of the point (x,y) by 8 units right.
So, new co-ordinates are,
A = (4, -2)
B = (2, -2)
C = (6, -6)
Then, the reflection of the point (x,y) across the x-axis is the point (x,-y).
So, new co-ordinates are,
A' = (4, 2)
B' = (2, 2)
C' = (6, 6)
These are the coordinates of ΔA'B'C' so the correct answer is Option(a).
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"The complete question is: Which sequence of rigid transformations will map the preimage ΔABC onto image ΔA′B′C′?
a) a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis
b) a translation 4 units down and 10 units to the right
c) a reflection across the line y = x followed by a rotation 90° counterclockwise
d) a rotation 180° clockwise followed by a reflection across the x-axis."
Related Questions
Given the system of linear equations ... \[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1) Write the system in the matrix form \( A . X=B \) (2 points) 2) Solve t
Answers
The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).
As per data the system of linear equations,
\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)
Write the system in the matrix form \(\( A . X=B \)\)
We know that the matrix form of the system of linear equations is as follows.
\(\[A. X = B\]\)
Where
\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)
and
\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)
To solve the system, we can use row reduction method.
\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)
Applying the elementary row operations
\(\[R_{2}\to R_{2}-2R_{1}\]\)
and
\(\[R_{3}\to R_{3}-3R_{1}\]\)
we get,
\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)
Now applying the elementary row operations
\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)
we get,
\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)
Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.
Now, using the second row,
\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)
Solving this equation, we get y = 0.
Finally, using the first row, we can get the value of x as
\(\[x + 2y + 3z = 9\]\\x = 3\]\)
Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).
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Which of the following modifications to a research study will result in a narrower confidence interval?Group of answer choicesA) increasing the confidence level, decreasing the sample sizeB) increasing the confidence level, increasing the sample sizeC) decreasing the confidence level, decreasing the sample sizeD) decreasing the confidence level, increasing the sample size
Answers
The modification to a research study that will result in a narrower confidence interval is option D is correct choice
The modification to a research study that will result in a narrower confidence interval is option D: decreasing the confidence level and increasing the sample size. By decreasing the confidence level, we are willing to accept a lower level of certainty in our results, which can lead to a narrower interval. Increasing the sample size also leads to a narrower interval as it reduces the variability in our data and increases the precision of our estimates.
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Determine the center and radius of the following circle equation:
x ^2 +y ^2 −18x+4y+60=0
Answers
Answer:
Step-by-step explanation:
you can answer this on photo math
A rectangular wooden block is measured to have the following dimensions 3.8±0.1 cm by 2.15±0.05 cm by 7.31±0.01 cm. a. Could either of these measurements have been made with either of the calipers in Question 5? Explain why or why not? b. What is the volume of the block in cubic meters, cm
3
? c. The block is found to have a mass of 42.0±0.1 g. What is the density of the block in g/cm
3
. d. Calculate the percent error if block is made of spruce wood and the accepted density of spruce is 0.715 g/cm
3
?
Answers
a) It is unlikely that either of these measurements could have been made with either of the calipers. b) Volume is 57.457 \(cm^3\) c) Density is 0.731 g/\(cm^3\) d) The percent error is 2.24%.
a. Calipers typically have a measuring range and precision that may not be suitable for measuring such small variations in dimensions. The given uncertainties for each dimension (0.1 cm, 0.05 cm, and 0.01 cm) are relatively small, which suggests that more precise measuring instruments would be required to obtain such precise measurements.
b. To calculate the volume of the block, we multiply the dimensions together:
Volume = Length * Width * Height
Volume = (3.8 cm) * (2.15 cm) * (7.31 cm)
Volume ≈ 57.457 \(cm^3\)
c. To calculate the density of the block, we divide the mass by the volume:
Density = Mass / Volume
Density = (42.0 g) / (57.457 \(cm^3\))
Density ≈ 0.731 g/\(cm^3\)
d. To calculate the percent error, we compare the calculated density to the accepted density and express the difference as a percentage:
Percent Error = |(Calculated Density - Accepted Density) / Accepted Density| * 100
Percent Error = |(0.731 g/\(cm^3\) - 0.715 g/\(cm^3\)) / 0.715 g/\(cm^3\)| * 100
Percent Error ≈ 2.24%
Therefore, the percent error is approximately 2.24% if the block is made of spruce wood with an accepted density of 0.715 g/\(cm^3\).
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What is the factor of x³ 3x² 9x 5?
Answers
(x+1) & (x-5) are the factors of given equation.
The given Equation is,
x3- \(3x^{3}\) - 9
Substitute - Substitute means to put something in the place of another and in mathematics substitution means putting numbers in the place of letters. It is used to calculate the value of an expression.Here, If we substitute x =5, in the given equation, then we find
(5)3 - 3(5)3 - 9*5 -5 = 0
x-5 is factor of given equation to find another factor dividing given equation by x-5
we will get =(x2+2x+1) after dividing the equation by x - 5
Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)
=(x+2)2 (x-5)
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Please Answer This, the question is on the picture. it needs to be a fraction
will mark brainllest if its right, no links!
Answers
Given degree = 41
Find hypothenuse
Sohcahtoa (use cah to find hypothenuse)
Cosine = adjacent/hypothenuse
Cos(41) = 14.7/h
0.7547095802 = 14.7/h
14.7/0.7547095802 = 19.477691
Round to nearest tenth:
Solution: 19.5
Answer:
x = 19.48 or 19 12/25
Step-by-step explanation:
cos 41° = 14.7/x
x = 19.48 or 19 12/25
What does “m” stand for in the slope formula?
Answers
Answer:
Slope = m
Step-by-step explanation:
None
Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are diamonds, your friend will pay you $29. Otherwise, you have to pay your friend $4.Step 2 of 2 : If this same bet is made 891 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.
Answers
Answer:
Ok, the probability of winning is:
For the first draw, we have 13 diamonds in a 52 card deck, the probability of drawing a diamond is:
p1 = 13/52
for the second draw we have 12 diamonds and 51 cards in the deck, now the probability is:
p2 = 12/51
the total probability is equal to the product of the individual probabilities, this is:
P = p1*p2= (13/52)*(12/51) = 0.059
now, the expected value can be calculated as follows.
EV = (P1*X1 + P2*X2)
where P1 is the probabilty of event 1, and X1 is the event 1,
In this case X1 is the event of winning $29, then P1 = 0.059
X2 will be the event of loosing $4, so P2 = 1 - 0.059 = 0.941
Then the expected value for 1 round of the game is:
EV = (0.059*$29 - 0.941*$4) = -$2.05
So if you play 891 times, expected value of 891 times the expected value for 1 round, this is:
891*EV = 891*(-$2.05) = -$1826.55
So you loss around $1826.55
Giving 40 points PLEASE help ASAP The ratio of the number of teachers to students in a school is 3:35. The ratio of male students to the number of female
students is 2:5. There are 500 female students. How many teachers are there?
In the box, type the answer and tell how you found it. You may also do your work on a separate sheet of paper and upload it
in the box below.
Answers
Answer: 500 female students. 2:5 ratio for males means 200 male students. 500 female plus 200 male equals 700 students total. There are three teachers for every 35 students, so 700/35 multiplied by three equals 60 teachers.
(Giving Brailniest) What is 18x+20
Answers
Answer:
\(2(9x+10)\)
Step-by-step explanation:
\(18x+20\)
First, we have to factor. We will have to factor out 2 to get the answer(Factor out 2 from 18x+20).
Answer:
\(2(9x+10)\)
Hope this helps!
Explain why the exponents cannot be added in the products 12 to the third power times 11 to the third power
Answers
Answer:
Because the exponent rule that let's the base to the sum of the exponents power equal the base too the x power times the base to the y power states that the bases must be the same. And the bases 12 and 11 are not equal.
A system of two linear equations in two variables has no solution. What statement is accurate about these two linear equations?
Responses
The two linear equations never intersect.
The two linear equations never intersect.
The two linear equations graph the same line.
The two linear equations graph the same line.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the y-axis.
The two linear equations do not cross the y-axis.
The two linear equations intersect at exactly one point.
Answers
The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.
How many types of solution are there for two linear equations ?
There are 2 types of solution :
Consistent :
A consistent system is said to be an independent system if it has a single solution.
A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.
Non-consistent :
Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.
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The two linear equations never intersect.
When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.
If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.
It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.
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to graph an exponential, you need to plot a few points, and then connect the dots and draw the graph. where do you come up with the values to use in the graph
Answers
When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.
The T-chart employs positive real numbers since this is the most typical form of exponential function.
Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.
The exponential function can be represented by the following equation:
\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.
When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.
The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.
Therefore, the correct answer is option A.
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what is the name for a data value that is far above or below the rest?
Answers
The name for a data value that is far above or below the rest is called an outlier.
An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.
When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.
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A pencil is made up of a cylindrical body with a cone shaped and hemisphere shaped eraser the cylinder portion is 10 cm long with a radius of 0.3 cm the cone has a slate height of 1 cm
Answers
A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.
A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:
Cylindrical Body:
Length: 10 cm
Radius: 0.3 cm
Cone-shaped Eraser:
Slant height: 1 cm (assumed height of the cone)
Hemisphere-shaped Eraser:
Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:
Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.
We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.
Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.
It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.
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a stone is dropped from the top of a cliff. it is observed to hit the ground 5.78 s later how high is the cliff?
Answers
Using the formula;
H= ut + 1/2 gt²
The initial velocity = 0
Hence H= 1/2 gt²
g= 10m/s t= 5.78 s
H = 1/2 x 10 x 5.78²
H = 167.042 m
H = 167 m approximately
cuanto es 1/3 mas 3/4 mas 1/2 lo necesito por favor ;_;
Answers
Answer:
19/12= 1 7/12
Step-by-step explanation:
So I got it wrong in my homework how do i translate it?
Answers
To translate something:
⇒ is to write out the equations
Let's examine what information this problem gives us:
Mrs. Albert has $400 ⇒ Total money = 400Mrs. Albert bought two adult tickets at $62.50 each⇒ with '2' being the number of adults tickets
⇒total charge from purchasing adult tickets = 2 * 62.5 = 125
Each child ticket costs $42.5⇒ with 'x' being the number of child tickets bought
⇒total charge from purchasing child tickets = 42.5x
Since the sum of total charge from purchasing adult tickets and total charge from purchasing child tickets is equal to 400:
⇒ 42.5x + 125 = 400 <== translated form
Let's solve:
\(42.5x+125=400\\42.5x=275\\x=6.47\)
Since we can only buy whole tickets:
Mrs. Albert could have bought at most 6 child tickets
Answer: Mrs. Albert can bring 6 kids
Hope that helps!
Explain why ac is equal to
Bc
Answers
Answer:
because length is same I hope it will help you please follow me
What is the length of the hypotenuse in the right
triangle?
O 2,593 cm
O 60 cm
14,225 cm
O 65 cm
Answers
Answer:
sqrt(2593)
Step-by-step explanation:
17^2+48^2 = 2593^2
Given that Z is a standard normal random variable, what is the probability P(Z > 1.96)?
a. 0.7745
b. 0.8413
c. 0.0919
d. 0.9332
Answers
A standard normal random variable probability is 0.0250.
The probability P(Z > 1.96) found by subtracting the cumulative probability from 1.
Using a standard normal distribution table or calculator, find the cumulative probability corresponding to 1.96, which is approximately 0.9750.
P(Z > 1.96) = 1 - P(Z ≤ 1.96) = 1 - 0.9750 = 0.0250.
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A cube has a side length x and an each dimension is being increased by y, guys. :)
A). Write an expression for the surface area of the new cube, and then expand, and simplify, guys. :)
B). Please find the difference of the surface areas of the new cube and the original cube, guys. :)
Answers
Surface area of old cube
6(side)²6x²Side of new cube
x+ySurface area
6(x+y)²6(x²+y²+2xy)6x²+6y²+12xyDifference
6y²+12xyAnswer:
A) 6(x + y)² = 6x² + 12xy +6y²
B) 12xy +6y²
Step-by-step explanation:
Surface area of a cube = 6s² (where s is the side length)
Part A
Given:
x = side length of original cube⇒ Surface area of the original cube = 6x²
If the side length of the cube is increased by y, then:
(x + y) = side length of new cube⇒ Surface area of the new cube = 6(x + y)²
Expand and simplify:
⇒ 6(x + y)²
⇒ 6(x + y)(x + y)
⇒ 6(x² + xy + xy + y²)
⇒ 6x² + 12xy +6y²
Part B
To find the difference between the surface areas of the new and original cubes, subtract the surface area of the original cube from the surface area of the new cube:
⇒ SA of new cube - SA of original cube
⇒ 6x² + 12xy +6y² - 6x²
⇒ 12xy +6y²
when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be group of answer choices reliable. standardized. valid. normally distributed.
Answers
When a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be standardized.
Standardization refers to the process of establishing norms or standards for a test by administering it to a representative and pretested sample of individuals. This allows for a comparison of an individual's test performance to that of the larger group. When a test is standardized, it means that it has undergone rigorous development and validation procedures to ensure that it is fair, consistent, and reliable.
Standardized tests provide a benchmark for evaluating an individual's performance by comparing their scores to those of the norm group. The norm group consists of individuals who have already taken the test and represents the population for which the test is intended. By comparing an individual's scores to the norm group, it is possible to determine how their performance ranks relative to others.
Therefore, when a person's test performance can be compared with that of a representative and pretested sample of people, it indicates that the test is standardized. Standardization is an essential characteristic of reliable and valid tests, as it ensures consistency and allows for meaningful comparisons among test-takers.
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Which is the most reasonable way to estimate 26% of 88?
One-fifth(90)
One-fifth(80)
One-fourth(90)
One-fourth(80)
Answers
Answer:
1/4(90)
Step-by-step explanation:
The most reasonable way to estimate 26% of 88 is one-fourth of 90. Therefore, the correct option is C.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, 26% of 88.
Now, 26/100 ×88
= 0.26×88
= 22.88
A) 1/5 ×90
= 18
B) 1/5 ×80
= 16
C) 1/4 ×90
= 22.5
D) 1/4 ×80
= 20
Therefore, option C is the correct answer.
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a water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. to monitor this, they take 2 oz. of water at 37 locations every hour, measure the ph at each of those locations, and find their average. if the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8.5 and a standard deviation of 0.22. if the ph level of the reservoir is ok, what is the probability that the sample average is more than 8.47? group of answer choices
Answers
The probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok
To calculate this, we will use a standard normal distribution table and the Z-score formula.
First, we need to calculate the Z-score for the sample average of 8.47. This is done by using the Z-score formula:
Z-score = (x - mean)/standard deviation
where x is the sample average, mean is the average of all samples, and standard deviation is the standard deviation of all samples.
In this case, the Z-score is:
Z-score = (8.47 - 8.50)/0.22 = -0.14
Then, we need to look up the Z-score in a standard normal distribution table. The probability of the sample average being more than 8.47 is equal to 1 minus the Z-score probability. So, in this case, the probability of the sample average being more than 8.47 is equal to 1 - 0.5594 = 0.4406.
Therefore, the probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok.
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Can some help me plzzzz
Answers
Answer:
Should be 9 grams
Step-by-step explanation:
240÷40=6 576÷2÷2÷2÷2÷2÷2=9
What is the equation of a line that goes through the point(0, 5/6) and has a slope of 1?
Answers
Using the point-slope formula in order to obtain the equation of the line.
The formula is,
\(y-y_1=m\left(x-x_1\right)\)Given:
\(\begin{gathered} \lparen x_1,y_1)=\left(0,\frac{5}{6}\right) \\ m=1 \end{gathered}\)Therefore,
\(y-\frac{5}{6}=1\left(x-0\right)\)Simplify
\(\begin{gathered} y-\frac{5}{6}=1\left(x\right) \\ y-\frac{5}{6}=x \\ \therefore y=x+\frac{5}{6} \end{gathered}\)Hence, the equation is
\(y=x+\frac{5}{6}\text{ \lparen OPTION 1\rparen}\)Help me pls!!!!!!!!!
Answers
-7 + 10y = 33 STEP BY STEP FULL ANSWER TO GET BRAINLIEST
Answers
Answer:
y = 4
Step-by-step explanation:
-7 + 10y = 33
10y = 33 +7
10y = 40
y = 40/10
y = 4
The same experiment was conducted 8 times. How many times should the
results have been similar for them to be valid?
A. 2
B. 6
C. 4
D. 8
Answers
Answer:
C. 4
Step-by-step explanation:
Because there is always a 50/50 chance of getting the similar result.
Hope this helps.
Answer:
8
Step-by-step explanation:
If other outcomes occurred it would not be valid.