The order of g is a power of 2, Hence G is abelian.
Everything is in order, with the exception of identification.
2, then a2=e
where a∈G
(including identity this time). So, a−1=a
for all a∈G
Hence ab=(ab)−1=b−1a−1=ba
for all a b∈G
For every x∈G
we have x2=e
where e
represents the identity in.
Then x−1=x
Now, let a,b
be two arbitrary elements in G
We have ab=(ab)−1=b−1a−1=ba
Hence G is abelian.
(First equality is true because ab
is also an element of G
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Which description is correct for the polynomial −5x3−4x+1?
Cubic monomial describes the polynomial 5x3x4x+1.
What is meant by Cubic monomial?One with a degree of three is said to be a cubic monomial. As a result, a cubic monomial is a single phrase that is made up of constants, variables, and/or positive integer powers of those variables, where the exponents of those variables add up to 3.A cubic binomial is a polynomial of degree 3 with exactly two terms, according to the criteria above. As an illustration, the cubic binomials x3 + 28x2 and 4x3 + 14 are both exactly two-term equations, and their maximum exponents are both three. A monomial is a type of algebraic expression that only has one term, while it is also possible for it to include several variables and a higher degree.The complete question is:
Which description is correct for the polynomial −5x3−4x+1?
A) quadratic trinomial
B) cubic binomial
C) quadratic binomial
D) cubic monomial
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Rombos BA(5x-11). AD(6x-18)
The value of x is 7.
And every side of the rhombus is 24 unit.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given:
ABCD is a rhombus.
BA = 5x - 11
And AD = 6x - 18
Then, BA = AD
5x - 11 = 6x - 18
x = 7
Therefore, the value of x is 7.
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Work out the size of angle x
HELP HELP HELP EASY MATH
(a) f(4) = -1, f(-6) = 1 and f(6) = 1
(b) x = 4 and -4, x = 0 and x = -7
(c) t = -8
(d) The set x = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
(a) The values of f(x) for the given values of x can be found from the graph by looking at the y values corresponding to the given x values.
f(4) = -1
f(-6) = 1
f(6) = 1
(b) By looking to the y values as the given numbers, we can find corresponding x values.
f(x) = -1 ⇒ x = 4 and -4
f(x) = -5 ⇒ x = 0
f(x) = 2 ⇒ x = -7
(c) We have to calculate the point (t, 3) where the y value is 3.
f(x) = 3 when x = -8
So t = -8
(d) f(x) < 0 for the set of values of x {-4, -3, -2, -1, 0, 1, 2, 3, 4}
Hence using the diagram of the graph of a function, we can compute all the values.
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Answer:
(a) f(4) = -1, f(-6) = 1 and f(6) = 1
(b) x = 4 and -4, x = 0 and x = -7
(c) t = -8
(d) The set x = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
Step-by-step explanation:
How do you solve algebraic expressions in Class 8?
One can solve basic algebraic expressions by following these steps.
In class 8, students typically learn to solve basic algebraic expressions by following these steps:
Identify the variable and the coefficient (number in front of the variable) in the expression.
Use the order of operations (PEMDAS) to simplify any arithmetic within the expression.
Use the distributive property to combine like terms.
Isolate the variable on one side of the equation by using inverse operations (such as adding or subtracting the same value from both sides, or dividing or multiplying both sides by the same non-zero value).
Substitute in a value for the variable to find the numerical value of the expression.
It's good to practice with a lot of examples and check the solutions, and ask for help if needed.
Example:
Solve for x: 3x + 2 = 12
variable is x, coefficient is 3
nothing to simplify
nothing to combine
subtract 2 from both sides: 3x = 10
divide both sides by 3: x = 10/3 or 3.3333
x = 3.3333
It's important to note that solving algebraic expressions can become more complex as the student progresses, but the basic steps remain the same.
Thus, One can solve basic algebraic expressions by following these steps.
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At a point A due South of the building the angle of elevation from the ground to the top of the building is 58ﾟ. At a point B on level ground with a 80 m due West of a the angle of elevation to the top of the building is 27ﾟ. Find the height of the building
The height of the building from the ground is 83.33 m.
Let h be the height of the building, d be the distance between point A and the building, and d' be the distance between point B and the building.
From the problem, we know that:
The angle of elevation from point A to the top of the building is 58°.The angle of elevation from point B to the top of the building is 27°.Point B is 80 m due West of point A.We can use trigonometry to find the height of the building:
h / d = tan 58°
h = d * tan 58°
Also,
h / d' = tan 27°
h = d' * tan 27°
Since h is the same for both equations, we can set them equal to each other and solve for d:
d * tan 58° = d' * tan 27°
d = d' * tan 27° / tan 58°
We also know that point B is 80 m due West of point A, so we can use the Pythagorean theorem to find the value of d':
d' = √(80² + h²)
Now, we can substitute that into the equation for d and solve for h:
d = d' * tan 27° / tan 58°
h/tan 58° = √(80² + h²) * tan 27° / tan 58°
h=√(80² + h²)*tan 27°
h²cot²27= 80²+h²
1.96h²= 80²+h²
0.96h²=80²
h²= 6944.44
h= 83.33
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What is the value of K roots of a quadratic equation?
When k is o doesn't satisfy the equation.
What is quadratic equation?We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0 The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible. To put it another way, if you have an equation with the form a squared by the expression after b plus b squared by the same expression but not squared plus c equal to 0, you have a quadratic equation.Value of [tex]$\mathrm{k}=(?)$[/tex], equation [tex]$\mathrm{kx}(\mathrm{x}-2)+6=0$[/tex] has equal roots.
[tex]& \Rightarrow \mathrm{kx}(\mathrm{x}-2)+6=0 \\[/tex]
[tex]& \mathrm{kx} x^2-2 \mathrm{kx}+6=0 \\[/tex]
two roots of quadratic equation
[tex]& \alpha, \beta= \frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 \mathrm{ac}}}{2 \mathrm{a}} \\[/tex]
[tex]& \alpha, \beta= \frac{+2 \mathrm{k} \pm \sqrt{(-2 \mathrm{k})^2-4 \times 6 \times \mathrm{k}}}{2 \times \mathrm{k}} \\[/tex]
[tex]& \alpha, \beta=2 \mathrm{k} \frac{\pm \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\[/tex]
[tex]\alpha=\beta \\[/tex] The roots are qual
[tex]& \Rightarrow \frac{2 \mathrm{k}+\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}}=\frac{2 \mathrm{k}-\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\[/tex]
[tex]& \Rightarrow 2 \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}=0 \\[/tex]
[tex]& \Rightarrow 4 \mathrm{k}^2-24 \mathrm{k}=0 \\[/tex]
[tex]& \Rightarrow 4 \mathrm{k}(\mathrm{k}-6)=0 \\[/tex]
[tex]& \Rightarrow \mathrm{k}=0 \text { or } \mathrm{k}=6[/tex]
[tex]$\Rightarrow \mathrm{k}=6[\because \mathrm{k} \equiv 0]$[/tex] as[tex]$\mathrm{k}=0$[/tex] doesn't satisfy the equation.
The complete question is,
For what value of [tex]$\mathrm{k}$[/tex], are the roots of the quadratic equation, [tex]$\mathrm{kx}(\mathrm{x}-2)+6=0$[/tex] equal?
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If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
A. 1 minute
B. 5 minutes
C. 10 minutes
D. 15 minutes
E. 100 minutes
A student wants to make the natural frequency of a tube increase.
How can the student accomplish this?
Responses
Increase the length of the tube.
Decrease the length of the tube.
Make holes in the tube.
Change the composition of the tube.
Increase the length of the tube.
The natural frequency of a tube is determined by the speed of sound in the material of the tube and the length of the tube. Increasing the length of the tube will increase the wavelength of the standing waves that can be formed inside the tube, which in turn will increase the natural frequency of the tube. Decreasing the length of the tube will have the opposite effect, decreasing the natural frequency. Making holes in the tube will change the boundary conditions and may affect the natural frequency, but it is not a guaranteed way to increase it. Changing the composition of the tube will change the speed of sound in the material, which may increase or decrease the natural frequency depending on the new material's properties.
I hope this helps :)
4. Represent Patty has
47 counters. She puts some
of them in stacks of ten.
Show two ways.
Answer:
Step-by-step explanation:
evaluate the integral by reversing the order of integration.
The integral by reversing the order of integration is [tex]\frac{1}{14}\left[e^{49}-1}\right][/tex].
In the given question, we have to evaluate the integral by reversing the order of integration.
The given integration is [tex]\int_{0}^{1}\int_{7y}^{7}e^{x^2}dxdy[/tex].
The given integral is in the form of dxdy. We must create an integral of order dydx in order to shift the order of integration. This indicates that x is the outer integral's variable. Its bounds must be fixed and match the complete range of x over the area D.
The limit of y and x is;
0 ≤ y ≤ 1; 7y ≤ x ≤ 7; dA = dxdy
Now changing the order of integration
0 ≤ x ≤ 7; 0 ≤ y ≤ x/7; dA = dydx
I = [tex]\int_{0}^{7}\int_{0}^{x/7}e^{x^2}dydx[/tex]
Now integrating with respect to dy
I = [tex]\int_{0}^{7}t[y]_{0}^{x/7}e^{x^2}dydx[/tex]
I = [tex]\int_{0}^{7}t[x/7 - 0]e^{x^2}dydx[/tex]
I = [tex]\frac{1}{7}\int_{0}^{7}xe^{x^2}dx[/tex]
Now integrating again
I = [tex]\frac{1}{14}\left[e^{x^2}\right]_{0}^{7}[/tex]
I = [tex]\frac{1}{14}\left[e^{(7)^2}-e^{(0)^2}\right][/tex]
I = [tex]\frac{1}{14}\left[e^{49}-1}\right][/tex]
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The complete question is:
Evaluate the integral by reversing the order of integration.
[tex]\int_{0}^{1}\int_{7y}^{7}e^{x^2}dxdy[/tex]
What are the two inverse properties of logarithms?
The inverse properties of the logarithm are [tex]log_{b}bx[/tex] = x and [tex]blog_{b}x[/tex] = x where x > 0.
What is logarithm ?
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
The inverse properties of the logarithm are logb bx=x and blogb x=x where x>0. The product property of the logarithm allows us to write a product as a sum: logb (xy)=logb x+logb y. The quotient property of the logarithm allows us to write a quotient as a difference: logb (xy)=logb x−logb y.
The inverse properties of the logarithm are [tex]log_{b}bx[/tex] = x and [tex]blog_{b}x[/tex] = x where x > 0.
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What is the volume of this sphere? Use pie = 3.14 and round to the nearest hundredth. Radius is 4
Answer:
268.08 cubic units.
Step-by-step explanation:
The volume of a sphere is given by the formula (4/3)πr^3, where r is the radius of the sphere.
Plugging in the given radius of 4, we get:
(4/3) * 3.14 * 4^3 = 268.08
So the volume of the sphere is approximately 268.08 cubic units.
A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the
system of equations?
(2.3)
a (1.2)
(2.2)
(2.4)
2
1
0
-14
5x-y=9
2x+6y=13
Answer:
(2,2)
Step-by-step explanation:
the intersection of the two lines represents the solution
visually, you can see the lines intersect closely to (2,2)
For what values of k the roots of the equation 3x² 10x K 0 are?
The equation 3x² + 10x + k = 0, the roots of the equation exist only for k ≤ 25.
What is equation?Equation is a mathematical statement that uses an equal sign to show a relationship between two expressions. An equation states that one expression is equal to the other expression. Equations are used to solve problems by finding the value of unknown variables. Equations can be used to describe the relationships between physical and mathematical phenomena.
In order to solve for the values of k, we must first understand the properties of quadratic equations. A quadratic equation is a polynomial equation of degree 2, meaning that it has at most two solutions. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants. In this case, the equation is 3x² + 10x + k = 0.
In order to solve for k, we must use the quadratic formula, which states that the two solutions of a quadratic equation are given by:
x = [-b ± √(b² - 4ac)]/2a
In this equation, a is equal to 3, b is equal to 10, and c is equal to k. Therefore, the two solutions of the equation 3x² + 10x + k = 0 are x = [-10 ± √(100 - 4*3*k)]/6.
The two solutions of the equation will only exist if the discriminant (√(b² - 4ac)) is greater than or equal to 0. Therefore, for the equation 3x² + 10x + k = 0, the two solutions will only exist if 100 - 4*3*k ≥ 0, or k ≤ 25.
Therefore, for the equation 3x² + 10x + k = 0, the roots of the equation exist only for k ≤ 25.
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Fill in the table using this function rule y=26-2x
On solving the provided question, we can say that function y=26-2x => x = 1 => y = 26-2 = 24
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
function y=26-2x
x = 1
y = 26-2 = 24
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Morgan is working two summer jobs, making $20 per hour tutoring and making $12 per hour clearing tables. In a given week, she can work no more than 16 total hours and must earn at least $240. If
�
x represents the number of hours tutoring and
�
y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution
A system of inequalities to describe this situation are as follows;
x + y ≤ 16
20x + 12y ≥ 240.
The system of inequalities has been solved graphically and one possible solution is (6, 10).
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hours tutoring purchased and number of hours clearing tables respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of hours tutoring.Let the variable y represent the number of hours clearing tables.In Mathematics, the inequality symbol for "no more than" is ≤ while the inequality symbol for "at least" is ≥.
Since Morgan makes $20 per hour tutoring and $12 per hour clearing tables and can work no more than 16 total hours and must earn at least $240, the system of linear inequalities that are required to model this situation include the following:
x + y ≤ 16
20x + 12y ≥ 240
Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (6, 10).
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If I’m a right triangle, the given legs are a=20and b=24, then by using the Pythagorean Theorem find the hypotenuse, c.
Hi! I don't think you'll need much help on this one. Just use the formula: a^2 + b^2 = c^2. You know already that 20 = a and 24 = b. Substitute them in and you'll get your answer!
Have a good day :_)
Which axis is Y =- 1 parallel to?
Y=-1 is parallel to the x-axis. This is because the y-intercept of a line is the point at which it crosses the y-axis, and y=-1 is the y-intercept of the line y=x. Therefore, the line y=-1 is parallel to the x-axis.
To demonstrate this mathematically, we can use the equation for a line in slope-intercept form, which is y=mx+b. Here, m is the slope of the line, and b is the y-intercept. Since the slope of the line is not given, we can assume that it is 0, since the line is parallel to the x-axis. Therefore, the equation of the line is y=0x+b, which simplifies to y=b. Substituting the given y-intercept, y=-1, into the equation, we get y=-1. Therefore, the equation of the line is y=-1, which is parallel to the x-axis.
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Figure tuvx figure abcd ab = 12 cd=6 da=4 what is the measure of vw?
Answer:
The measure of VW is 6. It's because since the figures are congruent their names are written in correspondence ....so since VW corresponds to CD , the answer must be 6.
Step-by-step explanation:
A jazz concert brought in $167,500 on the sale of 8,100 tickets. If the tickets sold for $15 $25 each, How many of each top of ticket were sold? The number of $15 tickets is?
So, 3,500 tickets were sold for $15 each and 4,600 tickets were sold for $25 each.
Let x be the number of $15 tickets and y be the number of $25 tickets.
We know that:
x + y = 8,100 (the total number of tickets sold)
15x + 25y = $167,500 (the total amount of money made from ticket sales)
We can use the first equation to express y in terms of x:
y = 8,100 - x
We can substitute this expression of y into the second equation:
15x + 25(8,100 - x) = $167,500
Solving for x:
15x + 25(8,100) - 25x = $167,500
15x + 202,500 - 25x = $167,500
-10x = -35,000
x = 3500
So, 3,500 tickets were sold for $15 each and 8,100 - 3,500 = 4,600 tickets were sold for $25 each.
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two diagonals of a regular decagon (a -sided polygon) are chosen at random. what is the probability that these diagonals intersect inside the decagon?
The probability that two diagonals chosen at random intersect inside the decagon is 7/45
A decagon is a 10-sided polygon, and it has 10 vertices.
In a regular decagon, there are 10C2 = 45 pairs of distinct vertices.
The total number of diagonals that can be drawn between these pairs of vertices is (10 * 9) / 2 = 45.
To find the number of diagonals that intersect inside the decagon, we need to find the number of diagonals that do not intersect at a vertex.
A diagonal that does not intersect at a vertex is called an interior diagonal, and the number of these is given by (n-3) where n is the number of sides in the polygon.
For a decagon, the number of interior diagonals is (10-3) = 7
Therefore, probability= favorable events/ total number of events = 7/45
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Suppose that Amanda raises chickens whose eggs have a mean weight of 57 grams and a
standard deviation of 6 grams. Her friend Bernardo also raises chickens, and their eggs have a
mean weight of 54 grams and a standard deviation of 8 grams.
They decide to have a contest where they'll each randomly select 60 of their eggs, calculate the
mean weight, and look at the difference between their sample means (A - TB).
What are the mean and standard deviation (in grams) of the sampling distribution of TA - TB? by
Therefore ,xa - xb = 3 and σa - σb = √(6/60) + (8/60) respectively are the units that were chosen and standard deviation difference.
The definition of standard deviationHow far the data points deviate from the mean is determined by descriptive statistics standard deviation. It quantifies how values are spread out over the sample data and gauges how far out of the mean data points are.
Here,
Given:
For Amanda's chicken, xa = 57 grammes is the average weight.
Chicken from Bernardo weighs, on average, 54 grammes.
The sample mean's difference is -
=> xa - xb
=> 57 - 54
=> 3
The chicken from Amanda's recipe had a standard deviation of 6 grammes.
The Bernardo's chicken standard deviation is b = 8 grammes.
N = 60 total observations were made.
The standard deviation formula is -
σ = √(x - μ)/n
σa - σb = √(6/60) + (8/60)
The figures are as follows: mean = 3; standard deviation = ((6/60) + (8/60).
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Select the correct answer. Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago. If Jenna’s age is x, which equation represents the situation? How many solutions does the equation have? A. x + 5 = (5 − x) − 5, which has one solution B. x + 5 = (x + 5) − 5, which has infinitely many solutions C. x + 5 = (x + 5) − 5, which has no solution D. x + 5 = (5 − x) − 5, which has infinitely many solutions E. (x + 5) + 5 = (x + 5) + 5, which has infinitely many solutions
x + 5 = (5 − x) − 5, which has one solution, represents the given situation.
Option A is correct.
What is the system of linear equations?
A system of linear equations is a collection of one or more linear equations that are solved simultaneously. A linear equation is an equation that can be written in the form ax + b = 0, where x is the variable, and a and b are coefficients.
A. x + 5 = (5 − x) − 5, which has one solution.
This is the correct answer because the equation represents the given situation that Jenna is x years old and in 5 years she will be as old as Jessica was 5 years ago which means Jenna's age in five years is x+5 and Jessica's age five years ago is 5 - x, by equating the age of Jenna in five years and Jessica's age five years ago we get x+5 = 5-x-5. Solving this equation we get x = 0, the age of Jenna is 0 and the age of Jessica is 5, which is a unique solution.
Hence, x + 5 = (5 − x) − 5, which has one solution, represents the given situation.
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6-3 proving that a quadrilateral is a parallelogram
A quadrilateral becomes a parallelogram if its diagonals cut each other in half.
A quadrilateral is a parallelogram if one set of its opposite sides is both congruent and parallel.
The following 5 examples will show that a quadrilateral is a parallelogram:
Demonstrate the congruence of the opposing sides.Show that the two opposing angles are similar.demonstrate the parallelism of the two sides.Show that adjacent angles add up to 180 degrees to be supplementary.Show that a given angle complements both of its adjacent angles.Know more about parallelograms
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What is the round of of 39 nearest 10?
The round of 39 nearest 10 is 40. Rounding is a mathematical process of estimating a number by replacing it with an approximate value that is close to the original number. For example, if the number is 39, it can be rounded to the nearest 10, which is 40.
Rounding is a useful mathematical process used to simplify a value. It involves replacing a number with an approximate value that is close to the original number. To round a number to the nearest 10, begin by examining the digit to the right of the ones place. If it is 5 or greater, round up to the next 10. If the digit is 4 or less, round down to the nearest 10. For example, to round 39 to the nearest 10, look at the digit in the ones place which is 9. Since 9 is greater than 5, round up to the next 10, which is 40. In summary, to round 39 to the nearest 10, the answer is 40.
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What type of language is used in the passage below?
Everyone is going crazy over "Weav-eo Bracelets," the new rubber band bracelet craft. Kids all over the country are
weaving and trading bracelets made of vibrant colors. Don't be left out! Get your Weav-eo Bracelet kit today.
O fictional
Ologic
3explanatory
O persuasive
The passage is using persuasive language to encourage readers to purchase the Weav-eo Bracelet kit. It is emphasizing the popularity of the craft and the vibrant colors of the bracelets in order to entice readers to buy the kit.
What is persuasive?Persuasive writing is a form of writing in which the author uses words and phrases to convince the reader to believe in a particular point of view. It is often used in advertising, speeches, and political campaigns. It is used to convince the reader to take a certain action, or to agree with a particular idea or opinion. The main goal of persuasive writing is to influence the reader’s opinion in some way. To achieve this, writers must use strong arguments, clear language, and emotional appeals. The writer must also make sure that the argument is logical and supported by evidence.
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Use substitution to solve the system of equations.
y=3x−34
y=2x−5
Answer:
(x, y) = (29, 53)
Step-by-step explanation:
You want to solve this system of equations by substitution:
y = 3x -34y = 2x -5SolutionSubstituting the first equation's expression for y into the second equation, we have ...
3x -34 = 2x -5
x = 29
Then substituting for x in the second equation gives ...
y = 2(29) -5 = 53
The solution is (x, y) = (29, 53).
<95141404393>
Please help me on this
Answer:
1.
2.
Step-by-step explanation:
V and Y aren't congruent bc V and Z are
A flower bed is 2 meters wide and 4 meters long. What is the area of the flower bed in square feet? Round intermediate calculations and your answer to the nearest hundredth.
The area of the flower bed is about ______ square feet.
I just need the answer not a explanation
Answer:
Step-by-step explanation:
0.305 meters I think almost positive. Hopes this helps!!!