The line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.
Describe Graph?A graph is a mathematical representation of a set of objects, called vertices or nodes, and the connections between them, called edges or arcs. Graphs are commonly used to model relationships between entities in various fields such as computer science, mathematics, physics, social sciences, and many others.
To determine the line that the angle has been reflected across, we need to find the line of reflection, which is the perpendicular bisector of the segment joining each point and its corresponding image.
We can start by finding the midpoint of the segment joining A and A', which is the point that is equidistant from these two points and lies on the line of reflection. The midpoint of AA' is:
Midpoint of AA' = ((x-coordinate of A + x-coordinate of A')/2, (y-coordinate of A + y-coordinate of A')/2)
Midpoint of AA' = ((4 + (-5))/2, (5 + (-4))/2)
Midpoint of AA' = (-1/2, 1/2)
Next, we can find the midpoint of the segment joining B and B':
Midpoint of BB' = ((x-coordinate of B + x-coordinate of B')/2, (y-coordinate of B + y-coordinate of B')/2)
Midpoint of BB' = ((1 + (-2))/2, (2 + (-1))/2)
Midpoint of BB' = (-1/2, 1/2)
We can see that the midpoint of AA' and the midpoint of BB' are the same point, which means that the line joining these midpoints is the perpendicular bisector of both segments, and therefore the line of reflection.
So, the line of reflection is the line passing through the points (-1/2, 1/2) and (-2, -1), which can be found using the slope formula:
slope of line of reflection = (y2 - y1) / (x2 - x1)
slope of line of reflection = (-1 - 1/2) / (-2 - (-1/2))
slope of line of reflection = (-3/2) / (-3/2)
slope of line of reflection = 1
We now have the slope of the line of reflection, and we can find its equation by using the point-slope form:
y - y1 = m(x - x1)
Using the point (-1/2, 1/2) and the slope 1, we get:
y - 1/2 = 1(x + 1/2)
Simplifying, we get:
y = x + 1
Therefore, the line that the angle has been reflected across is the line y = x + 1. This line passes through the midpoint of each segment joining a point and its image, and is perpendicular to these segments.
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Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and calculates the arc length to be inches. Whose paper is larger? Explain or show your reasoning.
A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The arc length of radius 6 inches is equal to,
Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches
The area of the circular paper = πr² = π×6×6 = 113.097²
The area of the square with a side of 6 inches = 36 in²
Therefore, the area of the circular paper is more than the area of the square.
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A3ft board weighs 2 pounds. How much
does a 12 ft board weigh?
Answer:
8 pounds
Step-by-step explanation:
3 ft board = 2lb
12 ft board is 4 times more so
2x4 = 8 lb
A cable extends from the top of a radio tower to a point 360 feet from the base of the tower. If the
cable is 850 feet long, how tall is the tower?
Step-by-step explanation:
we have a right-angled triangle :
the Hypotenuse (baseline opposite of the 90° angle) is the 850 ft cable from the top of the tower down to the point on the ground 360 ft away from the tower.
then the ground distance (360 ft) and the height of the tower are the 2 legs.
so, we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse.
in our case
850² = 360² + height²
height² = 850² - 360² = 592,900
height = 770 ft
the tower is 770 ft tall.
Answer:
770 feet
Step-by-step explanation:
Given
Cable = 850 feet longExtends from radio tower to a point 360 feet from the base of a towerSolving
Using the Pythagorean Theorem, we can find the height(distance from base)² + (height)² = (length of cable)²height² = (850)² - (360)²height² = 722,500 - 129,600height² = 592,900height = √592,900height = 770 feetPlease Help I don't understand at all !!!!!!! I'll give 50 brainly points
Students collected data and created an equation to model the spread of a winter cold among the students, teachers, and other staff. They decided this was best represented by the exponential function C(d) = 1*3d where d is the time in days since the cold began to spread.
How many people initially had the cold? _______ people
How many people would have the cold after 2 days? ______ people
Answer:
0 People initially had the cold.
6 People will have it after 2 days.
Step-by-step explanation:
To find out how many people had it initially, plug 0 in for x (implying 0 days later.)
C= 1*3(0)
C= 1*0
C=0
Nobody had the cold initially.
To find out how many people had it after 2 days, plug 2 in for x. (implying 2 days later.)
C= 1*3(2)
C= 1*6
C=6
Therefore 6 people had the cold after 2 days.
I hope this helps!
Regular expressions - recognizers of words in a language 1. Σ={a,b,c} where L={ all words in which a 's must follow the symbol b} 2. Σ={a,b,c} where L={ all words that have at least one occurrence of the string abc in them } Write a grammar for the following - grammars are generators of words in a language 3. Σ={a,b} where L={ all words that start with c and end with c and have only a's and b
′
s in between 4. Σ={a,b,c} where L={ all words using symbols a,b,c in which every b follows the symbol a} Is the following grammar ambiguous? Prove your statement. Why do we not want an ambiguous grammar for a programming language?
1. The regular expression for the language L={ all words in which a's must follow the symbol b} is \(^(b*(ab*)*)*a*$\).
2. The regular expression for the language L={ all words that have at least one occurrence of the string abc in them } is .*abc.*.
3. The grammar for the language L={ all words that start with c and end with c and have only a's and b's in between} is S -> cXc, X -> ε | aX | bX.
4. The grammar for the language L={ all words using symbols a,b,c in which every b follows the symbol a} is S -> ε | aSb | aA | c, A -> ε | aAb | aA | c. The grammar is ambiguous.
1. The regular expression \(^(b*(ab*)*)*a*$\) specifies that the word should start and end with any number of 'b' and 'a' in any order, and only 'a' should follow 'b'.
2. The regular expression .*abc.* matches any word that contains the substring 'abc' at least once.
3. The grammar S -> cXc, X -> ε | aX | bX generates words that start with 'c', followed by a sequence of 'a' or 'b', and ends with 'c'. Only 'a' and 'b' symbols are allowed in between.
4. The grammar S -> ε | aSb | aA | c, A -> ε | aAb | aA | c allows for words that can have multiple occurrences of 'a' followed by 'b', 'a' followed by 'a' or 'b', or just the symbol 'c'. This grammar is ambiguous because a single sentence can have multiple parse trees or interpretations.
An ambiguous grammar in a programming language can lead to different interpretations of code, resulting in confusion, inconsistencies, and difficulties in parsing and understanding the code.
Unintended or unexpected behavior can arise due to ambiguity, making it challenging to write reliable and predictable programs. To ensure clarity, correctness, and ease of interpretation, it is crucial to have an unambiguous grammar for a programming language.
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Given hexagon LMNOPQ is congruent to hexagon L'M'N'O'P'Q'. What is the measure of OP?
6 in
7 in
45 in
51 in
Answer:
51in
Step-by-step explanation:
Just set the equations of line OP and line O'P' equal to one another, then solve for x.
ie: 3(2x+3)=(8x-5)
To solve for x, distribute first. Then, subtract 6x from each side. Then, add 5 to each side.
ie: 6x+9=8x-5
ie: 14=2x
Now divide by 2.
ie: 7=x
Now that you have your x value, plug it back into one of the equations and solve for the measure of line OP. To check you answer, plug 7 for x into the equation where they are set equal, then solve them both and if the end result is true (51=51) it is correct.
Paul ate 42 out of the 68 skittles in the bag.
How would this ratio be expressed in decimal
form?
9514 1404 393
Answer:
\(0.6\overline{1764705882352941}\)
Step-by-step explanation:
The decimal form of a ratio is found by dividing the numerator by the denominator. You will find this reduces to the fraction 21/34, which has a 16-digit repeat when expressed as a decimal.
Using a calculator with suitable precision, you can see all of the repeating digits:
\(0.6\overline{1764705882352941}\)
Evaluate the expression when a=6 and b=4. b - 3a
-14 is the value of the expression b - 3a at a =6 and b = 4.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression b - 3a
For this expression given,
a = 6 and b = 4
Thus the value of expression at given values
=> b - 3a
=> 4 - 3 * 6
=>4 - 18
=> -14
Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.
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4 4/5 x 3 2/6 I don’t understand this pls help
Answer:
change to improper fraction
24/5 × 20/6=16 (you cross multiply)
Answer:
= 46 14/15
Step-by-step explanation:
Find the greatest common factor of the numerator and denominator:Factor out and cancel the greatest common factor:Multiply the fractions:Simplify the arithmetic:Simplify the arithmetic
Hope You Enjoy !
Write as an algebraic expression.
14 fewer than the product of 3 and a number
Answer:
3 x X - 14
Step-by-step explanation:
Is your algebra expression.
Answer:
3x-14
Step-by-step explanation:
Product of 3 and number is 3*x
For " 14 fewer than.." we simply subtract 14.
So we get 3x-14
Please help me I only have 3 days to get it done and if I don’t I won’t pass
(x, 7) and (-7, 4); slope: 1
Answer: x= -4
Step-by-step explanation: slope = (y2-y1)/(x2-x1).
(4-7)/(-7-x)
-3/-7-x=1
Multiply both sides by -7-x
-3=-7-x
Add 7 to both sides
4=-x so x = -4
what is the maximum of the sinusoidal function? enter your answer in the box.
Answer:
Step-by-step explanation:
B
The numbers of blue and green beads Emma uses to make five different pieces of jewelry are recorded below. Which of the following equations relate to the number of green beads, G, to the number of blue beads, b?
Answer:
a
Step-by-step explanation:
follow the proportions
Answer:
A
Step-by-step explanation:
Starting with the graph of f (I) = 4", write the equation of the graph that results from a. shifting f(3 ) 1 units
upward. b. reflecting f(z) about the y-axis. y c. shifting f(x) 6 units left. y =
The graph of f(x) = 4x is a parabola that opens upwards. Shifting the graph 1 unit upwards, reflecting the graph about the y-axis, and shifting the graph 6 units left will all result in new graphs that are transformations of the original graph. Therefore:
a. Shifting f(x) 1 unit upward: y = 4x + 1
b. Reflecting f(x) about the y-axis: y = -4x
c. Shifting f(x) 6 units left: y = 4(x - 6)
The equations of the graphs that result from the given transformations:
a. Shifting f(x) 1 unit upward.
The graph of f(x) = 4x is a parabola that opens upwards. Shifting the graph 1 unit upwards means that all the points on the graph are moved 1 unit upwards. The new equation of the graph is:
y = 4x + 1
b. Reflecting f(x) about the y-axis.
Reflecting the graph of f(x) = 4x about the y-axis means that the x-coordinates of all the points on the graph are negated. The new equation of the graph is:
y = -4x
c. Shifting f(x) 6 units left.
Shifting the graph of f(x) = 4x 6 units left means that all the x-coordinates of all the points on the graph are decreased by 6. The new equation of the graph is:
y = 4(x - 6)
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Month, Ticket
Sales, y
27
28
36
28
32
35
X
1
2
3
4
5
6
s
a. Use a graphing calculator to find an equation of line of best fit.
b. Identify the correlation coefficient.
c. Use a graphing calculator to find the standard deviation of the ticket sales
d. Plot the graph in a scatter plot.
a. The equation of line of best fit is ŷ = 1.26x + 26.6
b. The correlation coefficient is 0.60
c. undefined
d. The graph is attached
a. Find an equation of line of best fit.From the question, we have the following parameters that can be used in our computation:
The table of values
From the graphing calculator, the summary of the above dataset is:
Sum of X = 21Sum of Y = 186Mean X = 3.5Mean Y = 31Sum of squares (SSX) = 17.5Sum of products (SP) = 22The regression equation is represented as
ŷ = bx + a
Where
b = SP/SSX = 22/17.5 = 1.25714
a = MY - bMX = 31 - (1.26*3.5) = 26.6
So, we have
ŷ = 1.26x + 26.6
So, the linear regression model to represent the data set is ŷ = 1.26x + 26.6
b. Identify the correlation coefficient.From the graphing tool, we have
r = 0.6032
This means that the correlation coefficient is 0.60
c. Use a graphing calculator to find the standard deviation of the ticket salesThis cannot be calculated
d. Plot the graph in a scatter plot.See attachment
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What is the matching line that is parallel to the line y=3x+12 through the point (2,-5)?
Answer:
y=3x-11
Step-by-step explanation:
-5 = 3(2) + b
-5 = 6 + b
b = -11
Find the point P such that v = PQ has the components (7,6,9) and 0 = (2, -4,3)
The point P is (9, 2, 12).
To find the point P, we need to add the vector v = PQ to the given point 0.
Given that v = PQ has the components (7, 6, 9) and the point 0 has the components (2, -4, 3), we can calculate the coordinates of point P as follows:
P = 0 + v = (2 + 7, -4 + 6, 3 + 9) = (9, 2, 12)
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4+( ) Rewrite the expression 4-11 as the sum of two numbers
Answer:
4+(-11)
Step-by-step explanation:
you need to put the negative 11 in ()
A Question 9 (3 points) Retake question 4Listen ► When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when? advances are not given for sho
When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when the advances are not given for shows. This is to ensure that the performer is fully committed to performing at the event and to cover any expenses that may be incurred in the process.
The advance fee is usually non-refundable and is paid by the promoter or venue operator to the booking agent. This is to show their commitment to the performer and to demonstrate that they are serious about booking them for the event. The remaining balance is then usually paid on the day of the performance or shortly after.
The booking agent should also ensure that all parties involved in the booking are aware of the terms and conditions and have signed a contract or agreement to confirm their agreement.
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¿por qué no está definida la raíz de índice par de un número negativo?
Answer:
Porque se convierte en positivo cada vez que haces la raíz cuadrada.
Word problem:Sophia wants to buy a tablet so she can watch tv and play games as well as complete her school work. She is researching all her different options and the tablet she chose says the length is (-4x^2-2x-3)cm and the width is (4x+3)cm. Question: What is the area of Sophia’s tablet (the red outline)? You must show and explain all your work and do not forget units of measurement.
Yonna, this is the solution to the problem:
Side 1 of the tablet = (4x + 3) cm
Side 2 of the tablet = (-4x² - 2x - 3) cm
Area of the tablet = Side 1 * Side 2
Area of the tablet = (4x + 3) * (-4x² - 2x - 3) cm²
Area of the tablet = (4x * -4x²) + (4x * -2x) + (4x * -3) + (3 * -4x²) + (3 * -2x) + (3 * -3)
Area of the tablet = -16x³ - 8x² - 12x - 12x² - 6x - 9 cm²
Area of the tablet = -16x³ - 20x² - 18x - 9 cm²
Please help on this!
Answer:
18cm,21cm,27cm
Step-by-step explanation:
explanation in picture
The oxygen atoms in the thermosphere absorb high-energy solar radiation and convert it into heat energy.
true
false
Step-by-step explanation:
Nitrogen and oxygen absorb solar radiation and release thermal energy, which causes temperatures in the thermosphere to be 1000 °C or higher. When most people think of an area that has high temperatures, they think of a place that is very hot. Although the thermosphere has very high temperatures, it does not feel hot. The answer is true
A survey of students showed that 32 students enjoyed country, 14 enjoy jazz, and 8 enjoy both, which of the following Venn diagram represents the result of the survey? (image)
The Venn diagram that represents the result of the survey is; Venn Diagram in Option A
What is a Venn Diagram?
Venn diagrams are used in sets in mathematics to group the union and intersection of subsets.
We are told that;
Number of students that enjoyed country = 32
Number of students that enjoyed jazz = 14
Number of students that enjoyed both country and jazz = 8
Now, the number of the students that enjoyed country and jazz should be the intersection of both circles in the venn diagram.
Secondly number of students that listened to only country = 32 - 8 = 24
Number that listened to only jazz = 14 - 8 = 6
Thus, the only correct option is Option A
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a 6 ft board is cut into two pieces, on twice as long as the other. How long are the pieces?
Answer:One is 2 feet and one is 4 feet
Step-by-step explanation:
Divide using long division.
Therefore, the quotient is -4x⁴ - 4x³ + 54x² + 18x + 30 and the remainder is 150x + 84.
Explain Long Division?Long division is a method of dividing two numbers using written arithmetic. It is a process of breaking down a division problem into a sequence of smaller and easier steps to obtain the quotient and remainder. Long division is typically used for dividing large numbers or when the division is not exact.
To perform long division, we follow the following steps:
Write the dividend (the number being divided) on the long division symbol, with the divisor (the number we are dividing by) outside the symbol.Determine how many times the divisor goes into the first digit of the dividend. Write this quotient above the first digit of the dividend.Multiply the divisor by the quotient and write the result below the first digit of the dividend.Subtract this result from the first digit of the dividend to obtain the remainder.Bring down the next digit of the dividend and write it next to the remainder.Repeat steps 2 to 5 until all digits of the dividend have been used.The final result is the quotient and the last remainder obtained.
__________________________
x³ + 6x² - 3x - 5 | -3x⁵ - 22x⁴ - 13x³ + 39x² + 14x - 6
-3x⁵ - 18x⁴ + 9x³ + 15x²
----------------------------
-4x⁴ - 4x³ + 54x²
-4x⁴ - 24x³ + 12x² + 20x
-------------------------
18x³ + 42x²
18x³ + 108x² - 54x - 90
------------------------
150x + 84
Therefore, the quotient is -4x⁴ - 4x³ + 54x² + 18x + 30 and the remainder is 150x + 84.
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The town of Valley View conducted a census this year, which showed that it has a population
of 1,800 people. Based on the census data, it is estimated that the population of Valley View
will grow by 12% each decade.
Write an exponential equation in the form y = a(b) that can model the town population, y, x
decades after this census was taken.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential function to model the population of Valley View is \(y = 1800(1.012)^t\).
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
An exponential function is written in the form -
\(y=ab^t\)
Here, y is the function, a is the base value b is the rate and t is time period.
The number of people in Valley view is 1800. So, the base is a = 1800.
The function y depicts the towns population.
Each decade the population grows by 12%.
The growth rate per year is = 12 / 10
The growth rate is 1.2%
The value for b will be = 1 + r
b = 1 + 1.2/100
b = 1 + 0.012
b = 1.012
So, the exponential equation will be -
\(y = 1800(1.012)^t\)
Therefore, the exponential equation is \(y = 1800(1.012)^t\).
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Complete the following statement. Write your answer as a decimal or whole number.
__% of $3,000,000 = $2,250,000
Submit
Answer: 75
Step-by-step explanation:
\(x\)% x 3000000 = 2250000
\(x\)/100 x 3000000 = 2250000
\(x\) x 30000 = 2250000
\(x\) = 2250000/30000
\(x\) = 75
A=1/2w(b+c) solve for c
9514 1404 393
Answer:
c = 2A/w -b
Step-by-step explanation:
Multiply by the inverse of the coefficient of the parentheses.
\(A=\dfrac{w}{2}(b+c)\\\\\dfrac{2A}{w}=b+c\\\\\boxed{c=\dfrac{2A}{w}-b} \qquad\text{subtract $b$}\)