plot the image of triangle ABC under a reflection across line l
Answers
The image of the triangle ΔABC under a reflection across the line l can be obtained my making use of the laws of reflection, and the rules of a reflection transformation, to obtain the triangle ΔA'B'C', with vertices at A'(10, -5), B'(13, -6), and C'(12, -3)
Please find attached the plot of the image of the triangle ΔABC, created with MS Excel
What is a reflection transformation?A reflection transformation is one that forms a mirror image of the object across the line of reflection, such that lines joining corresponding points on the pre-image and the image are perpendicular to the line of reflection, and the corresponding points on the pre-image and the image are equidistant from the line of reflection.
Taking the coordinate of the vertices of the triangle ΔABC as A(10, 5), B(13, 6), C(12, 3), and the line l as coinciding with the x-axis, we get:
The coordinates of the image of a point (x, y) following a reflection about the x-axis is the point (x, -y)
Therefor, the coordinates of the vertices of the image of the triangle under a reflection across the line l are;
A'(10, -5), B(13, -6), C'(12, -3)Please find attached the plot of the image of the triangle ABC under a reflection, across line l, created with MS Excel.
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Related Questions
Order ³√97, 78/9, √45 from greatest to least.
³√97, 78/9, √45
78/9, √45, ³√97
³√97, √45, 78/9
78/9, ³√97, √45
Answers
78/9, √45 , ³√97 is the order of numbers from greatest to least.
Given,
The numbers;
³√97, 78/9, √45
We have to order these numbers from greatest to least.
Ordering of numbers;
A series of numbers can be arranged in numerical order. Both ascending and descending orders are possible. For instance, suppose you arranged a group of numbers in ascending order as 2, 55, 103, 256, and 802, for instance. This can make it much simpler to look through a large collection of numbers.
Here,
First we have to find the values of the numbers.
The value of ³√97 = 4.59
The value of 78/9 = 8.66
The value of √45 = 6.71
So,
The greatest one is 78/9 and the least one is ³√97
Therefore,
The order of numbers from greatest to least is 78/9, √45 , ³√97
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Lauren visits the park every 4 days and goes to the library every 10 days. If Lauren does both of these today, how many days will pass before Lauren gets to do them both on the same day again?
A.20 days
B. 14 days
C. 6 days
D. 40 days
Answers
Answer:
20 days
Step-by-step explanation:
Refer to the golden ticket parking lottery example (page 296). At the following month's school assembly, the two lucky winners were once again members of the AP Statistics class. This raised suspicions about how the lottery was being conducted. How would you modify the simulation in the
example to estimate the probability of getting two winners from the AP Statistics class in back-to-back
months just by chance?
Answers
Answer: i dont kno man
Step-by-step explanation:
Solve for the short leg of the 30-60-90 triangle.
Answers
Answer:
b = 2
Step-by-step explanation:
because of the 60° in the corner we know this triangle is the left half of an equilateral triangle (where all 3 sides are equally long, and all 3 angles are 60°).
therefore, b is half of the baseline of that equilateral triangle = 4/2 = 2.
so, b = 2 is the correct answer.
A 14 km road needs repaired. Workers can repair 3 1/2 km of the road per week. How many weeks will it take to repair the road?
Answers
Answer:
3×1/2 = 1.5km per week
14÷1.5=9.33 if you round it it would take 9weeks
evaluate 150-(2=x)3 when x=2
Answers
The value of the expression 150 - 3x when x =2 is 144.
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Given expression,
150 - 3x.
And we have x = 2.
Substituting the value of x to the expression
So,
150 -3x = 150 - 3(x = 2)
= 150 - 3(2)
= 150 - 6
= 144
Therefore, the answer is 144.
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What is 45 less than the product of 18 and a number written as an algebraic expression? 18n − 45 45 − 18n 18(n − 45) n(18 − 45)
Answers
The algebraic expression 18n - 45 is correct for the statement "45 less than the product of 18 and a number written as an algebraic expression"
Word problem in algebraWe can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.
Let us represent the unknown number with the letter "n"
The product of 18 and the number will be;
18 × n = 18n
45 less than the product of 18 and the number (n) is thus written algebraically as;
18n - 45
Therefore, 45 less than the product of 18 and a number(n) is written as an algebraic expression as 18n - 45.
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plsssssssssssss helppppppppppppp ....
Answers
Answer:3/4 10
Step-by-step explanation:
Which of the scatter plots below shows the most accurate line of best fit?
PLS LOOK AT PICTURE AND HELP ME, IM BEING TIMED
Answers
Answer:
Z
Step-by-step explanation:
The average number of cars waiting at a drive-up window at 9am follows a Poisson distribution with a mean of 2 cars Calculate the following probability of cars waiting at the drive-up window. X = 1, 2, ..., 10 a. P(x=0) = b. P(x=2)
Answers
Probability of cars waiting at the drive-up window is P (X=0) = 0.1353 and P (X=2) = 0.2707
What is probability ?The variety of strategies for achievement. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one method to acquire a head and there are a total of 2 potential outcomes (a head or tail). We specify P(heads) = 1/2.
There are typically 2. chance of automobiles waiting at the drive-up window on any given morning at 9 o'clock, according to a Poisson distribution. a. P(x=0) P(x=0) X = 1, 2,..., 10
X≅ P(2)
a. P(x=0)
P(x=0)
[tex]e^{-2}[/tex] . [tex]2^{0}[/tex] ÷ 0!
[tex]e^{-2}[/tex]
0.1353
b. P(x=2)
[tex]e^{-2}[/tex] .[tex]2^{2}[/tex] ÷ 2!
2[tex]e^{-2}[/tex]
0.2707
So
Probability of cars waiting at the drive-up window is P (X=0) = 0.1353 and P (X=2) = 0.2707
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bella answered 33 questions on her math test. she earned a 92% on the test. how many questions did she answer correct
Answers
Answer: 30.36
Step-by-step explanation:
92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.
Two cars leave town at the same time. One travels west at 56 mph, and the other
travels south at 42 mph. After one hour, how far apart are the cars?
ongo if starting in
Answers
The distance between the cars after a hour is 14 meters.
How to calculate the distance of the cars?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
In this case, the cars leave town at the same time. One travels west at 56 mph, and the other travels south at 42 mph.
With the speed, the total distance after an hour will be:
= 56 - 42
= 14 meters
The cars are 14 meters apart.
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Write an inequality for the graph of (-2,-2) (0,-6)
Answers
The answer is 24
sorry if i did not say more its hard to explain sorry again
Which of the following properly expresses the
verbal
statement "The square root of a number, x, is 5
less than
the sum of the number and 2" ?
F. √x = 5-(x + 2)
G√√√x = (x + 2)-5
Answers
"The square root of a number, x, is 5less than the sum of the number and 2" is √x = (x+2)-5
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given verbal statement is "The square root of a number, x, is 5
less than the sum of the number and 2"
The x is the given number.
So square root of a number, x means √x
5 less than the sum of the number and 2.
sum of the number and 2 means x+2 and 5 less than the sum of the number and 2 means (x+2)-5
So √x = (x+2)-5 is the equation.
Hence, √x = (x+2)-5 expresses the verbal statement "The square root of a number, x, is 5less than the sum of the number and 2"
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17 - 39 - (-82) + 65
Answers
Answer:
125
Step-by-step explanation:
In the picture below, which lines are lines of symmetry for the figure?
A. only 2
B. 1, 2, and 3
C. 2 and 3
D. 1 and 3
Answers
(A) only 2 is the line of symmetry of the given figure.
What are lines of symmetry?A form or item is divided into two equal and symmetrical portions by a line of symmetry.
Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.
The four lines of symmetry in a square are lines across the opposing vertices and the midpoints of the opposing sides.
Together, these four lines of symmetry make up a square.
Consequently, a square has two diagonal, one horizontal, and one vertical line of symmetry.
So, according to the given figure we can easily observe and tell that line 2 is the only one that divides the diagram into 2 identical parts.
Therefore, (A) only 2 is the line of symmetry of the given figure.
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Find the critical z value for a confidence level of 85%. (round answer to 2 decimal places)
. I want to know what Z-table to use and how to read it because it get me confused in reading the z table to answer this type of question
Answers
Using a z-table for the value, the critical z-value for a confidence level of 85% is; ±1.439.
How to find the critical z-value?The critical value of a distribution is defined as the value beyond which the rejection region lies.
Now, for a confidence interval , the rejection region lies beyond two values, the positive and the negative critical value.
We are given that the confidence level is 85%.
Thus, the computation of the critical value of z for 85% confidence level is expressed as follows;
±z_α/2 = ±z_0.15/2
This is simplified to get;
±z_0.075 = ±1.439
That value is concluded to be the critical z-value at the given confidence level.
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This design covers the floor of a huge hall. What fraction of the floor is covered by black tiles? What fraction of the floor is covered by white tiles?
Answers
The fraction of the floor is covered by white tiles is 1/3.
What fraction of the floor is covered by white tiles?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Assumed figure:
Places covered by white tiles = 18
Total tiles = 54
The Fraction covered by white tiles will be:
= Number of whitw tiles / Total tiles
= 18/54
= 1/3
The Fraction is 1/3.
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Matthew has 8.2 meters of wire. He uses 3.65 meters for craft project. He wants to use the wire he left to complete one of the following projects. For which of the projects does he have enough wire? Choose all the correct answers.
Answers
He can make another project and still have 0.90 m of wire left.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Matthew has 8.2 meters of wire.
He uses 3.65 meters for the craft project.
Now, He wants to use the wire he left to complete one of the following projects.
The left wire is 8.2-3.65 = 4.55 m
So he can make another project and still have 0.90 m of wire left.
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In the parallelogram, m
Answers
By the concept of the sum of the adjacent angle in a parallelogram, we determine m∠PQR = 76°.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
We know a parallelogram has opposite angles of equal measure and the sum of adjacent angles is 180°.
Given, m∠QRP = 38° and m∠PRS = 66°.
∴ m∠PQR = 180° - 38° - 66°.
m∠PQR = 76°.
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13. 30% of what number is 97 14. 50% of what number is 11? 15. 25% of what number is 20? 16. 60% of what number is 217 17. 75% of what number is 127 18. 10% of what number is o? 19. 120% of what number is 48? 150% of what number is 75? 21. The length of a rectangle is lo inches. If the width 50% of its length, what is the width of the rectang 20.
Answers
The values are (13) 323.33 (14) 22 (15) 80, (16) 361.67, (17) 169.33, (18) 0 (19) 40, (20) 50 (21) the width is 5 inches
How to solve for percentage?We should know that percentage is a ration of fraction of 100
The given percentages are as follows:
(13) 30% of what gives 97
let the number be x in all cases
(30/100)*x=97
30x=9700
x=323.33
(14) (50/100)*x=11
50x=1100
x=22
(15) (25/100)*x=20
25x=2000
x=80
(16) (60/100)*x=217
60x=21700
x=361.64
(17) (75/100)*x=127
75x=12700
x=169.33
(18) (10/100)*x=0
10x=100*0
10x=0
x=0
(19) (120/100)*x=48
120x=100*48
120x=4800
x=40
(20) (150/100)*x=75
150x=7500
x=50
(21) lenght = 10 inches
width = 50% of 10
= (50/100)*10
= 5 inches
Therefore the width is 5 inches
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A 55 inch pipe is cut into two pieces. One piece is four times the length of the other find the length of the shorter piece.
Answers
Answer:
11 inches
Step-by-step explanation:
4x + x = 55 Combine like terms
5x = 55 Divide both sides by 5
x = 11 This is the length of the shortest piece the other piece is 44 4(11)
Answer:
11 inches, 44 inches
Step-by-step explanation:
First of all, we need to make this equation, into an algebraic one:
4x + x = 55
The x represents the number of inches for the rope.
Now you simplify:
5x = 55
This equation can be simplified to a regular division problem:
55/5 = x
Using basic division, x is equal to 11 inches.
Now, this is just the shorter rope.
Note that the other piece is 4 times larger than the short one:
4 x 11 = 44
Thus 11 inches and 44 inches is the answer
A company loses $80 as a result of a shipping delay. The 4 owners of the company must share the loss equally. Write an expression for the earnings per person. Evaluate the expression
Answers
Answer:20
Step-by-step explanation: 80 divided by 4 is 20
Which function represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis?
g(x) = −4(2)x
g(x) = 4(2)−x
g(x) = −4(one-half) Superscript x
g(x) = 4(one-half) Superscript negative x
Answers
Answer:
The function that represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis, is g(x) = −4(one-half) Superscript x. This function is obtained by negating the exponent of the original function, which reverses the direction of the exponential growth and creates a mirror image of the original function across the x-axis. The other options listed do not correctly reflect the original function across the x-axis.
Step-by-step explanation:
A recreation center charges $50 to rent the gym for 1 hour, and $100 to rent the gym for 3 hours. Jon says the price per hour is $50. Find and correct Jon’s mistake. Assume the relationship is linear.
Answers
The rent of the gym for one hour is $50 and for three hours it is $100.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given:
A recreation center charges $50 to rent the gym for 1 hour, and $100 to rent the gym for 3 hours,
Calculate the price if you rent a gym for 3 hrs = 100 / 3 = $33.33
Therefore, the rent of the gym for one hour is $50 and for three hours it is $100.
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Suppose particular plane needs to attain speed of k feet per second In order to take off: The plane can attaln that speed in 30 seconds Assume acceleration Is constant; v(o) = 0, and s(0) when answering the questlons below. Use lower case k. (a) Flnd formulas for acceleration_ velocity, and position of the plane_ Your answers will have k In It: a(t) Select-= v(t) Select s(t) Selec (D) If the plane accelerates to feet per second in 30 seconds how far will it travel In that time? Your answer will have k In It. feet (c) If a runway Is 3450 feet long and the plane uses the entire runway to take off, what Is the value of k?
Answers
Formula available for acceleration, velocity and position of plane are
k²=2as, k=30a, s=450a and the value of k is 230 ft/sec
what is velocity?rate of changes of distances with respect to time.
what is acceleration?rate of changes of velocity with respect to time.
Given, final velocity, v= k ft/s
time needed to attain speed k is 30 s
time, t= 30 sec
acceleration, a = constant
initially at time t=o, velocity and distance travel by aircraft was also o
initial velocity u =0, distance s = 0
as per the formula regarding velocity, distance, time and acceleration
v² = u²+2as
as per the question final velocity v= k, initial velocity u=0
k² = 2as
again, the formula v= u+at
the velocity of v after 30 second
k= a×30
acceleration, a= k/30
from the other formula, s=ut+1/2×at²
distance travel by aircraft after 30 second with initial velocity 0.
s= u×0+1/2×a(30) ²
s= 450a
previously we got a=k/30
now, s =450×k/30= 15k
if the runway is 3450 feet long and the plane needs to use the entire runway to take off then the value of k will be
s=15k
k=230 ft/sec
hence, the value of k is 230 ft/sec
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Factor the expression using the GCF.18h+30k The factored from is
Answers
The given expression can be factorized to obtain 18h + 30k = 6(3h + 5k).
How to factorize an algebraic expression by GCF method?First find the greatest factor common to all the terms of the given expression. Then, take out that term as a common and the remaining terms are written inside a bracket.
The given expression is 18h + 30k.
The GCF of 18 h and 30 k is 6.
Now, the given expression can be factorized as follows,
18h + 30k
= 6 × 3h + 6 × 5k
= 6(3h + 5k)
Hence, the factored form of the given expression is 6(3h + 5k).
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Solving System with 3 variables
Problem 1: Solve for x, y, and z. Show all your work!
x-5y+3=39
3x+8y-z=-19
2x-6y-5z=-29
Answers
Answer:
x = 2
y = -2
z = 9
(2,-2,9)
Step-by-step explanation:
The graph below shows the number of free throws made by five players on a basketball team.
Weekly Free Throw Numbers for Players
#Free Throws
10+
99876543N
Player 1 Player 2 Player 3 Player 4 Player 5
Week 1 Week 2 Week 3
What was the total number of free throws made for Player 2?
24
17
23
8
Answers
Total number of free throws made for player 2 are 23 using histogram.
Define histogram.A histogram is a graphical depiction of continuous or discrete data. In a histogram, the frequency is represented by the area of a bar. Frequency density, which is proportional to frequency, is plotted on the y-axis, and intervals representing the range of values are plotted on the x-axis. One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution. A histogram is a graph in which the horizontal axis represents the values of the observations, and the vertical axis represents the density of those observations.
Given,
Histogram given,
Total number of free throws made for player 2 are:
8 + 9 + 6
23
Total number of free throws made for player 2 are 23 using histogram.
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PLEASE HELP 70 BRAINLY POINTS IF YOU ANSWER THIS QUESTION
A probability value is listed at the top of each column. Determine the probability for each situation, then drag and drop each situation into the column under its correct probability.
Answers
Probability of drawing a even number of dice is 0.5, The probability of flipping a head on a coin is 0.5,The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks is 0.2, The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs is 0.5 and The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball is 0.2.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The probability of drawing a even number of dice.
A dice has 3 even numbers, 2, 4 and 6.
probability of drawing a even number of dice=3/6=1/2=0.5
The probability of flipping a head on a coin =1/2=0.5
The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks.
1/5=0.2
The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs.
4/8=1/2=0.5
The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball.
The probability is 0.2
Hence, probability of drawing a even number of dice is 0.5, The probability of flipping a head on a coin is 0.5,The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks is 0.2, The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs is 0.5 and The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball is 0.2.
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