The equation y = x² represents a parabola as a curve
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The equation y = x² represents a parabola as a curve
The equation is given as:
y = x²
The above equation has a degree of 2
Polynomials that have a degree of 2 are referred to as quadratic equations
The curve of a quadratic equations are called parabola
Hence, the equation y = x² represents a parabola as a curve
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solve this system of equations by using the elimination method.
x+2y=4 x+3y=10
Answer: The elimination method is a method for solving a system of equations by eliminating one of the variables. One way to do this is to multiply one equation by a constant and then add or subtract it from the other equation to cancel out one of the variables.
We will start by multiplying the first equation by -1:
x + 2y = 4 ----> -x - 2y = -4
Now we will add the second equation to the modified first equation:
-x - 2y = -4
(x + 3y = 10)
0x + 1y = 6
Now we can solve for y:
y = 6
Now that we know y = 6, we can substitute this back into one of the original equations, for example the first one:
x + 2y = 4
x + 2(6) = 4
x = -8
So the solution to the system of equations is x = -8 and y = 6
Therefore, the solution is (-8,6)
Step-by-step explanation:
Compute the probability of being dealt at random and without replacement a 13-card bridge hand consisting of: (a) 6 spades, 4 hearts, 2 diamonds, and 1 club; (b) 13 cards of the same suit.
The probabilities are found to be 0.00196 in case- 1 and
1 / 158753389900 in case - 2.
Note that there are a total of 52 cards in bridge, so by combinations that there are a total of
(13
52) numbers to deal 13 cards. There are a total of 13 spades, hearts, diamonds and clubs, respectively, so there are
(13
6) ways to get spades, etc., so that by multiplication principle the probability in we're looking for:
( a ) ( 13 (13 (13 (13
6) 4) 2) 1)
(52
13)
= 1716x715x78x13 / 635013559600
= 0.00196.
( b) there are a total of 4 drawings where all 13 cards are are of the same suit, corresponding to a choice of either spades, hearts, diamond, or clubs. Therefore the probability here is given by :
4 / ( 52 = 4/ 635013559600
13)
= 1 / 158753389900 .
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The sum of the differences between sample observations and the sample mean is
a. Zero
b. The range
c. The mean deviation
d. The standard deviation
The sum of the differences between sample observations and the sample mean is zero.
Statistics is a science that deals with methods of collecting data, processing data, presenting data, analyzing data, drawing conclusions, and making reasonable decisions based on existing facts.
There are some terms that are frequently used in statistics:
Range is the difference between the largest and the smallest values in a data set;Mean is the average of the sample values;Mean deviation is the average deviation of the data from the mean;Variance is a measure of how far the data is spread from its average value, which is equal to the average distances of the sample observations from the sample mean;Standard deviation is a value used to determine the distribution of data in a sample and see how close the data is to the mean value. The standard deviation is equal to the square root value of the variance.The sum of the differences between sample observations and the sample mean can be denoted as ∑(xi - mean), where n is the size of the sample and i = 1,2,3,...,n
∑(xi - mean) = ∑xi - n*mean,
= n*mean - n*mean
= 0
Thus the sum of the differences between sample observations and the sample mean is zero.
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y varies jointly with x and the square of z
The equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 is Y= 11/14 xz^2.
How can the equation of variation be determined?The concept that will be used here is variation.
since Y varies jointly with respect to z^2 and x the we will introduce K which is the proportionality constant, then we have:
Y= Kxz^2.
The we can introduce Y, x and z to solve for the single unknown and have the answer for the equation of variation.
231=K (6) (7^2)
231=6*49*K
231=(K*294)
231/294=K.
K = 11/14
We can have Y= 11/14 xz^2 which is the equation of variation.
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complete question:
Find an equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 the equation of varation is y
FILL IN THE BLANK for a positive angle, the rotation from the initial side to the terminal side takes place in a ______direction. For a negative angle, the rotation takes place in a _______direction. (?;?)
For a positive angle, the rotation from the initial side to the terminal side takes place in a counter clockwise where as for a negative angle, the rotation takes place in a clockwise.
In math the term angle is defined as a figure in which two rays emerge from a common point and this is called the vertex of the angle and the two rays forming the angle are called its arms or sides.
Here we have to know that the angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.
Here we need to find the missing term in the given statement.
According to the definition of angle we have know that the rotation is measured from the initial side to the terminal side of the angle.
If it has Positive angles result from counterclockwise rotation, and negative angles result from clockwise rotation.
Here we have know that the angle with its initial side on the x‐axis is said to be in standard position.
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Whats BD? Please help. Thanks
The value of side BD of the kite is 12 units
How to find the value of side BD of the kite?
In mathematics, kite is a quadrilateral which has two pairs of congruent adjacent sides.
A kite is a geometric shape which is symmetrical. It has two pairs of congruent adjacent sides, and two pairs of congruent opposite angles. The diagonals of a kite are perpendicular bisectors of each other.
Using Pythagoras theorem:
BC² = CE² + BE²
BE = √(BC² - CE²)
BE = √(10² - 8²) = 6 units
Since ΔCDE is identical to ΔBCE.
Thus, DE = BE
DE = 6 units
Since BD = BE + DE
Thus, BD = 6 + 6 = 12 units
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What expression is equivlent to -4(3x-5)?
The answer to this question is -12x+20
two dimensions of a right triang;e are 5 units and 13 units. a student writes tje equation 5^2 13^2
The equation is incorrectly written by the student to find the third side of the triangle.
The right triangle states that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or a right triangle.
(Hypotenuse)² = (Base)² + (Altitude)²
If the two sides are right angle triangle is 5 units and 13 units and the equation is 5²+13²=c² then the value of c is
c=√25+169
c=13.92 and 13.92 is not an integer number.
so, the equation written by the student to find the third side is incorrect.
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 - Tanner's beaker had 45 milliliters of water in it at first. After each of his friends poured in 8 milliliters, the
beaker contained 93 milliliters. How many friends poured water into Tanner's beaker?
Answer:
x=6
Step-by-step explanation:
hope this helps you with your question
9 Show that efficiency E, the force ratio (MA) and the velocity ratio (VR) of a machine are related by the equation MA E= × 100%. VR The efficiency of a machine is 80%. Determine the work done by a person using this machine to raise a load of 200 kg through a vertical distance of 3.0 m (Take g = 10 ms ).show your workings
The Work done by a person is 24 x 103 J.
What is defined as force ratio and velocity ratio?Force ratio is the ratio of two forces. It is often used in the context of mechanics, where a force is the product of mass and acceleration, and is measured in newtons (N).
Velocity ratio, on the other hand, is the ratio of two velocities. It is also used in mechanics and is measured in meters per second (m/s).
Force ratio and velocity ratio are closely related, as they are both used to measure mechanical properties of an object.
Force ratio is used to measure the ratio of two forces acting on an object, while velocity ratio is used to measure the ratio of two velocities.
Both force ratio and velocity ratio can be used to analyze the movement of an object, as well as its response to external forces.
Force ratio and velocity ratio are important concepts in mechanics, as they can help to analyze the dynamics of an object and its behavior over time.
Let M.A. = F1 and V.R. = F2
E = M.A. x 100% V.R.
Substituting the given values,
E = 80 = F1 x 100% F2
Work done by a person = Force x Displacement
= F1 x F2 x 200 kg x 3.0 m
= (80 x 100%) x 200 kg x 3.0 m
= (8 x 103) N x 3.0 m
= 24 x 103 J
Work done by a person = 24 x 103 J
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The table shows the balance of Rob’s checking account at the end of the day. This is $95.50 less than the amount he had the beginning of the day.
Which of the following equations can be used to determine Rob’s account balance at the beginning of the day?
a. x has an average of 5 and a standard deviation of 80. b. x has a bell shaped distribution with an average of 5 and a standard deviation of 80. c. x has a uniform distribution with an average of 80 and a standard deviation of 5. d. x has a bell shaped distribution with an average of 80 and a standard deviation of 5. e. secret statisticians code meaning that ohio state graduates are morons. 10 points question 2 what is the notation for the following (in matching order): standard deviation of a population, average of a sample, a set of sample averages, mean of a population, standard deviation of a sample, is distributed, bell shape a. s, mu, sampling distribution, x-bar, sigma, ~, n b. sigma, x-bar, sampling distribution, mu, s, n, ~ c. sigma, x-bar, sampling distribution, mu, s, ~, n d. s, x-bar, sampling distribution, mu, sigma, ~, n 10 points question 3 what is the meaning of x-bar ~ n(80,1) a. the random variable x is distributed with a bell shape, an average of 80 and a standard deviation of 1. b. the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1. c. the random variable x is distributed with a bell shape, an average of 1 and a standard deviation of 80. d. the set of x-bars is distributed with a bell shape, an average of 1 and a standard deviation of 8
The answer to question 1 is not a statistical question. The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
Question 1: e. secret statisticians code meaning that ohio state graduates are morons.
This is not a statistical question and does not have a correct answer.
Question 2: c. sigma, x-bar, sampling distribution, mu, s, ~, n
The notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape).
Question 3: b. the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
The notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
The answer to question 1 is that it does not have a correct answer as it is not a statistical question. The answer to question 2 is that the notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape). The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
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which statement is true? a. the graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g. b. the graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g. c. the graph of
The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
The graph of a function is a visual representation of the function's mathematical relationship between inputs and outputs. When a function is said to be "stretched", this means that the graph is being transformed in some way. In this case, the graph of function f is being stretched vertically by a factor of 3 to create the graph of function g. This means that the vertical distance between each point on the graph of function f will be 3 times as great on the graph of function g. For example, if the graph of function f has a point (1,2) then the corresponding point on the graph of function g would be (1, 6). This transformation will change the shape of the graph and the values of the inputs and outputs of the function. The graph of the transformed function g will be wider, taller, and have different values for the inputs and outputs.
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MP Reason Hugo walk5/6 mile from his home to the library on
Monday. He walks 1/3 mile from his home to the park on Tuesday.
• How much farther does he walk on Monday than on Tuesday?
• Is your answer reasonable? Explain.
He travels 2.5 times as farther on Monday than on Tuesday.
How to obtain the ratio between the distances?The ratio between the distances is obtained applying the proportions in the context of this problem, as the Monday's distance is divided by the Tuesday's distance.
It gives how much farther he traveled on Monday than on Tuesday.
Then the ratio is given as follows:
(5/6)/(1/3) = 15/6 = 2.5.
(the ratio between two amounts is obtained dividing the two amounts).
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Step It Out 12 Find the product. Identify any properties that you used. A. (4)(-0.5)(-3) (-3) Turn Tused the order of operations and multiplied from The product is even / odd. B. (-)(-7X(-9) =) (-)(-9) because the number of negative factors is -O) -00 (3) = -21 89 to I used the the order of the factors, and then I used the Property of Multiplication to group factors to make the multiplication easier. The product is because the number of negative factors is even / odd Property of Multiplication to switch
The solution to the product is -18 and the property is negative factors
How to determine the productFrom the question, we have the following parameters that can be used in our computation:
(4)(-0.5)(-3) (-3)
Using the property of negative factors, we have
(4)(-0.5)(3) (3)
Next, we remove the brackets
This gives
4 * -0.5 * 3 * 3
Evaluate the product
-18
Hence, the solution is -18
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The number 1465 rounded to its highest place value is?
A 54-foot long wire will be attached to the top of a pole for support, and will be pulled tight and anchored to the ground.
If the wire makes a 13 degree angle with the ground, how tall is the pole?
The height of the pole used in the question is; 12.15 ft
How to use trigonometric ratios?The 3 main trigonometric ratios are;
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, since the guy wire makes an angle of 13 degrees with the ground, it means the guy wire will be the hypotenuse of the right angle triangle and the height of the pole which we will label as h will be the opposite side of the triangle. Thus;
height/54 = sin 13
height = 54 * sin 13
height = 54 * 0.225
Height = 12.15 ft
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Frank rented a unicycle at the circus. He paid a flat rental fee of $15 plus $2 and hour. The total cost was $23. Write and solve an equation you can use to find the number of hours he rented the unicycle.
Answer:
4 hrs
Step-by-step explanation:
let x = # of hours he rented the unicycle
$15 + ($2/hr)x = $23
($2/hr)x = $23 - $15 = $8
x = ($8) / ($2/hr) = 4 hours
The three interior angles of a triangle measure x°, (x-4)°, and (x+16)°. Which is the measure of one of the three angles?
OA) 48°
O B) 52°
O C) 60°
OD) 70°
=======================================================
Explanation:
Every triangle has the rule where the inside angles add to 180.
(angle1)+(angle2)+(angle3) = 180
x + (x-4) + (x+16) = 180
3x+12 = 180
3x = 180-12
3x = 168
x = 168/3
x = 56
Then we can determine each angle.
angle1 = x = 56 degreesangle2 = x-4 = 56-4 = 52 degrees (choice B)angle3 = x+16 = 56+16 = 72 degreesAs a check:
angle1+angle2+angle3 = 56+52+72 = 180
This confirms the answer is correct.
How do you factor and simplify 4x^2+ 25
Answer:
(4x + 5)(4x + 5)
Step-by-step explanation:
4x * 4x = 4x^2, and 5 * 5 = 25. Thus being 4x^2 + 25
What is the measure of AC
Side AC of the similar triangle system has a length of 6 units. (Correct choice: C)
How to determine the missing length in a system of two similar right triangles
Two triangles are similar when both have congruent angles but sides are not congruent though proportional. In this problem we find the case of two similar right triangles, whose relationship is shown below:
AD / AC = CD / BC = AC / AB
If we know that AD = 4 and AB = 9, then the length of side AC is:
4 / AC = AC / 9
AC ² = 36
AC = 6
The length of side AC is equal to 6 units.
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Find the total surface area
The total surface area is 3994ft sq.
How to find the volume and base's area of a right rectangular pyramid?Suppose the base of the pyramid has length = l units, and width = w units.
Surface area of rectangular prism = 2lb +2lh+2bh
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Given;
Length= 32ft
Breadth= 21ft
Height= 25ft
Now,
Surface area of rectangular prism = 2lb +2lh+2bh
=2*32*21+2*32*25+2*21*25
=1344+1600+1050
=3994
Therefore, the area will be 3994ft sq.
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Issues on which there are competing perspectives are generally most appropriate forpersuasive speeches.A)TrueB)False.
False. A persuasive speech is a type of public speaking that attempts to convince the audience to adopt a certain viewpoint or take a specific action.
While there are often competing perspectives on issues, a persuasive speech is not the most appropriate way to address them. Instead, a better approach to discussing issues with competing perspectives is to use an informative speech. An informative speech provides an unbiased overview of the issue, presenting both sides fairly and objectively. This allows the audience to develop their own opinion on the matter based on the facts presented. Although a persuasive speech may be used to present a particular point of view, informative speeches are the best tool for discussing issues with multiple perspectives.
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What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.
0.11 to 0.21
0.10 to 0.23
0.16 to 0.17
0.11 to 0.16
The 95% confidence interval for this population proportion is (0.10,0.23).
sample size n = 125
number of people planned to take an extended vacation = 21
sample proportion (p) = 21/125 = 0.168
Confidence level = 0.95
significance level (α) = 1-0.95 = 0.05
Z score = Z(0.05) = 1.96, from the Z table.
confidence interval for a population proportion is-
p±Zα/2 *[tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.168± 1.96[tex]* \sqrt{\frac{0.168(1-0.168)}{125} }[/tex]
= 0.168 ± 1.96*0.334
= 0.168 ± 0.0655
= (0.1025, 0.2335)
= (0.10,0.23)
Hence, the confidence interval is (0.10,0.23).
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A parabola can be drawn given a focus of ((7,6) and a directrix of y=-8y=−8. What can be said about the parabola?
The parabola has a vertex at (7 , -1) has a p-value of -0.5 and it opens downwards.
How to interpret the equation of a parabola?The axis of symmetry of a parabola is basically perpendicular to the directrix and contains the focus and vertex.
Thus, the axis of symmetry is the vertical line x = 7.
The vertex lies halfway between the focus and directrix. Thus, we can say that the vertex is (7, (6 - 8)/2) = (7, -1)
Due to the fact that the vertex lies above the focus and the directrix is horizontal, then it means that the parabola opens downward.
Therefore, the focus is (7 - 8)/2 = -0.5 units below the vertex, so, p = -0.5
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HELP PLEASE someone ?????
The answer are assuming the information provided, such as cost per visit, co-payments, admission charge etc . The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.
What is the total cost for Sharon and Franklin family for their deductible, co-payments, and hospital charges?"Sharon Wilson
a. The amount she paid for the deductible is $2,000.
b. In total co-payments, she paid $9 * $35 + $10 * $50 + $15 * $95 + $2 * $5 + $3 * $10 = $1,085 for physician and specialist visits, physical therapy and pharmacy co-payments.
c. In hospital charges, she paid $240 + $54,860 = $55,100.
d. In total costs, she paid $2,000 + $1,085 + $55,100 = $58,185.
The Franklin family
a. They paid $17 * $75 + $9 * $100 + $4 * $90 = $1,865 for physician and specialist visits and physical therapy.
b. They paid $2 * $1,500 + $350 = $3,650 for emergency room visits and ambulance fees.
c. They paid $350 + $21,675 = $22,025 in hospital charges.
d. The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.
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Write the following ratio using two other notations.
6:5
Use only the numbers above (not any others).
Notation one:
Notation two:
0.
3
0=0
0:00 to
0<0 0>
The ratio may be written if it is a component of a percentage.
6 is to 5 is 12 is to 10 .
What is a ratio notation?Ratios can be expressed as a notation, like 1/2, or as a ratio, like 6:5. A ratio's value is determined by dividing the first and second numbers. Consider the ratio 12:10 as an example. "6 to 5" should be read as the ratio. Any fraction, like 6/5, can also be expressed as a ratio, which is written as 6:5.
A colon or a fraction bar are two typical symbols representing ratios. You can also use words.
6 : 5 = 6/5 = 6 to 5
The ratio may be written if it is a component of a percentage.
6 is to 5
as in ...
12 is to 10 what 6 is to 5, and vice versa.
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Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant.
sin(t), cos(t); Quadrant II
sin(t)=_____________
If the terminal point determined by t is in the given quadrant.sin(t), cos(t); sin(t)= -cos(t) in Quadrant II.
In Quadrant II, the sine function is positive and the cosine function is negative. The sine and cosine functions are related by the Pythagorean identity, which states that sin^2(t) + cos^2(t) = 1.
Since the sine is positive and the cosine is negative in Quadrant II, we can square the sine function and subtract it from 1 to get:
1 - sin^2(t) = cos^2(t)
We can then take the square root of both sides to get:
cos(t) = sqrt(1 - sin^2(t))
And since the cosine is negative in Quadrant II, we can then multiply the equation by -1 to get:
sin(t) = -cos(t)
This equation is only valid in Quadrant II.
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1. Is G (cost) a function of t (time)? Explain your reasoning
2. Is t (time) a function of G (cost)? Explain your reasoning.
{G} is the function of {t} and vice - versa is also true.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a graph as shown in the image.
{ 1 } -
Yes, the given function G{t} is the function of {t}. It is a piecewise function.
{2} -
Let the given function is -
y = G{t}
We can find the inverse as -
t = G⁻¹{y}
Yes, {t] is also the function of {G}.
Therefore, it can be concluded that {G} is the function of {t} and vice - versa is also true.
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Select the correct answer from each drop-down menu.
Consider the function f(x) = |₂³| − 1.
The piecewise functions that coincide with the given function are
[(x + 3)-1, when x is greater than or equal to 3,
[(x-3)/2] -1, when x is less than 3,
[(x+3)/2] -1, when x is greater than -3,
[-(x+3)/2] -1, when x is greater than or equal to -3,
and
Yes, the piecewise functions that coincide with the given function are [(x + 3)-1, when x is greater than or equal to 3, [(x-3)/2] -1, when x is less than 3, [(x+3)/2] -1, when x is greater than -3, and -(x+3)/2] -1, when x is greater than or equal to -3.
Piecewise functionThe piecewise functions that coincide with the given function are as follows: when x is greater than or equal to 3, the piecewise function is (x + 3)-1; when x is less than 3, the piecewise function is (x-3)/2 -1; when x is greater than -3, the piecewise function is (x+3)/2 -1; and when x is greater than or equal to -3, the piecewise function is -(x+3)/2 -1.This means that, depending on the value of x, the resulting value of the function f(x) = |₂³| − 1 will be different.For example, when x is equal to 3, then f(x) = 0; when x is equal to -3, then f(x) = -2; and when x is equal to 1, then f(x) = -1.Thus, the piecewise functions correctly express the given function, as they correctly capture the different values of f(x) for different values of x.No, the piecewise functions that coincide with the given function are[(x + 3)-1, when x is greater than or equal to 3,[(x-3)/2] -1, when x is less than 3,[-(x-3)/2] -1, when x is less than or equal to -3,[(x-3)/2] -1, when x is greater than -3.To learn more about Piecewise function refer to:
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