The reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).
A translation is a type of transformation that moves all the points of a figure the same distance and in the same direction.
The shape and size of the figure do not change, only its position in the plane.
(3, 6)--->(1,6)
3-x=1
x=-2
(x-2, y)
To find the reflection rule that maps the triangle D(3, 6), E(-4,-3), F(6, 1) onto its image D'(1, 6), E(8, -3), F'(-2, 1), we need to determine the line of reflection.
In triangle the point where the perpendicular bisectors intersect will be the center of the reflection.
We find that the midpoint of DE is (−0.5,1.5), the midpoint of DF is (4.5,3.5), and the midpoint of EF is (1,−1).
The perpendicular bisectors of DE and DF intersect at (2,2), and the perpendicular bisectors of DE and EF intersect at (−1.25,2.75).
Therefore, the reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).
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PLEASE HELP!! WIKL GIVE BRAINLIEST!!
Action. 2,150
Comedy. 1,271
Drama. 829
Romance. 300
The manager of the theater expects to sell 8,000 movie tickets next month. The theater earns $4.53 profit on each movie ticket sold. Based on last month's results, how much profit can the theater manager expect to earn from ticket sales to romance movies next month?
Answer:
$2174.40
Step-by-step explanation:
2150+1721+829+300=5000
They sold 5000 tickets last month.
300÷5000=0.06
So 6% of the tickets each month are romance.
They expect to sell 8000 next month.
8000x.06=480
They should sell 480 romance tickets next month.
480x4.53=2174.40
If Hannah place is 6500 into account and a 5% interest compounded continuously how much will she have after 10 years?
angles c and d are complementary. the measure of angle d is 15 degrees greater than the measure of angle. what is the measure of each angle.
The measure of the angles is c = 37. 5 degrees
d = 15 + 37.5 = 52. 5 degrees
How to determine the anglesTo determine the value, we need to know what complementary angles are;
Complementary angles are defined as pair of angles whose sum is equal to 90 degrees
From the information given, we have that;
Angle c and d are both complementary angles
Also, the measure of angle d is 15 degrees greater than the measure of angle c
Then, we have;
d = 15 + c
Substitute the values
c + 15 +c = 90
collect like terms
2c = 90 - 15
2c = 75
Divide both sides by the coefficient
c = 37. 5 degrees
Substitute the value for angles d
d = 15 + 37.5 = 52. 5 degrees
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x is proportional to the square root of y, where y > 0
y is increased by 44%
Work out the percentage increase in x
When Y is increased by 44%, X increases by 20%.
If X is proportional to the square root of Y, then we can express this relationship as X = k√Y, where k is the constant of proportionality. Now, let's consider the scenario where Y is increased by 44%.
Let's denote the initial value of Y as Y₀. When Y is increased by 44%, the new value of Y becomes Y₁ = Y₀ + 0.44Y₀ = 1.44Y₀.
Since X is proportional to the square root of Y, we can write the initial value of X as X₀ = k√Y₀, and the new value of X as X₁ = k√(1.44Y₀).
To find the percentage increase in X, we can calculate the difference between the new and initial values of X and express it as a percentage of the initial value:
Percentage increase in X = ((X₁ - X₀) / X₀) * 100
Substituting the values, we get:
Percentage increase in X = ((k√(1.44Y₀) - k√Y₀) / k√Y₀) * 100
Simplifying the expression, we find:
Percentage increase in X = ((√1.44 - √1) / √1) * 100
Percentage increase in X = (1.2 - 1) x 100
Percentage increase in X = 0.2 x 100
Percentage increase in X = 20%
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ABCD is a quadrilateral.
a
b) When ABCD is drawn to scale, would
the lines AD and BC be parallel or not? A
You must justify your answer without
using a scale drawing.
Justify your answer
Yes/No
The value of x is 45 in the provided assertion, and the Centerior angles do sum up to 180°, indicating that AD and BC are parallel.
We have,
Parallel in mathematics refers to two lines which never cross one another; picture an equal symbol. Three close pals' parallel lives could be depicted in a tale.
(a)
3x + x + 2x + 90 = 360
6x = 360 - 90
6x = 270
x = 45
(b) The answer will be yes, they would be parallel.
We can justify this using co-interior angles, which state that 2 angles subtended by parallel lines add up to 180°
We can check this with both angles 3x & x, or 2x & 90°.
If AD and BC are parallel, then 3x + x = 180, and since you already found the value of x we can substitute this in:
3(45) + (45) = 180
135 + 45 = 180
180 = 180
So the co-interior angles do add up to 180°, which means that AD and BC are parallel.
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bryan’s hockey team is purchasing jerseys the company charges 250$ for a one time set up fee and 23$ for each printed jersey which expression represents the total cost of x number of jerseys for the yeam
Answer:
23x+250 and that would equal your total cost
There are 1000 cubic centimeters and 1 Liters in 1000 cubic millimeters in 1 milliliter. How many cubic millimeters are there in 1000 cubic centimeters
Answer:Set up a proportion, letting = the amount of cubic millimeters in 1,000 cubic centimeters. Solve for : 1,000,000 cubic millimeters are in 1,000 cubic centimeters.
please help I don’t know how to do this graph
The graph of the functions f(x) and g(x) is given below.
Given that:
Function, f(x) = x³
Translated function, g(x) = (x + 6)³
If the function is translated by 'h' units horizontally and 'k' units vertically, then x and y are replaced with (x - h) and (y - k), respectively.
The curve of the function g(x) is translated left side by 6 units.
The graph of the functions is given below.
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4.1 Find the intervals on which the function = [tex]x^{3}[/tex] −
4[tex]x^{2}[/tex]$ + 10 is increasing or decreasing.
The intervals on f(x) is increasing on (-∞, 0) and (8/3, ∞), and decreasing on (0, 8/3).
The intervals on which the function f(x) = x³ − 4x² + 10 is increasing or decreasing need to find its derivative and determine its sign.
f(x) = x³ − 4x² + 10
f'(x) = 3x² − 8x
The critical points we set f'(x) = 0 and solve for x:
3x² − 8x = 0
x(3x − 8) = 0
x = 0 or x = 8/3
These are the critical points of the function.
Now we can determine the sign of f'(x) in each interval:
Interval (-∞, 0):
Choose x = -1. f'(-1)
= 3(-1)² - 8(-1)
= 11 is positive.
So f(x) is increasing on (-∞, 0).
Interval (0, 8/3):
Choose x = 1. f'(1) = 3(1)² - 8(1)
= -5 is negative.
So f(x) is decreasing on (0, 8/3).
Interval (8/3, ∞):
Choose x = 3. f'(3) = 3(3)² - 8(3)
= 19 is positive.
So f(x) is increasing on (8/3, ∞).
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Select the correct answer.
Which statement is true?
OA
Point estimates are used to make inferences about population parameters.
OB. When we use the population mean and proportion to summarize information about the entire population, we call them point
estimates.
OC. The population mean and proportion are always equal to their corresponding point estimates.
O D.
The sample mean and sample proportion of a population are called population parameters.
Answer:
A. Point estimates are used to make inferences about population parameters.
If the Coach chooses the Three-Year Plan, what is the total amount he will spend after 12 months? ANSWER QUICK ILL GIVE BRAINLIST!
Answer:
$17,320 after 12 months.
Step-by-step explanation:
f the Coach chooses the Three-Year Plan, the total amount he will spend after 12 months can be calculated as follows:
First, we need to calculate the total amount of monthly payments made in 12 months:
12 months x $610 per month = $7,320
Then, we need to add the down payment made at the time of purchase:
$7,320 + $10,000 = $17,320
Therefore, if the Coach chooses the Three-Year Plan, he will spend a total of $17,320 after 12 months.
8) John wishes to make a line
plot of the heights in inches for a soccer team. The heights are
listed below. How many dots
would be above the greatest
height recorded?
Answer options
1
2
3
4
There are three dots above the greatest height.
We have,
The greatest height is 75
The smallest height is 62
Now,
We can make a line plot as:
* *
* * * * *
* * * * *
62 66 68 72 75
Thus,
There are three dots above the greatest height.
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calculate for me question 4, please
Answer:
f(x) = x^2 - 5x + 6
f'(x) = 2x - 5
Since the slope of h(x) is 1/3, the slope of the tangent line to f(x) will have slope -3.
2x - 5 = -3
2x = 2, so x = 1
A certain car has a fuel efficiency of 28.1 miles per gallon (mi/gal). Express this efficiency in kilometers per liter (km/L).
Answer:
the answer is 10.63km/L.
Solve 44 = K + 58 for K
Answer:
-14 = k
Step-by-step explanation:
44 = k+58
Subtract 58 from each side.
44-58 = k+58-58
-14 = k
Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years.
Determine the quartiles.
0.76
1.08
1.32
1.55
1.83
2.09
2.57
2.83
3.01
3.25
3.63
3.78
4.09
4.32
4.64
4.93
5.23
5.34
5.44
5.73
The quartiles of rainfall in April for the city are:
Q1 = 1.96Q2 = 3.44Q3 = 4.79.What are the quartiles of rainfall?The quartiles refers to the e values that split sorted data into four parts each with an equal number of observations
To determine quartiles, we first need to sort the data in ascending order which are:
[tex]0.76, 1.08, 1.32, 1.55, 1.83, 2.09, 2.57, 2.83, 3.01, 3.25,\\3.63, 3.78, 4.09, 4.32, 4.64, 4.93, 5.23, 5.34, 5.44, 5.73[/tex]
There are 20 data points, so, median (Q2) will be the average of the 10th and 11th values.
Q2 = (3.25 + 3.63) / 2
Q2 = 3.44.
Q1 = (1.83 + 2.09) / 2
Q1 = 1.96.
Q3 = (4.64 + 4.93) / 2
Q3 = 4.79.
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Which of the following reflective symmetries
apply to the hexagon below?
Symmetry
D
E
F
C
A
Reflective symmetry over AD
Reflective symmetry over CE
B
Applies to th
Yes/No
Yes/No
The table can be filled as Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No
We are given that;
The hexagon DEFCA
Now,
the hexagon has reflective symmetry over AD, because if we fold it along AD, the vertices B and F will match, as well as the vertices C and E. Therefore, the answer for reflective symmetry over AD is Yes.
However, the hexagon does not have reflective symmetry over CE, because if we fold it along CE, the vertices A and F will not match, nor will the vertices B and D. Therefore, the answer for reflective symmetry over CE is No.
Therefore, Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No.
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There are 8 strawberry plants in each row. Each plant has 11 strawberries on it. What equation could you use to find how many strawberries there are in 7 rows?
8 + 11 x 7 = ___
8 x 11 + 7 = ___
8 x 11 x 7 = ___
8 x 11 ÷ 7 = ___
Which systems is the only inconsistent system?
A.
Y=2x+3
Y=2x-1
B.
Y=x+3
Y=-x+7
C.
Y=x-5
2y=2x-10
D.
Y=x+3
Y=2x+4
Answer:
C
Step-by-step explanation:
Both equations are the same
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equivalent value of the equation is 18x-9=72 and x=4.5
Given data ,
Let the equation be represented as A
Now , the value of A is
(3/5)(30x-15)=72
On simplifying the equation , we get
3(6x-3)=72
On further simplification , we get
18x-9=72
x=81/18
x=4.5
Hence , the equation is 18x-9=72
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round 12.083 to the neatest tenth
Answer: 12.1
Step-by-step explanation: rounding 12.083 to the nearest tenth will leave you with- 12.1
hope this helps!
Does anybody know this? From a group of five boys and three girls, a boy and a girl will be selected to attend a conference in how many ways can the selection be made?
¿Para qué valor de la constante "b" la función real
f(x) = 2bx³ + 2x² − 3 tiene un extremo relativo en x = -1/6
a) b=4
b) b=-4
c) c=-6
d) b=6
e) b=-3
Let f(x) = 5 sin(x). Describe the graph of each of the following in terms of the graph off.
1. g(x) = 5 sin(x) + 4
2. h(x) = 5 sin(x + 1)
3. k(x) = 20 sin(x) + 10
4. m(x) = 5 sin(4x - 1)
I
The graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units,The graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit,The graph of k(x) is 20 and every y-coordinate is increased by 10 units and the graph of m(x) is horizontally squeezed.
To describe the graphs of the given functions, let's first analyze the effects of the transformations applied to the original function f(x) = 5 sin(x).
1. g(x) = 5 sin(x) + 4:
The function g(x) is obtained by vertically shifting the graph of f(x) by 4 units upward. This means that the graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units.
2. h(x) = 5 sin(x + 1):
The function h(x) is obtained by horizontally shifting the graph of f(x) to the left by 1 unit. This means that the graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit. The period of the function remains the same.
3. k(x) = 20 sin(x) + 10:
The function k(x) is obtained by vertically stretching the graph of f(x) by a factor of 20 and then shifting it 10 units upward. This means that the amplitude of the graph of k(x) is 20 (compared to the amplitude of 5 in f(x)), and every y-coordinate is increased by 10 units.
4. m(x) = 5 sin(4x - 1):
The function m(x) is obtained by compressing the graph of f(x) horizontally by a factor of 4, reflecting it across the y-axis, and shifting it 1 unit to the right. This means that the period of m(x) is 1/4 of the period of f(x), and the graph is horizontally squeezed. The reflection across the y-axis means that the graph of m(x) will be inverted compared to f(x). The amplitude remains the same.
Remember that the graph of the original function f(x) = 5 sin(x) represents a sine wave with an amplitude of 5 and a period of 2π. Applying the transformations described above will modify the position, scale, and shape of the graph, resulting in the respective graphs for each function g(x), h(x), k(x), and m(x).
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Can u find “V”
XXX* YV=••••+666=799Y
The letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.
How to simplify equations?The equation can be simplified to XXX × YV=1335.
If both sides of the equation are divided by 3, X × YV = 445.
If now all the X's is replaced with 5's, 5 × YV = 445.
This gives the following equation:
5 × YV = 445
Now multiply both sides of the equation by Y, to get 5Y = 445.
This gives us the following equation:
5Y = 445
Finally, divide both sides of the equation by 5, to get Y=89.
Therefore, the letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.
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What is this expression in simplified form?
✔-1, 728
O A. -12
OB. -36
O C.
-42
OD. -576
This proportion can be solved to find the unknown length, x
, in the smaller triangle.
Answer:
x=3
Step-by-step explanation:
1.25/5.00=2/8=x/12=1/4
12=x×4
x=12÷4
x=3
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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A multiple choice question has five Anne’ answer options of which two options are correct what is the probability of randomly choosing the correct pair of answer options
Answer:
1/10
Step-by-step explanation:
2/5 * 1/4 = 2/20 = 1/10
2 right answers, 5 possible choices
Select one right choice = 2/5
After selecting one right choice, there are 4 possible choices with one more right choice left.
Select another right choice = 1/4
What are the zeros of the function defined by y = x2 + 6x + 5?