Coordinate Proof!
Given: Isosceles ∆ABC; M is the midpoint of AC-.
Prove: area ∆ABM = area ∆CBM
Proof
AM = √(x₂ − x₁)² + (y₂-y₁)²
= √(4-0)² + (0-0)²
= √4² = _
BM = √(x2-x₁)² + (1₂-y₁)²
= √(4-4)² + (6-0)2
= √6² = _
AM- ≅ CM- ____
AM = CM ____
CM = 4. Subst.
area ∆ABM
A = 1/2 bh
= 1/2 ___
= ___
area ∆CBM
A = 1/2 bh
= 1/2 ___
= ___
Therefore: Area ∆ABM = area ∆CBM by ___
Answers
The completed calculation with regards to the area of the congruent triangles can be presented as follows;
The distance formula indicates;
AM = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, we get;
AM = √((4 - 0)² + (0 - 0)²) = √(4²)
AM = √(4²) = 4
BM = √((x₂ - x₁)² + (y₂ - y₁)²)
BM = √((4 - 4)² + (6 - 0)²) = √(6²)
BM = √(6²) = 6
AM ≅ CM Definition of the midpoint of AC
AM = CM Definition of congruent segments
CM = 4 Substitution property
Area ΔABM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Area ΔCBM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Therefore Area ΔABM = area ΔCBM by congruence
What are congruent triangles?Triangles are congruent if they have the same size and shape.
The details of the reasons for the calculation steps and values are presented as follows;
Definition of midpoint of a segment
The midpoint of a line segment is the point that divides the segment into two parts of the same length
Definition of congruence?
Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement
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Related Questions
PLEASE ANSWER TODAY FAST
New homeowners hire a painter to paint rooms in their house. The painter pays $100 for supplies and charges the homeowners $25 for each room they want painted.
Which of the following graphs shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints?
Answers
Answer:
I can explain how the relationship between the amount of money the painter earns and the number of rooms he paints can be represented in a graph.
The amount of money the painter earns depends on the number of rooms he paints. The painter charges $25 for each room he paints, so the amount of money he earns can be calculated by multiplying the number of rooms painted by $25. However, he also has to pay $100 for supplies regardless of the number of rooms painted.
Therefore, the relationship between the amount of money the painter earns and the number of rooms painted is a linear function, where the y-intercept (when no rooms are painted) is -$100 and the slope (how much he earns per room painted) is $25. This relationship can be represented in a graph as a straight line with a positive slope that intersects the y-axis at -$100.
I hope this helps
Option C is the correct graph for the given condition.
What is the significant use of graphs in real life?Graphs are a not unusual place technique to visually illustrate relationships withinside the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately withinside the textual content and in much less space.
Let's assume that the number of rooms painted is represented by the variable "x". The cost of painting x rooms can be calculated using the following equation:
Cost = 100 + 25x
The $100 is a fixed cost for the supplies, and the $25 is the cost per room painted. The variable "x" represents the number of rooms painted, which can vary.
We can draw a graph of this equation by plotting points for different values of "x" and connecting them with a straight line. For example:
If x = 0, then Cost = 100 + 25(0) = $100, which is the y-intercept (where the line intersects the y-axis).If x = 1, then Cost = 100 + 25(1) = $125, which gives us the point (1, 125) on the line.If x = 2, then Cost = 100 + 25(2) = $150, which gives us the point (2, 150) on the line.If x = 3, then Cost = 100 + 25(3) = $175, which gives us the point (3, 175) on the line.We can continue this process to find additional points, and then plot them on a coordinate grid. Here's what the graph might look like:
The line passes through the point (0, 100), which is the y-intercept. As we move to the right along the x-axis (increasing the number of rooms painted), the cost increases at a constant rate of $25 per room. The slope of the line is therefore 25.
The equation for the line is in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. In this case, we have:
Cost = 25x + 100
This equation gives us the cost of painting x rooms, where x can be any non-negative integer.
The correct graph is option C
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Solve the following for θ, in radians, where 0≤θ<2π.
3cos2(θ)+7cos(θ)−8=0
Select all that apply:
0.3
0.74
0.57
1.98
1.65
5.71
Answers
Answer:correct answer is 0.57
5.71
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
3u^2 + 7u - 8 = 0
Now we can factor the quadratic:
(3u - 1)(u + 8) = 0
Therefore, either:
3cos(θ) - 1 = 0
cos(θ) = 1/3
or:
cos(θ) + 8 = 0
cos(θ) = -8 (not possible, since cos(θ) is between -1 and 1)
So, we have cos(θ) = 1/3. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:
θ = arccos(1/3)
Using a calculator, we find:
θ ≈ 1.2309 or θ ≈ 5.1102
Therefore, in radians, the solutions for θ are approximately:
1.2309 (which is less than 2π)
5.1102 (which is greater than 2π)
So the only answer that satisfies 0 ≤ θ < 2π is:
1.2309 (rounded to four decimal places)
Therefore, the answer is:
ASAPPPPPP 100 POINTS GUYS CMON LAST HW QUESTION
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 6 feet and a height of 9 feet. Container B has a radius of 5 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
To the nearest tenth, what is the percent of Container A that is full after the pumping is complete?
Answers
Answer:
The nearest tenth, Container A is about 46.3% full after the pumping is complete.
Step-by-step explanation:
To solve this problem, we need to find the volume of water in Container A and compare it to the volume of Container B.
The volume of water in Container A can be found using the formula for the volume of a cylinder:
V_A = πr^2h = π(6^2)(9) = 324π cubic feet
The volume of Container B can also be found using the same formula:
V_B = πr^2h = π(5^2)(12) = 300π cubic feet
After the water is pumped from Container A to Container B, Container B will be completely full, which means it will contain 300π cubic feet of water. To find the height of the water level in Container A, we need to find the height of the cylinder that would contain 300π cubic feet if it had a radius of 6 feet:
V_A' = πr^2h' = 300π
h' = 300/(36π) = 25/6 feet
So the height of the water level in Container A is 25/6 feet. Since the height of Container A is 9 feet, the percent of Container A that is full is:
(25/6) / 9 * 100% ≈ 46.3%
Therefore, to the nearest tenth, Container A is about 46.3% full after the pumping is complete.
Help 100 pts. I don’t get it
Answers
The area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.
Given that, the dimensions of rectangular flower bed are length= 6 feet and width = 4 feet.
Dimensions of large rectangle are Length = 6+2x and width = 4+2x
Now, area of large rectangle = (6+2x)×(4+2x)
= 24+8x+12x+4x²
Area of a rectangular flower bed = 6×4
= 24 square feet
Tulips and Daisy have same area to plant
So, the equation is 24+20x+4x²=24
4x²+20x=0
Therefore, the area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.
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Analyze the diagram below and complete the instructions that follow.
W
X14
Determine if the proportion is true. If it is not true, correct the error.
A true
B.
Z
Mark this and return
V
X
Save and Exit
Next
Answers
Determining if the proportion is true. If is not true and correcting the error v/x = x/v+w is: B. false, it should be w/x = x/v+w.
What is the proportion?In order for us to know whether the proportion v/x = x/v+w is true or not we need to cross multiply and simplify both sides:
v(x + v + w) = x^2
Expand the left-hand side:
vx + v^2 + vw = x^2
Subtract vx from both sides:
v^2 + vw = x^2 - vx
Factor out v on the left-hand side and x on the right-hand side:
v(v + w) = x(x - v)
Divide both sides by (v + w)x:
v/(v + w) = x/(x - v)
Therefore the correct option is B.
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10 points. please awnser
Answers
The angle measures for the triangles are given as follows:
m < G = 105º.m < H = 55º.m < I = 20º.What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle Z is given as follows:
m < Z + 20 + 105 = 180
m < Z + 125 = 180
m < Z = 55º.
Hence the measures are given as follows:
m < G = 105º. -> equivalent to X.m < H = 55º. -> equivalent to Z.m < I = 20º. -> equivalent to I.More can be learned about similar triangles at brainly.com/question/14285697
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I still have no clue what the teacher wants us to do
Answers
The objective of the above task to to check your ability to compute various parts of a parallelogram given various inputs. See the solution attached.
What is parallelogram?A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.
Note that the corners angles (AB,C,D)are derived as follows;
A = C = θ
B = D = Φ
A + B = 180° = π radians
for a parallelogram that is not a rectangle or square,
0 < A< 90° (0 < A < π/2),
90° < B < 180° (π/2 < B < π)
The diagonals are derived as follows:
Diagonals: d, c
d = √( a² + b² - 2ab cos(A) ) = √( a² + b² + 2ab cos(B) )
c = √( a² + b² + 2ab cos(A) ) = √( a² + b² - 2ab cos(B) )
d² + c² = 2(a² + b²)
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Suppose you draw 6 samples of marbles from a jar and get these results for red marbles. 26,25,25,30,28,28 What is the mean number of red marbles drawn?
Answers
Answer:
Mean-27
Step-by-step explanation:
Add all of the numbers and it equals 162
Then divide 162 by the amount of numbers presented.
Since there are 6 numbers listed we divide by 6
162/6=27
find the number of lamps should be manufactured annually
Answers
The solution is :Total manufacturing cost per Lamp is $15.10 per lamp.
Explanation:
Cost per part of Material handling = $3000/6000 parts
Cost per part of Material handling = $0.50 per part
Assembling per hour = $7200/3000
Assembling per hour = $2.40 per hour
Packaging per lamp = $4000/2000
Packaging per lamp = $2 per lamp
Total manufacturing cost per Lamp = $8 + (9*$0.50) + ($2.40/4) + $2
Total manufacturing cost per Lamp = $8 + $4.5 + $0.6 + $2
Total manufacturing cost per Lamp = $15.10 per lamp
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complete question:
Traditions Home Accessories Company manufactures decorative lamps using an activity-based costing system to allocate all manufacturing conversion costs. The following information is provided for the month of June: Activity Estimated Indirect Activity Costs Allocation Base Estimated Quantity of Allocation Base Materials handling $3,000 Number of parts 6,000 parts Assembling $7,200 Number of hours 3,000 hours Packaging $4,000 Number of lamps 2,000 lamps Four lamps can be assembled in 1 hour. Each lamp consists of 9 parts. The total direct materials cost per lamp is $8.00. What is the total manufacturing cost per lamp
The histogram shows data collected about the number of passengers using city bus transportation at a specific time of day. A histogram titled City Bus Transportation. The x-axis is labeled Number Of Passengers and has intervals of 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 9. There is a shaded bar for 1 to 10 that stops at 2, for 11 to 20 that stops at 4, for 21 to 30 that stops at 5, for 31 to 40 that stops at 6, and for 42 to 50 that stops at 3. Which of the following data sets best represents what is displayed in the histogram? (4, 5, 7, 8, 10, 12, 13, 15, 18, 21, 23, 28, 32, 34, 36, 40, 41, 41, 42, 42) (4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42) (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42) (4, 6, 11, 12, 16, 18, 21, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 41, 41, 42)
Answers
The data set that best describes the histogram is
(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
We have,
The histogram shows that there are different intervals on the x-axis, and for each interval, there is a corresponding frequency on the y-axis.
From the given data, we can see that there are more passengers in the 11 to 20 interval than in the 1 to 10 interval, and so on.
Looking at the answer choices, we need to choose the data set that matches the histogram.
The first step is to check if the data set has the same range as the histogram.
The histogram has intervals from 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50.
Now,
The first answer choice has numbers less than 1 and greater than 50, so it cannot be the correct choice.
The second answer choice has a range from 4 to 42, which matches the histogram.
We can check if the frequencies in the data set match the heights of the bars in the histogram.
For example, the histogram has a bar for the 11 to 20 interval that stops at 4, which means there are 4 passengers in that interval.
The second data set has 4 passengers in the 11 to 20 interval, so it matches.
We can do the same for the other intervals and find that the second data set matches the histogram.
Therefore,
The data set that best describes the histogram is
(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
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A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
Answers
The frequency table is plotted and the order for the restaurant is given
Given data ,
A restaurant had 160 lunch customers last weekend.
90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both.
There were 45 customers who ordered seltzer and a veggie sandwich.
Eleven more people ordered a veggie sandwich than a tuna sandwich.
On simplifying the equation , we get
A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2
D=11
Thus C = 22
F = 45 + C
F = 45 + 22
F = 22
G = A + D = 18
Chicken Veggie Tuna Total
Seltzer 38 45 7 90
Iced Tea B 22 11 70
Total 75 67 18 160
Hence , the frequency is completed
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The complete question is attached below :
A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
click on the region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2
Answers
Answer: The region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2 is the area bounded by the two lines and the x-axis.
Step-by-step explanation:
Michael solved the given problem. Determine whether Michael's work is correct. If not, which step is incorrect?
Responses
A Step 1
B Step 4
C Step 3
D Step 2
Answers
Based on the information, the incorrect step is C. step 3.
How to calculate the valueStep 1: 4(3x – 3y = 6) –3(4x – 7y = 2)
Step 2: 12x – 12y = 24 –12x + 21y = –6
Step 3: 9y = 18
Step 4: y equals 1 over 2
Correct calculation:
3x – 3y = 6 (1)
4x – 7y = 2 (2)
make x the subject in ....(1)
3x - 3y = 6
3x = 6 + 3y
x = 6 + 3y/ 3
x = 2 + y
substitute x = 2 + y into (2)
4x – 7y = 2 (2)
4(2 + y) - 7y = 2
8 + 4y - 7y = 2
8 - 3y = 2
8 + 2 = -3y
10 = -3y
y = 10/-3
y = -3 1/3
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Michael solved the system of linear equations and provided the solution. 3x – 3y = 6 4x – 7y = 2 Step 1 4(3x – 3y = 6) –3(4x – 7y = 2) Step 2 12x – 12y = 24 –12x + 21y = –6 Step 3 9y = 18 Step 4 y equals 1 over 2 In which step did Michael show his first error? Step 2 Step 3 Step 4
PLEASE HELP THANK UUUUU
Answers
The ratio in simplest form is 1:4, the correct option is C.
We are given that;
The options A. 2/3 B. 3/4 C. 1/4 D. 4/1
Now,
The letters D and O are used 2 times and 4 times respectively in the words “RATIOS AND PROPORTIONS”. So we can write the ratio as 2:4.
The GCF of 2 and 4 is 2, since 2 is the largest number that can divide both 2 and 4 without leaving a remainder.
To simplify the ratio, we divide both terms by 2:
2:4 = (2/2):(4/2) = 1:2
Therefore, by the ratio the answer will be 1/4.
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5. A group of students were asked whether they play a sport and whether
they like physical education class. The results are in the table.
Like Physical Education
Do Not Like Physical
Education
A 28%
B. 16%
c. 15%
Play a Sport
150
To the nearest percent, of students who play a sport, what percent do not
like physical education?
D. 7%
Do Not Play a Sport
Answers
Answer: 7
Step-by-step explanation:
The percentage of students who play a sport but do not like physical education = 16%
The correct answer is an option (B)
The complete two way frequency table for given situation would be,
Play a Sport Do not Play a Sport Total
Like Physical Education 150 72 222
Do Not Like Physical Education 28 164 192
Total 178 236 414
Now we find the percentage of students who play a sport, and do not like physical education.
The total number of students who play sport.
n = 178
And the number of students who play a sport but do not like physical education are 28.
Using percentage formula, the required percentgae would be,
P = 28/178 × 100
P = 15.73%
P ≈ 16%
Therefore, the correct answer is an option (B)
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Find the complete question below.
Please help !!!!!!!!!!!!!!!!!!!
Answers
a) Latonya is correct, as the scale factor of the dilation is of 12.8/4.8.
b) The scale factor was obtained dividing the side length on the dilated figure by the equivalent side length of the original figure.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The ratios for the scale factor are given as follows:
12.8/4.8 = 7.2/2.7 = 4.8/1.8 = 4/1.5 = 8/3.
8/3 as 4 x 2 = 8 and 1.5 x 2 = 3.
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Find the x - and y -intercepts of the following equation: 3x-2y=5 ?
Answers
The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).
The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.
Given the equation: 3x - 2y = 5
Setting y = 0, we get;
3x - 2(0) = 5
3x = 5
x = 5/3
So, the x-intercept is (5/3, 0).
The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.
Setting x = 0, we get;
3(0) - 2y = 5
-2y = 5
y = -5/2
So, the y-intercept is (0, -5/2).
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Rearrange the formula = 2√
3
and make ‘’ the subject.
Answers
Making x as a subject, we get equation as x=(y+2)/5.
The given equation is y=5x-2.
To make x as the subject
y+2=5x
x=(y+2)/5
Therefore, making x as a subject, we get equation as x=(y+2)/5.
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"Your question is incomplete, probably the complete question/missing part is:"
Rearrange the formula to make x the subject y=5x-2.
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $24 per linear foot to install and the farmer is not willing to spend more than $6000, find the dimensions for the plot that would enclose the most area. Leave in terms of (width, length): (,)
Answers
The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).
We have,
Let's assume that the barn wall is located on the south side of the rectangular plot, and the fencing is required on the remaining three sides (east, north, and west).
Let's denote the width of the plot as x and the length of the plot as y.
Then, the length of fencing required can be expressed as:
L = x + y + x/2
where x/2 is the length of the shared fencing with the neighbor.
The cost of fencing can be expressed as:
C = 24L
Substituting the value of L, we get:
C = 24(x + y + x/2)
Since the farmer is not willing to spend more than $6000, we have:
24(x + y + x/2) ≤ 6000
Simplifying this inequality, we get:
3x + 4y ≤ 500
Now, we need to maximize the area of the rectangular plot, which is given by:
A = xy
Using the inequality constraint, we can express y in terms of x as:
y ≤ (500 - 3x)/4
Substituting this value of y in the expression for A, we get:
A = x((500 - 3x)/4)
Simplifying this expression, we get:
A = (125/4)x - (3/4)x^2
To find the value of x that maximizes A, we can take the derivative of A with respect to x and set it equal to zero:
dA/dx = 125/4 - (3/2)x = 0
Solving for x, we get:
x = 125/6
Substituting this value of x in the expression for y, we get:
y = (500 - 3(125/6))/4 = 125/3
Therefore,
The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).
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(Time limit) Give me the domain and range and tell me if the graph is a function or not.
Answers
Yes, The given graph is shows a function.
And, Range = {y | y ≥ - 2}
Domain = (- ∞ , ∞)
We have to given that;
the graph is shown in image.
Now, We can check the graph is a function or not by vertical line test.
Hence, By vertical line test it's shows the function as it cut at one point for each value of y.
Thus, The given graph is shows a function.
Since, The set of all inputs of the function is called Domain of set.
Hence, We get;
Domain = (- ∞ , ∞)
And, The set of all outputs of the function is called range of set.
Hence, We get;
Range = {y | y ≥ - 2}
Thus, Yes, The given graph is shows a function.
And, Range = {y | y ≥ - 2}
Domain = (- ∞ , ∞)
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Every number has only one quality: its distance from zero.
O A. True
OB. False
Answers
Answer:
True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Every number has multiple qualities beyond its distance from zero. Some of the qualities of a number include its sign (positive or negative), its magnitude (Absolute Value), its parity (whether it is even or odd), and its relationship to other numbers (greater than, less than, or equal to). Additionally, numbers can have properties such as being prime or composite, rational or irrational, and real or complex. Therefore, a number is characterized by more than just its distance from zero.
Let f be a function defined on binary strings as follows: If u is a string such that u = abc where la| = |b| = |c| then f(u) = a. %3D For example, if u = 101101011, then f(u) = 101. Which of the following statements are true? a. The cardinality of the set {u | f(u) = u} is 1. b.f is a total function. c. If Jul = 24, then f(f(u) is not defined. d. F is an injection. e. The range of f is the set of all binary strings. f. fis onto the set of all binary strings.
Answers
f is onto the set of all binary strings:
This statement is false for the same reason as (e). The range of f is limited to a subset of all binary strings.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
a. The cardinality of the set {u | f(u) = u} is 1:
This statement is true because f(u) returns only the first third of the input string u. Therefore, if f(u) = u, then the second and third thirds of the string u must be empty, and hence u must consist entirely of the first third, which means there can be only one such string.
b. f is a total function:
This statement is false because not all binary strings can be decomposed into three parts with the described property. For instance, a binary string of length 5 cannot be decomposed in this way.
c. If |u| = 24, then f(f(u)) is not defined:
This statement is false. If |u| = 24, then u can be decomposed into three parts with 8 bits in each part. Therefore, f(u) will return the first 8 bits of u, which can be decomposed into three parts with 2, 3, and 3 bits, respectively. Therefore, f(f(u)) will return the first 2 bits of the first third of u, which is well-defined.
d. f is an injection:
This statement is false. Since f only returns the first third of its input, there can be multiple inputs that yield the same output.
e. The range of f is the set of all binary strings:
This statement is false. The range of f only consists of binary strings that are the first third of some input string that can be decomposed as described.
f. f is onto the set of all binary strings:
This statement is false for the same reason as (e). The range of f is limited to a subset of all binary strings.
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Need problem please please
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The formula for the nth term of the geometric sequence is given as follows:
[tex]a_n = 7(-3)^{n - 1}[/tex]
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The formula for the nth term of the sequence is given as follows:
[tex]a_n = a_1q^{n-1}[/tex]
The first term of the sequence is given as follows:
[tex]a_1 = 7[/tex]
Each term is the previous term multiplied by -3, hence the common ratio is given as follows:
q = -3.
Thus the formula for the sequence is given as follows:
[tex]a_n = 7(-3)^{n - 1}[/tex]
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A teacher was interested in the cafeteria food that students preferred in a particular school. She gathered data from a random sample of 200 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for her data?
Stem-and-leaf plot
Line plot
Box plot
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Answer:
A stem-and-leaf plot is a graphical representation of a dataset where the numbers are separated into two parts: the stem (the leftmost digit or digits) and the leaf (the rightmost digit). The stem values are listed vertically and the corresponding leaf values are listed to the right of the stem in a row. This type of plot allows for quick and easy data analysis, as it shows the distribution of the data and provides information about the frequency and range of the values. It is particularly useful for smaller datasets and can be easily constructed by hand or with software.
Rectangle BCDE has vertices B(-9,-4), C(-6,-8), D(10,4), and E(7,8). What is the area of BCDE?
Answers
Answer:
To find the area of the rectangle BCDE, we can use the formula:
Area = length x width
First, we need to find the length and width of the rectangle.
The length of the rectangle is the distance between points B and C, which can be calculated using the distance formula:
distance BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-6 - (-9))^2 + (-8 - (-4))^2)
= sqrt(3^2 + (-4)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5
The width of the rectangle is the distance between points C and D:
distance CD = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((10 - (-6))^2 + (4 - (-8))^2)
= sqrt(16^2 + 12^2)
= sqrt(256 + 144)
= sqrt(400)
= 20
Since BCDE is a rectangle, the length and width are perpendicular. Therefore, the area of the rectangle can be calculated by multiplying the length and width:
Area = length x width = 5 x 20 = 100
Therefore, the area of BCDE is 100 square units.
Step-by-step explanation:
A college student takes the same number of credits each semester. Before beginning college, the student had some credits earned while in high school. After 2 semesters, the student had 39 credits, and after 5 semesters, the student had 75 credits.
If C(t) is the number of credits after t semesters, write an equation that represents this situation.
Provide your answer below:
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The equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.
Let x be the number of credits the student had before starting college, and let y be the number of credits the student takes each semester. We can use this information to write an equation that represents the number of credits the student has earned after t semesters.
After 2 semesters, the student had 39 credits, which means the student earned 2y + x credits in those two semesters. Similarly, after 5 semesters, the student had 75 credits, which means the student earned 5y + x credits in those five semesters.
Using this information, we can write the following equation:
C(t) = yt + x
where C(t) represents the number of credits the student has earned after t semesters.
We know that C(2) = 2y + x = 39 and C(5) = 5y + x = 75. We can use these two equations to solve for x and y:
2y + x = 39
5y + x = 75
Subtracting the first equation from the second equation gives:
3y = 36
Therefore, y = 12, which means the student takes 12 credits each semester. Substituting y = 12 into either of the two equations above gives x = 15, which means the student had 15 credits before starting college.
Thus, the equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.
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please help for question 3
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Reflecting the triangle Q over the line y = 1 would map it onto triangle T
Reflecting the triangle PReflection over line x = 1
This means that we draw a vertical line that passes through x = 1
And then we create a triangle that is a mirror of the triangle P across the reflection line
The reflection of the triangle is attached
Reflection over line y = 2
This means that we draw a vertical line that passes through y = 2
As done in part (a), we then create a triangle that is a mirror of the triangle P across the reflection line
The reflection of the triangle is also attached
Description of the transformationUsing the same transformation rule above;
A reflection over the line y = 1 would map the triangle Q onto triangle T
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apllo traveld 48 leauges in 3 day then he tripled his rate how long would it take him to travel 336 leagues at this new speed
Answers
48 leagues / 3 days = 16 leagues per day
Next, we know that Apollo tripled his rate, which means his new speed is:
16 leagues per day x 3 = 48 leagues per day
To find out how long it will take him to travel 336 leagues at this new speed, we can use the formula:
time = distance / speed
In this case, the distance is 336 leagues, and the speed is 48 leagues per day. So we have:
time = 336 leagues / 48 leagues per day = 7 days
Therefore, it would take Apollo 7 days to travel 336 leagues at his new speed.
For each of the following functions, match the function to the graph.
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The function that matches the above graph is Option C - F(x) = (1/2)^x - 3
What are the properties ofthe function ?
Here are the properties of the function are given as follows
Domain - The domain of the function is all real numbers, as there are no restrictions on the input value x .
Range - the range of the function is (-3, infinity), as the output values approach but never reach - 3 as x approaches negative infinity, and the output values can be arbitrarily large as x approaches infinity.
x -intercept - The x-intercept of the function is (log(2, 3), 0), as F(log(2, 3)) = [( 1/2)^ (log(2, 3) ) ] - 3 = 0.
y-intercept - The y-intercept of the function is (0, -2.5), as F(0) = [(1/2)^0] - 3 = -2.5.
Asymptotes - The horizontal asymptote of the function is y = -3, as the output values approach but never reach -3 as x approaches infinity. There are no vertical asymptotes.
Decreasing function - The function is a decreasing function, as the output values decrease as x increases.
Continuous function - The function is continuous for all real numbers.
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PLEASE HELP (WILL GIVE BRAINLIEST)
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Answer:d
Step-by-step explanation: