The equivalent of two reflections across parallel lines is a glide reflection. Therefore, choice A is the best one.
What is isometry in a nutshell?d(f(x,y))=d(x,y) is a bijective map between two metric spaces that maintains distances, where f is the map and d(a,b) is the distance function. Congruence transformations are another name for isometries. Congruent refers to two figures that an isometry can change into one another (Coxeter and Greitzer 1967, p. 80). A linear transformation with length preservation is called an isometry of the plane. Rotation, translation, reflection, gliding, and the identity map are all examples of isometries. Geometrically congruent refers to two geometric figures that are connected by an isometry (Coxeter and Greitzer 1967, p. 80).
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The equivalent of two reflections across parallel lines is a glide reflection. Therefore, choice A is the best one.
What is isometry in a nutshell?A mapping of a metric space such that any two points' distances in the original space are equal to the distances between their images in the second space. d(f(x,y))=d(x,y) is a bijective map between two metric spaces that maintain distances, where f is the map and d(a,b) is the distance function. Congruence transformations are another name for isometries. Congruent refers to two figures that an isometry can change into one another. A linear transformation with length preservation is called an isometry of the plane. Rotation, translation, reflection, gliding, and the identity map are all examples of isometries.
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Where do you find the solution to a system?.
There are several methods for finding the solution to a system of equations, which include:
1. Graphing: This method involves plotting the equations on a coordinate plane and finding the point(s) of intersection. This method is useful when the system has a small number of variables and the equations are in the form of y = mx + b.
2. Substitution: This method involves solving one of the equations for one variable and then substituting that expression into the other equation. This method is useful when one equation is easier to solve than the other or when one equation is a simpler form than the other.
3. Elimination: This method involves adding or subtracting the equations to eliminate one of the variables. This method is useful when the variables are in similar forms and the coefficients are easy to add or subtract.
4. Matrix method: This method involves solving the system of equations in matrix form using matrix algebra techniques such as Gaussian elimination, Gauss-Jordan elimination and Cramer's rule. This method is useful when the system of equations have a large number of variables and when you want to solve system of equations in a more efficient and less time-consuming way.
5. Numerical methods: This method involves using numerical techniques such as Newton-Raphson method, Iterative methods to approximate the solution of a system of equations.
It is important to note that in some cases, a system may have no solution or infinitely many solutions. A system has no solution when the equations are inconsistent, meaning they cannot be true at the same time. A system has infinitely many solutions when the equations are dependent, meaning one equation can be derived from the other equation
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QS is a midsegment of PRT
IF PT=x+67 and QS=x+27, what is the value of x?
The value of x is 13 if QS is a midsegment of PRT
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that QS is a midsegment of PRT
IF PT=x+67 and QS=x+27,
We need to find the value of x
From midsegment theorem we have
QS=1/2(PT)
x+27=1/2(x+67)
x+27=x/2+67/2
x-x/2=67/2-27
x/2=13/2
x=13
Hence, the value of x is 13 if QS is a midsegment of PRT
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what is the solution to the system or equations graphed below?
y = -3/2 x + 2 y = 5x = 28
A. (-4,8)
B.(4,8)
C.(-8,4)
D.(0,2)
Answer:
It is A im preety sure
Step-by-step explanation:
very sorry if im wrong but im almost possitive its A
Carl is attempting to find the value of x by using the side splitter theorem. Carl set up the proportion 63=12x. If carl is correct, what should his answer be? if carl is incorrect, what is the correct proportion and answer?.
Carl is correct the value of x by using the side splitter theorem is 6
[tex]\frac{6}{3} = \frac{12}{x}[/tex]
Required
Is Carl correct?
The side splitter theorem is a theorem that states that when a line passes through the two sides of a triangle and is parallel to the third remaining side, the line divides the two sides proportionally.
Using the side splitter theorem, the proportion is:
[tex]\frac{AB}{BC} = \frac{AE}{ED}\\[/tex]
This gives:
[tex]\frac{6}{3} = \frac{12}{x}[/tex]
This proportion is equivalent to Carl's.
Hence, Carl is correct.
Solving further: Cross Multiply
6 * x = 12 * 3
6x = 36
Make x the subject
[tex]x=\frac{36}{6}[/tex]
x =6
Carl is correct the value of x by using the side splitter theorem is 6
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How do you solve log base questions?.
The answer to the equation for the logarithm of 1 in base 7 is x=0, where x is the power to which 1 must be raised in order to obtain the value 7.
The definition of the logarithm function, which is the inverse of the exponential function and reads log b(x) = y, is by = x. To put it another way, it reflects the increment in base b that must be raised in order to obtain the value x.
When solving log 7(1), we are seeking the power to which 7 must be increased in order to obtain the value 1.
Since 1 is the result of raising any number to the power of 0, we may state that 70 = 1, which implies that log 7(1) = 0.
Finding the value of x that makes the equation log 7(x) = 1 true is necessary to solve log base 7 1.
Log b(x) = y signifies that b = y using the definition of a logarithm.
Therefore, we can put 1 = 7x and obtain x = log7(1) = 0 to solve log7(1).
So, x=0 is the answer to the logarithm in base 7 of 1.
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Can X² 1 be the quotient on division of X 2x² x 1 by a polynomial in x in degree 5?.
After solving, we check that [tex]x^2[/tex] - 1 cannot be the quotient of p(x).
In the given question, we have to check whether the quotient is [tex]x^2[/tex] - 1.
The given polynomial is [tex]x^6 + 2x^3[/tex] + x - 1 is divided by a polynomial in x of degree 5.
Given a polynomial p(x) and a non-zero polynomial g(x), the division algorithm asserts that there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).
5th degree polynomial because the power of the dividend should equal the degree of the product of the quotient and the divisor.
Degree 1 will result from the division of a degree of polynomial 6 by a degree of polynomials 5 and 6.
From the given question,
P(x) = [tex]x^6 + 2x^3[/tex] + x - 1
g(x) = x in degree of 5
q(x) = x² - 1
So,
[tex]x^6 + 2x^3[/tex] + x - 1 = (x in degree of 5)([tex]x^2[/tex] - 1) + r(x)
[tex]x^6 + 2x^3[/tex] + x - 1 = x in degree of 7
Hence, [tex]x^2[/tex] - 1 cannot be the quotient of p(x).
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The complete question is:
Can [tex]x^2[/tex] - 1 be the quotient on division of [tex]x^6 + 2x^3[/tex] + x - 1 by a polynomial in x of degree 5?
2.
Recall that Stella is the pacesetter the 4:10
pace group of a marathon and is required to
finish within 2 minutes of the pace time.
Stella must run between
minutes and
meet the requirement.
minutes in order to
Stella must run between 248 minutes and 252 minutes in order to meet the requirement.
What is the time-to-minute conversion?
As an hour consists of 60 minutes, we can convert hours into minutes by multiplying hour by 60. So, for example, if one wants to convert 3 hours into minutes, one can do it by multiplying 3 by sixty which will give 3 x 60 = 180 minutes.
To figure out the range of times within which Stella must finish the marathon in order to meet the requirement of finishing within 2 minutes of the 4:10 pace time,
we can use the following steps:
Convert the pace time of 4:10 to minutes.
Since there are 60 minutes in an hour, 4:10 is equal to 4 * 60 + 10 = 250 minutes.
Add 2 minutes to the pace time. Since Stella must finish within 2 minutes of the pace time, this gives us a finish time of 250 + 2 = 252 minutes.
Subtract 2 minutes from the pace time. Since Stella must finish within 2 minutes of the pace time, this gives us a finish time of 250 - 2 = 248 minutes.
The range of times within which Stella must finish the marathon in order to meet the requirement is 248 to 252 minutes.
Hence, Stella must run between 248 minutes and 252 minutes in order to meet the requirement.
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explain how you could write a quadratic function in factored form that would have vertex with an x-coordinate of 3 and two roots
Please help
Explain one concept that you’ve learned in geometry. Please answer in at least two complete sentences
Will mark brainliest
Answer: Law of Sines: When we divide side a by the sine of angle A
it is equal to side b divided by the sine of angle B. It's also equal to side c divided by the sine of angle C.
How do you find the sum of a partial series?.
The sum of a partial series is calculated by Sn=∑ni=1ai=n(a1+an)2.
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.
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What are the 4 lines of symmetry?.
The 4 lines of symmetry is square.
In math the imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
Here we need to find the 4 lines of symmetry.
As we all know that the line of symmetry is known as a balanced and proportionate similarity that is found in two halves of an object.
So, based on these definition, we have identified that A square has four lines of symmetry.
Because it can be folded in half over either diagonal or the horizontal segment which cuts the square in half or the vertical segment which cuts the square in half.
Therefore the square has four lines of symmetry.
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you want to buy a pair of shoes that cost $65 but you have a coupon that will reduce the prove by $15 what would the percent decrease be
Answer: 76.92%
Step-by-step explanation:
To find the percent decrease is simple. First let's find the difference: 65 - 15 which gives you 50. 50/65 * 100 = 76.92%. Have a good day ;)
Determine whether each scenario is best represented by a discrete or continuous domain.
1. The distance a woman walks and runs during her morning workout. Discrete or continuous?
2. The local candy store sells ring pops for 5 cents each. Discrete or continuous?
3. The baseball’s height compared to it’s horizontal distance after being thrown by a player. Discrete or continuous?
4. The market sells grapes by the pond. Discrete or continuous?
5. The amount paid when purchasing cans of peas. Discrete or continuous?
The scenario is best represented by a discrete or continuous domain is
a. discrete
b. continuous
c. discrete
d. continuous
e. discrete
What is discrete?Constituting a distinct entity being unique in one's own right. divided into multiple independent portions; made up of separate or unrelated components: having a limited or countably infinite range of values is referred to as being noncontinuous. continuous probabilities. having a separate existence or form from other entities with a similar nature; separate.There are four distinct neighborhoods in this area, all clustered around a school. different from others; distinct; set apart: six separate pieces. containing or characterized by separate or different components; discontinuous."Discrete" means separately separate, different, or unconnected, whereas "discreet" means to do anything in a clandestine, low-profile, or cautious manner.opposite of cautious and sensible in words or behavior. Indiscreet, ill-advised, hasty, and unwise.To learn more about Discrete refer to:
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____ is standard deviation a measure of center or a measure of variation
Standard deviation is a measure of variation.
The degree of variance or dispersion in a set of data values is measured statistically using the standard deviation. It reveals how far the data values differ from the data set's average. Data points tend to be close to the mean when the standard deviation is low, and are dispersed over a larger range when the standard deviation is high.
While measurements of the centre, such as mean, median, and mode, are used to describe a data set's central tendency. The median is the midway value when a data set is ordered, and the mode is the value that appears in a data set the most frequently. The mean is the sum of the data divided by the number of observations.
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What is the quadratic polynomial whose sum and the product of zeroes is √ 2?.
The quadratic polynomial whose sum and the product of zeroes is x^2 - √2x + 1.
A degree two polynomial is a quadratic polynomial. The formula for a univariate quadratic polynomial is f(x)=a 2x2+a 1x+a 0. A quadratic equation is one that contains a quadratic polynomial. For the answers of any arbitrary quadratic problem, there is a closed-form solution known as the quadratic formula.
A quadratic polynomial's general formula is represented as f(x)=ax2 + bx + ca. A parabola is the name of the quadratic polynomial's curve. A quadratic polynomial is one that has the formula ax2 + bx + c, where a, b, and c are all real values and an is 0.
Only a few quadratic polynomials are amenable to the factorization technique. The quadratic polynomial formula, however, can be used for any quadratic problem.
In addition, the discriminant's value can be used to examine the characteristics of a quadratic polynomial's roots.
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Which vehicle gets the best mileage per gallon?
A 4-column table with 3 rows. Column 1 is labeled Vehicle with entries Sedan, Minivan, Truck. Column 2 is labeled Miles Traveled with entries 630, 798, 864. Column 3 is labeled Gasoline Used (gallon) with entries 35, 42, 54. Column 4 is labeled Unit Rate with entries 18, 19, 16.
The vehicle with best mileage per gallon is Minivan vehicle .The maximum milage value is 19 miles/gallon.
We have, a table as present in above figure. The table contains 4-column and 3 rows. Column 1 is labeled different Vehicles, Column 2 is labeled Miles Traveled and Column 3 is labeled Gasoline Used (gallon). We have determine the vehicle gets the best mileage per gallon. Milage of a vehicle means how many distance vehicle going to run per quantity of fuel. In this cas milage of vehicle is miles going to run per gallons of fuel.
The formula to calculate gas mileage is
Milage = Miles Traveled/ Gasoline used (gal).
Now, we consider each row one by one.
Milage for Sedan = 630/35 = 18 miles/gallon
Milage for Minivan = 798/42 = 19 miles/gallon
Milage for Truck = 864/54 = 16 miles/gallon
Hence, the required vehicle is Minivan with milage of 19 miles/gallon.
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Complete question:
Which vehicle gets the best mileage per gallon? The above table complete the question. A 4-column table with 3 rows. Column 1 is labeled Vehicle with entries Sedan, Minivan, Truck. Column 2 is labeled Miles Traveled with entries 630, 798, 864. Column 3 is labeled Gasoline Used (gallon) with entries 35, 42, 54. Column 4 is labeled Unit Rate with entries 18, 19, 16.
What is the general equation for a double-displacement reaction?
Answer:
AB + CD → AD + CB
Explanation:
The double-replacement reaction generally takes the form of AB + CD → AD + CB where A and C are positively-charged cations, while B and D are negatively-charged anions.
What is the solution to the equation 1 h 5 2 h 5?.
The solution to the equation 1 h 5 2 h 5 is 7.
In this case option A is correct
The solution can be obtained by following steps-
The given equation is the least common multiple of the denominators, which we multiply through to obtain, and then we eliminate common factors to obtain. Multiply 1 h5 1 h - 5 by h+5 h+5 h+5 h + 5 h + 5 to create a fraction with a common denominator. Multiply 2 h+5 by h+5 h+5 h- 5 h- 5 to get 2 h+5 written as a fraction with a common denominator.We group like terms to get, we expand the brackets to get, this simplifies to, we now divide through by three to get,
[tex]h+ 2h= 16-5+ 10\\3h= 21\\h=7[/tex]
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What is the solution to the equation 1 h 5 2 h 5?.
7890How tall will your hair be if its 3 inches and you make a mow Mohawk, and it gets another 1.5 inches how long your hair is.
We'll cut straight to it: On average, hair grows at a rate of about half an inch per month, or six inches per year. Each hair on your head grows from an individual follicle.
How tall will your hair be if its 3 inches and you make a mow Mohawk?We'll cut straight to it: On average, hair grows at a rate of about half an inch per month, or six inches per year. Each hair on your head grows from an individual follicle.
The average person's hair grows ½ an inch each month which sums up to 6 inches of growth per year.
For you I'd say maybe anywhere from 3 to 5 months it would be around the length you're looking for. It may take a year to get it to your shoulders.
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5 1/5 + 3 1/3 = 9 2/3 is this correct?
Please help yall!
What is the total sales for bicycles for store 1 and 2?
What is the total cost for bicycles for store 1 and 2?
What is the total profit for bicycles for store 1 and 2?
The total sales for bicycles for store 1 and 2 = 54 bicycles.
Thee total cost for bicycles for store 1 and 2= $7,530
The total profit for bicycles for store 1 and 2= $12,420
How to calculate the number of sales?The total sales for bicycles for store 1 and 2 can be calculated as thus;
Store 1 = 15+20 = 35
Store 2 = 10+9 = 19
Total sales for store 1 and 2 = 35+19 = 54
The total cost for bicycles for store 1 and 2=
Store 1 = 150×35= $5,250
Store 2 = 19× 120 = $2,280
The total cost for bicycles in both stores= $5,250+$2,280= $7,530.
The total profit for bicycles for store 1 and 2=
Store 1 = 230×35 = $8,050
Store 2 = 230×19 = $4,370
The total profit from both stores = $8,050+$4,370= $12,420.
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Exponential functions
The average rate of change between 2006 and 2010 is 172.
What is average rate?Average rate is a statistical measure used to compare a set of values or quantities. It is calculated by taking the sum of the values, then dividing by the number of values in the set. Average rate is most often used to measure the average performance of a group, individual, or business over a certain period of time.
The average rate of change between 2006 and 2010 is calculated by taking the difference in the values of the function for the two given years and then dividing it by the difference in the two years.
In this case, the difference in the values of the function for 2006 and 2010 is 1725 - 1037 = 688. The difference in the two years is 2010 - 2006 = 4.
Thus, the average rate of change is 688/4 = 172.
Therefore, the average rate of change between 2006 and 2010 is 172.
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For each function, 1) find the inverse (if it exists), 2) find the domain and range for both f and f^-1
1) y=1/5^(1-x)+2
2)1-5^x/5^(x-1)
3)y=log1/5(x+1/2)-1
Answer:
1. y = 1/5^(1-x) + 2
The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.
So, x = 1/5^(1-y) + 2
To find the inverse, we need to solve for y:
y = 1 - log(5, x-2)
Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.
The domain of f is all x such that x > 2. And the range of f is all y such that y > 2. The domain of f^-1 is all x such that x > 2 and the range of f^-1 is all y such that y > 1.
----------------------------------------------------------
2. 1 - 5^x/5^(x-1)
The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.
So, x = 1 - 5^y/5^(y-1)
To find the inverse, we need to solve for y:
y = log(5, 1/(x+1)) + 1
Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.
The domain of f is all x such that x < 1. And the range of f is all y such that 0 < y < 1. The domain of f^-1 is all x such that x < 1 and the range of f^-1 is all y such that y > 1.
--------------------------------------------------------------
3. y = log1/5(x+1/2)-1
The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.
So, x = log1/5(y+1) - 1/2
To find the inverse, we need to solve for y:
y = 5^(x+1/2) - 1
Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.
The domain of f is all x such that x exists. And the range of f is all y such that y > -1. The domain of f^-1 is all x such that x exists and the range of f^-1 is all y such that y > 0.
-----------------------------------------------------------------
In summary,
1. f^-1(x) = 1 - log(5, x-2) Domain: x>2, Range: y>2.
2. f^-1(x) = log(5, 1/(x+1)) + 1 Domain: x<1, Range: 0<y<1.
3. f^-1(x) = 5^(x+1/2) - 1 Domain: x exists, Range: y>-1.
How do you solve 3x 4y =- 12?.
The solution of equation 3x + 4y = -12 for y is y = -3 - 3/4 x.
In the given question, we have to solve 3x + 4y = -12 for y.
The given equation is 3x + 4y = -12.
To solve this equation for y, we have to isolate the y.
Now solving the given equation.
3x + 4y = -12
Subtract 3x on both side, we get
4y = -12 - 3x
Divide by 4 on both side, we get
y = [tex]\frac{1}{4}[/tex](-12 - 3x)
Now simplifying the expression.
y = -12/4 - 3/4 x
y = -3 - 3/4 x
Hence, the solution of equation 3x + 4y = -12 for y is y = -3 - 3/4 x.
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The complete question is:
How do you solve 3x + 4y = -12 for y?
what are the steps to evaluate an exponential expression
The steps to evaluate an exponential expression include:
Identify the base and the exponent in the expressionReplace the base with the value that you want to use.Use the exponent to determine how many times the base should be multiplied by itself.Perform the multiplication and simplify the expression.How to evaluate an exponential expression ?First, you need to identify the base which is the number being raised to a power, and the exponent is the power to which the base is being raised. Then replace this base with the value that is needed to be used.
Use this exponent such that you can find out the number of times the base will multiply itself and then do the multiplication and simplify the expression.
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How do you solve system of 2 linear equations using graphical method?.
The graphical technique is a strategy for resolving a set of linear equations by creating a graph. The following are the steps needed to solve a system of two linear equations graphically.
Get the two-variable linear equation system that is supplied.
Plot the first equation's graph on the same coordinate system as the second equation.
Plotting the graphs may result in the following three situations:
The presented system has a singular solution provided by the coordinates at the point of intersection if the line intersects at that place.
The system is consistent and contains an endless number of solutions if the lines coincide.
If the lines are parallel, the provided equation system is inconsistent, meaning it cannot be solved.
Consider two linear equations,
y = x - 1
y = 2x + 2
The equations should now be graphed in the coordinate plane.
The graph shows that the common point (-3, -4) where the two linear equations cross is the answer to the given system of linear equations.
As a result, we can solve linear equations graphically by plotting the graph on the coordinate system.
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which variable is it?
first or second one?
Answer:
p is the dependant variable and w is the dependent variable
Step-by-step explanation:
The number of plots is dependent because the number of plots doesnt change. The amount of wheat depends on the amount of plots you have.
Estimate the amount of the tip by rounding the bill to the nearest ten dollars before calculating.
20% tip on a bill of $542.11
The amount of the tip is approximately $
.
Answer: $ 108.42
Step-by-step explanation: Take 20% of the total.
1/7 (x + 3/4) = 1/8 solve for x
Answer: 1/8
Step-by-step explanation:
How many symmetrical lines do they have?
Answer:3 symmetrical lines
Step-by-step explanation: just look in the middle and draw a line
