The absolute value of a number is the non-negative distance between the number and zero on a number line, regardless of sign.
This means that the absolute value of a negative number is always positive. Therefore, if a and b both are negative numbers, their absolute values will be positive numbers. If a is greater than b, then the absolute value of a must be greater than the absolute value of b. This can be expressed mathematically as follows:
|a| > |b|
This equation states that the absolute value of a is greater than the absolute value of b. In other words, the distance between a and zero is greater than the distance between b and zero on a number line.
To illustrate this, let’s take an example of two negative numbers, a=-3 and b=-5. The absolute values of these two numbers are 3 and 5 respectively. Since 3 is greater than 5, the absolute value of a is greater than the absolute value of b. This holds true regardless of the sign of the numbers, as long as a is greater than b.
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Solve the word problem below. Enter your answer as a fraction in simplest
terms, using the slash (/) as the fraction bar.
If of all books at a library are nonfiction and of the nonfiction books are
4
biographies, then what fraction of the library's books are nonfiction
biographies?
Answer:
Step-by-step explanation:
Answer:
4/25
Step-by-step explanation:
There are a total of 25 books at the library, of which 4 are nonfiction biographies. Therefore, 4 out of the 25 books are nonfiction biographies, which can be expressed as the fraction 4/25.
Suppose that ΔFAR is similar to ΔSUN. : Identify the corresponding sides.
FA is the corresponding side to SU
AR is the corresponding side to UN
RF is the corresponding side to NS
What are Corresponding Sides ?
Corresponding sides are the sides that are in the same position in any different 2-dimensional shapes. For any two polygons to be congruent, they must have exactly the same shape and size. This means that all their interior angles and their corresponding sides must be the same measure. For any two polygons to be similar, the ratios of the lengths of each pair of corresponding sides must be equal.
In the below-given images, the two triangles are congruent and their corresponding sides are color-coded.
In the above two triangles ABC and XYZ,
AB is the corresponding side to XY
BC is the corresponding side to YZ
CA is the corresponding side to ZX
Similarly , if ΔFAR is similar to ΔSUN
then ,
FA is the corresponding side to SU
AR is the corresponding side to UN
RF is the corresponding side to NS
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2)
Two triangles on the coordinate plane are shown below.
C
Part A. What transformation (s) could be applied to map
triangle EBD onto triangle CBA?
Part B. Once the transformation is completed, how can you
determine if the two triangles are congruent?
Two triangles are congruent because the sides of two triangles and angles are congruent and the transformation applied to map triangle EBD onto triangle CBA is rotation of 90 degrees.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
There are two triangles in the coordinate plane.
Triangle ABC and triangle EBD are in plane.
We need to find the transformation applied to EBD onto triangle CBA.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
The triangle EBD undergoes a rotation of 90 degrees in clockwise direction to get triangle CBA.
The two triangles are congruent because the sides of two triangles and angles are congruent. So we conclude that the two triangles are congruent.
Hence, rotation of 90 degrees is the transformation (s) could be applied to map triangle EBD onto triangle CBA.
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What is the graph of y² 4x?
The graph of y² 4x is a parabola with vertex (0,0) and x- and y-intercepts (0,0). The graph opens downward and can be written as y=4x².
The graph of y² 4x is a parabola in the shape of a "U" that opens downward. This parabola can be written in the standard form of y=a(x-h)²+k. In this case, a=4, h=0, and k=0. This means that the equation for the graph of y² 4x is y=4x².
To calculate the graph, we must first determine the vertex, which is the point of the parabola that has the maximum or minimum value. To do this, we use the formula for the vertex of a parabola, which is (h,k)=(-b/2a,f(h)). With a=4 and b=0, the vertex of the parabola is (0,0).
We can then calculate the x-intercepts, which are the points at which the graph of y² 4x crosses the x-axis. To do this, we set y=0 in the equation y=4x² and solve for x. This gives us x=±√(0/4) or x=0. This means that the x-intercepts of the graph of y² 4x are (0,0).
Finally, we can calculate the y-intercept, which is the point at which the graph of y² 4x crosses the y-axis. To do this, we set x=0 in the equation y=4x² and solve for y. This gives us y=0. This means that the y-intercept of the graph of y² 4x is (0,0).
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A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 15 minutes. air traffic control approved a new flight plan that will allow her to arrive two times faster than she calculated in her original flight plan. let x represent the time, in minutes, of her original flight. create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
The equation y= 2x-15 can be used to estimate how many minutes will pass after 4:00 pm until she reaches her destination.
The following equation can be used to estimate how many minutes after 4:00 p.m. the pilot will reach her destination:
y = 2x - 15
This equation represents the number of minutes after 4:00 p.m. the pilot will arrive at her destination. The variable x represents the time, in minutes, of her original flight, and y represents the number of minutes after 4:00 p.m. she will arrive at her destination. The expression "2x" represents the time the pilot will arrive at her destination if she had traveled at twice her original speed, and the "-15" represents the delay caused by air traffic.
To solve this equation, you would substitute the value of x into the equation and solve for y. For example, if the pilot's original flight time was 60 minutes, the equation would be:
y = 2(60) - 15
= 120 - 15
= 105
This means that the pilot will arrive 105 minutes after 4:00 p.m., or at 5:45 p.m.
The complete question is:-
A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 15 minutes. Air traffic control approved a new flight plan that
will allow her to arrive two times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation
that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
y = 2x + 15
©y=-*x+15
y = x-15
y = 2x - 15
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In 1990, the postal rate was 25 cents for the first ounce and 20 cents for each additional ounce or part of an ounce. What did it cost to mail a package that weighed 6.8 ounces?
Answer:
$1.41
Step-by-step explanation:
0.20 * 5.8 ounces = $1.16
0.25 * 1.16 = $1.41
The mail weighing 6.8 ounces cost 145 cents
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given here, the first ounce cost 25 cents and all subsequent ounces or parts of an ounce cost 20 cents each
therefore cost of the first ounce = 25
and cost of 5.8 ounces = 20× 6
= 120 cents
thus total cost is 120+25 =145 cents
Hence, the total cost to mail a package is 145 cents
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Is 800 a passing SAT score?
In 2015, about 895. 5 million passengers traveled by plane in the united states. Which value is the best estimate of the number of passengers?.
As per the unitary method, the best estimate of the number of passengers is 9 x 10⁸
the term unitary method in math is defined as the quantity of one object when the quantity of another object and the ratio between two are given.
Here we have given that in 2015, about 895. 5 million passengers traveled by plane in the united states.
And we need to find the best estimate of the number of passengers
While we looking into the given question, we know that the about 895. 5 million passengers traveled by plane in the united states.
So, it can be written as,
=> x = 895.5 million
Here we know that 1 million = 1 x 10⁶
So, it can be rewritten as the number of passengers as,
=> x = 895.5 x 10⁶
Here we have to round off the values, then we get
=> x = 900 x 10⁶
When we further simplify this then we get
=> x = 9 x 10⁸
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Help with this question
The theoretical and experimental probabilities are equal.
What is probability?Probability determines the likelihood of a random event occurring. The ratio of the number of favorable outcomes to the total number of possible outcomes is known as theoretical probability.
Theoretical probability = number of odd sides/ die sides
Here given that the numbers that are odd comes 6
So,
6/20 = 3/10 theoretical probability
The outcome of an experiment that has been repeated multiple times is used to calculate experimental probability.
Experimental probability = number of times Tani landed on a odd number divided by the number of times the experiment was performed
6/ 20= 3/10.
Therefore here , both experimental and theoretical probabilities are equal.
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literally anybody help me please!! all you have to do is find the slope on the graph. PLEASE HELP ME ASAP!!
Answer:
m = 3
Step-by-step explanation:
rise over run
Answer:
Hope it helps you ...........
What is the missing term?
What is the factor of x³ 2x² 5x 6?
The factors of x³ 2x² 5x 6 are two binomials. The first binomial is x² + 2, and the second binomial is x + 3. These two binomials can be multiplied together to get the original equation, x³ 2x² 5x 6.
To find the factors of x³ 2x² 5x 6, we need to use the factorization process. This involves breaking down the equation into its prime factors. First, we need to factor out the greatest common factor (GCF) from the equation. The greatest common factor of x³ 2x² 5x 6 is x, so we can factor out x to get x² 2x 5 6. Now, we can use the difference of squares formula to factor out the remaining terms. The difference of squares is (a + b)(a - b). We can use this formula with 2x and 5 to get (2x + 5)(2x - 5). This leaves us with the two binomials (x² + 2)(x + 3). These two binomials can be multiplied together to get the original equation, x³ 2x² 5x 6.
x³ 2x² 5x 6 = (x)(x² 2x 5 6)
= (x)(2x + 5)(2x - 5)
= (x)(x² + 2)(x + 3)
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joe gets a new pair of running shoes. if he runs 1 mile each day in week 1 and adds 1 10 mile to his daily routine each week, what is the total mileage on joe's shoes after week 21?
The total mileage on Joe's shoes after the 21 weeks is 2,457 miles.
What is the total mileage of joe's shoes?The total mileage of Joe's shoes is the sum of all the distance travelled by Joe within the given time of period of 21 weeks.
The distance travelled by Joe in 1 week is calculated as follows;
1 week = 7 daysnumber of miles in a day = 1 miledistance travelled by Joe in 1 week = 1 mile/day x 7 days = 7 miles
The distance travelled by Joe in 21 weeks is calculated as follows;
distance travelled in 21 weeks = ( 7 miles / week ) x ( 21 weeks )
distance travelled in 21 weeks = 147 miles
the number of additional mile added each week = 110 mile
for 21 weeks = 21 x 110 mile = 2,310 miles
The total mileage on Joe's shoes after the 21 weeks is calculated as follows;
total mileage = 2,310 miles + 147 miles
total mileage = 2,457 miles
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a population grows exponentially with a proportionality constant of . how long will it take the population to double?
When population grows exponentially with a proportionality constant, k , this population will take 4.620 time to double.
What is Exponential Growth of a Population?If the population is growing exponentially, the rate of population change is directly proportional to its current size. So assume that the total population at some point in time t is y.
Next, write the differential equation subject to the condition that it increases in proportion to its magnitude. We can get rid of the proportional sign by introducing a constant of proportionality. We then isolate and integrate the variables of the differential equation thus formed and use the initial values to find the value of the constant of proportionality. We have , a population grows exponentially.
The proportionality constant, k = 15% = 0.15
The exponential growth function is y = y₀ eᵏᵗ
where y₀ --> initial population or at t = 0
k --> proportionality constant
t --> time
y --> is value of y at any t
let there be population y₀ at t = 0 . Then, we have to calculate how much time take the population to double.
2 yo = yo e⁰·¹⁵ᵗ
=> 2 = e⁰·¹⁵ᵗ
Introducing natural logarithms on both sides of above equation,
=> ln (2) = ln ( e⁰·¹⁵ᵗ )
=> ln (2) = 0.15t ( since ln e = 1)
=> t = ln(2)/1.5 = 4.620
Hence, required time is 4.620.
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To find out how much raw material will be removed from a product your company manufactures, find the common denominator needed to subtract the following fractions. The common denominator is _____ five-sixths minus two-sevenths.
The common denominator needed to subtract the given fractions is 42.
Given that,
5/6 - 2/7
The denominator is the number that is placed below the horizontal line of a fraction. It is the bottom number of a fraction that shows the total number of equal parts an object is divided into.
Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators the same first and then subtract them.
Here, the LCM of denominators 6 and 7 is 42.
Now, 35/42 - 12/42
= 23/42
So, the common denominator is 42.
Hence, the common denominator needed to subtract the given fractions is 42.
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The quantity written below a fraction's horizontal line is known as the denominator. The total number of equally spaced sections into which an object is divided is indicated by the bottom number of a fraction.
When subtracting fractions, it's possible to use either the same or distinct denominators for two or more of the fractions. While unlike fractions must first have their denominators made the same before being subtracted, like fractions can be done so immediately.
The LCM of denominators 6 and 7 in this case is 42.
Now, 35/42 - 12/42
= 23/42
Therefore, 42 is the common denominator.
Consequently, 42 is the common denominator required to remove the provided fractions.
a spring with spring constant 2.5×104 n/m has a 1.4-kg cart at its end.
The frequency of oscillation for the spring with the constant value of 2.5×10⁴ is 0.0012
The term frequency is defined as the number of waves that pass a fixed point in unit time and it is also known as the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.
Here we have given the following values,
Spring constant = 2.5 × 10⁴
And the weight of the cart = 1.4 kg
Now, we have calculated the value of the frequency of oscillation as,
=> v = 1/T
Here T refers the time period.
Where it can be rewritten as,
=> 1/2π x √(k/m)
Now, we have to apply the values on it then we get
=> 1/2π x √(1.4/2.5 x 10⁴)
=> 0.1592 x 0.0074
=> 0.0012
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A circular clock has a minute hand that rotates from the center of the clock. This distance from the point on the minute hand from where it rotates to its end is 12 centimeters. Find how far the end of the minute hand moves in 20 minutes.
The distance the 12 centimeters minute hand moves in 20 minutes obtained by converting the angular motion to translational motion is about 25.133 centimeters
What is an angular motion?Angular motion is the circular motion of an object around a point or location.
The complete 360° rotation of the minute hand = 60 minutes
Therefore;
60 minutes is equivalent to 360°
1 minute is equivalent to 360°/60 = 6°
20 minutes is equivalent to 20 × 6° = 120°
The circular path motion following an angular rotation of angle theta = Radius × Theta
Where, theta is in radians
The radius of the minute hand = 12 centimeters
360° = 2•π radians
120° = 360°/3 = (2•π/3) radians
The distance moved by the the minute hand = 12 cm × (2•π/3) radians = 8•π cm
8•π cm ≈ 25.133 cm
The distance the minute hand moves in 20 minutes is about 25.133 cm
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How many cans of paint are needed to cover an area?
We need 6 cans of paint are needed to cover an area of 2 200 square units.
In this question we need to find the number of cans of paint needed to cover an area of 2 200 square units.
We have been given one can of paint covers an area of 400 square units.
Let x cans of paint are needed to cover an area of 2200 square units..
1 can = 400 square units
x cans = 2200 square units
Bu Unitary method,
x = 2200/400
x = 22/4
x = 11/2
x = 5.5
x ≈ 6
Therefore, six cans of paint are needed to cover an area of 2 200 square units.
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A complete question is:
How many cans of paint are needed to cover an area of 2 200 square units if one can of paint covers an area of 400 square units?
How do you know if there is no solution or infinite solutions?
There are countless possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable. If we try to solve an equation and receive a variable or a number equal to itself, there are infinitely many solutions to the equation.
Single-solution equations:
Some equations only have one precise solution. The variable in these equations can only take on one value in order for the equation to be true. When you solve an equation and the result is a variable equal to a number, you know that the equation only has one solution.
Example: For x, find the solution to the equation 6x-3=21.
6x \s= 24
To both sides, add 3.
x \s= 4
Subtract 6 from both sides.
For a single value of the variable, x=4, the equation is true. Consequently, there is only one solution to the equation 6x-3=21
Non-solvable equations:
There are certain equations with no answers. These equations don't have a value for the variable that would make them true. If you attempt to solve an equation and the result is false, the problem has no solutions.
Example: Solve the equation 4x+12=2x+12+2x.
4x+12
= 2x+12+2x
4x+12
= 4x+12 Combine like terms 2x and 2x.
12
= 12 Subtract 4x from both sides.
Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.
Equations that have infinitely many solutions:
The number of solutions to some equations is limitless. When a variable is used in these equations, any value makes the equation true. If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions.
Solve the equation 4x+12=2x+12+2x.
4x+12
= 2x+12+2x
4x+12
= 4x+12 Combine like terms 2x and 2x.
12
= 12 Subtract 4x from both sides
Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.
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a contour map is shown for a function f on the square r = [0, 2] ⨯ [0, 2].
For a contour map as shown in the figure attached, for a function f on the square r = [0, 2] ⨯ [0, 2], estimated value of ∫∫f(x,y)dA using midpoint rule where m = n = 2 is 91 and the average value of f is 22.75.
Using the midpoint rule, the total volume
V ≈ ∑(i=1 to m) ∑(j = 1 to n) f(xij*⁻, yij*⁻)ΔA
where Δx = (b - a)/ m,
Δy = (c - d)/ n and
ΔA = ΔxΔy
Here r = [0, 2] ⨯ [0, 2] and m = n = 2
Therefore a = d = 0 and b = c = 2
Δx = (2 - 0)/ 2 = 1
Δy = (2 - 0)/ 2 = 1
ΔA = 1×1 = 1
∫∫f(x,y)dA ≈ ∑(i=1 to m) ∑(j = 1 to n) f(xij*⁻, yij*⁻)ΔA
= ΔA(f(0.5, 0.5) + f(0.5, 1.5) + f(1.5, 1.5) + f(1.5, 0.5))
= ΔA( 37 + 4 + 27 + 23)
= 1 × 91
= 91
The average value of f
f avg = 1/ A(r) × (∫∫f(x,y)dA)
f avg = 91/ (2×2)
f avg = 22.75
-- The question is incomplete, complete question is given below--
"A contour map is shown for a function f on the square r = [0, 2] ⨯ [0, 2].
a) Use the Midpoint Rule with m=n=2 to estimate the value of ∫∫f(x,y)dA.
b) Estimate the average value of f."
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The function f(x) = -√x is shown on the graph.
714
6
16
5
4
3-
2+
1-
7-6-5-4-3-2-1₁ 1 2 3 4
-2+
2 3 4
-3-
4-
-5
5
-6
5 6 7x
Which statement is correct?
O The domain of the function is all real numbers less
than or equal to -1.
O The range of the function is all real numbers greater
than or equal to 0.
O The range of the function is all real numbers less
than or equal to 0.
O The domain of the function is all real numbers less
than or equal to 0.
Answer:
(c) The range of the function is all real numbers less than or equal to 0
Step-by-step explanation:
You want the true statement describing the domain or range of f(x) = -√x.
DomainThe domain of the function is the set of values x for which the function is defined. The square root is only defined for non-negative arguments:
x ≥ 0 . . . . . . not an answer choice
RangeThe range is of the function is the set of values f(x) that the function can produce. The square root function can produce any non-negative value, so the opposite of the square root function will produce any non-positive value:
f(x) ≤ 0 . . . . . the range is real numbers less than or equal to zero
Simplify:
4y (4y-4)-4(-4y+5+4y ^2)
A. -20
B. 16y^+16y-20
C. 16y^2+16y
D. 16y – 20
Answer:
D. 16y – 20
Step-by-step explanation:
Answer:
-20
Step-by-step explanation:
16y^2-16y-4(-4y+5+4y^2)
16y^2-16y+16y-20-16y^2
16y^2-20-16y^2
16y^2-16y^2-20
-20
7. Which is the following formula solved for a?
x = b + vt + ¹⁄2at²
a. x − b - vt = at²
2
b. a = x − b + vt + ½t²
-
c. a =
d. a =
2(x-b-vt)
2
t
2
b+vt+t²
1/2
Please help meeeee!!!!
Answer:
c.) a = (2(x-b-vy))/t^2
Step-by-step explanation:
Manipulate the given equation to isolate a on the left side:
x=b+vy+(1/2)at^2
x=b+vy+(1/2)at^2
(1/2)at^2 = x-b-vy
at^2 = 2(x-b-vy)
a = (2(x-b-vy))/t^2
Determine if each pair of lines is parallel, perpendicular, or neither.
Answer:
a)perpendicular
b) parallel
c) none
d) parallel
e) none
Step-by-step explanation:
How to find this probability?
To find the probability of an event, you will need to use the probability formula
which is expressed as P(Event) = Favorable Outcomes/Total Outcomes = x/n. You can calculate the probability by dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1, as the favorable number of outcomes can never cross the total number of outcomes, and the favorable number of outcomes cannot be negative.
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What is equidistant in coordinate geometry?
A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.
For a triangle the circumcentre is a point equidistant from each of the three vertices. Every non-degenerate triangle has such a point. This result can be generalised to cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant from the points of tangency of the polygon's sides with the circle.
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Use the formula to solve the problem. Area of a trapezoid = (1/2)(a + b)h, where a and b are the lengths of the two parallel sides and h is the altitude. The area of a trapezoid is 375 m2. If the two parallel sides are 20 m and 30 m, respectively, what is the altitude of the trapezoid? altitude, h = m.
Answer:
h = 1.25m
Step-by-step explanation:
a=20m, b= 30m
Area = (½) (a+b) (h)
375= ½ (20+30) h
375= 300h
300h = 375
h= 375÷300
= 1.25m
choose the correct snapshot graph d(x,t=0s) of this wave at t=0s.
The snapshot of the graph of the function d(x, t=0s) of the wave is illustrated below.
The term function in math referred as a relation between a set of inputs having one output each.
Here we have given that d(x,t=0s) of this wave at t=0s.
And we need to find graph of the function
While we looking into the given question we have identified that the history graph of the wave is given at distance is written as,
=> x=2m
Then the velocity of the wave is given as v= 1 m/.sec
Here we have identified the wave is traveling to the right.
Then snapshot graph shows the displacement of the wave with respect to the position at a given time whereas a history graph shows the displacement of the wave with respect to the time at a given position.
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What is the coefficient of x² in 5x²y?
The coefficient of the variable x squared is number 5.
What are the coefficients?
The coefficients are the numbers on the left side or before each variable.
What is an algebraic expression?Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In this problem we have an expression given by:
5x²y
And we want to know what is the coefficient of x²
5 is the coefficient
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Does I 2 equal 1 or?
The value of "i" squared results in:
(-1) = i²
What are numeric sets?Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.
Complex NumbersAmong the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
√(-1) = i[√(-1)]² = i²(-1) = i²
Learn more about complex numbers at:
brainly.com/question/12241782
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