Domain where x is not equal to 3 and a range where y is not equal to 2 for function (x+5)/(x-3)
Domain = Set of all input values of a function.
range = set of all output values of a function.
Given: Domain: x≠3 ; range = y≠2
We do not include a value for domain if it makes the expression indeterminant .
Since all the functions in options are fractions, here the denominator does not equal to 0.
But in option C and D, the denominator can be zero if x=3.
So , domain for then it x ∈ R-3
for option C if 2=2(x+5)/(x-3)
x-3=x+5
-3=5 which is not possible
Where as in option D, 2=(x+5)/(x-3)
2x-6=x+5
x=11
Hence, domain where x is not equal to 3 and a range where y is not equal to 2 for function (x+5)/(x-3)
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Which function has a domain where x does not =3 and a range where y does not =2? A. f(x)=(x-5)/(x+3) B. f(x)=2(x+5)/(x+3) C. 2(x+5)/(x-3) D. (x+5)/(x-3)
what point on number line is 7/9 the way from the point -3.6 to the point 10?
The point on the number line that is 7/9 of the way from -3.6 to 10 is approximately 6.97777777778.
To find the point on the number line that is 7/9 of the way from -3.6 to 10, we can use the following formula:
Point = Starting point + (Fraction of distance) x (Total distance)
In this case, the starting point is -3.6, the total distance is the distance from -3.6 to 10 (which is 10 - (-3.6) = 13.6), and the fraction of distance is 7/9.
Plugging in these values, we get:
Point = -3.6 + (7/9) x (13.6)
Simplifying,
Point = -3.6 + (7/9) x (13.6)
Point = -3.6 + 9.9556
Point = 6.97777777778
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A committee of four people is formed by selecting members from a list of 12 people.
How many different committees can be formed?
__ committees
The number of different committees that can be formed is 495
How many different committees can be formed?From the question, we have the following parameters that can be used in our computation:
People = 12
Committee = 4
These can be represented as
n = 12 and r = 4
The number of different committees that can be formed is
Number = nCr
So, we have
Number = 12C4
Evaluate
Number = 495
Hence, the committee are 495
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Determine whether the graph of the equation is symmetric with respect to the x axis, y axis and or the origin.
X^2 + Y -36 =0
The graph of the equation x² + y - 36 = 0 is symmetric with respect to the y-axis and the origin, but not with respect to the x-axis.
x² + y - 36 = 0
Symmetry with respect to the x-axis:
Replace y with -y: x² - y - 36 = 0
This equation is not equivalent to the original equation, so the graph is not symmetric with respect to the x-axis.
Symmetry with respect to the y-axis:
Replace x with -x: (-x)² + y - 36 = 0
Simplifying, we get x² + y - 36 = 0, which is equivalent to the original equation.
Therefore, the graph is symmetric with respect to the y-axis.
Symmetry with respect to the origin:
Replace x with -x and y with -y: (-x)² + (-y) - 36 = 0
Simplifying, we get x² + y - 36 = 0, which is equivalent to the original equation.
Therefore, the graph is symmetric with respect to the origin.
Hence, the graph of the equation x² + y - 36 = 0 is symmetric with respect to the y-axis and the origin, but not with respect to the x-axis.
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Please help !!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
It does not belong because like the other ones it is not side ways, as well as it's common sense.
A researcher is interested in how client expectations of success before therapy relate to satisfaction with the sessions afterward. Ratings (on a 1-10 scale) for 10 participants are presented in the table below. This dataset will be used for Questions 1-4. Compute the Pearson r correlation coefficient for these data. Note: Show your work on a separate sheet of paper. You will be asked to upload a scan/picture of your work at the end of the test.
Client Expectations (x) Satisfaction (y)
1 3
1 1
2 3
3 7
3 9
4 5
6 8
6 7
7 10
7 7
Questions:
1.) What is the value of the Pearson correlation coefficient (r)? Please round your answer to 3 decimal places.
2.) What would the critical value (rcrit) be for a 2-tailed test with a .05 alpha level using the Client Expectation-Satisfaction dataset shown in Question 1? (Express your answer to 3 decimal places)
3.) Based on the correlation you calculated in Question 1 and the critical value you identified in Question 2, was the correlation statistically significant (i.e., would you reject the null hypothesis)?
1. Using the formula for Pearson correlation coefficient, we have:
x y xy x^2 y^2
1 3 3 1 9
1 1 1 1 1
2 3 6 4 9
3 7 21 9 49
3 9 27 9 81
4 5 20 16 25
6 8 48 36 64
6 7 42 36 49
7 10 70 49 100
7 7 49 49 49
n = 10
sum(x) = 40, sum(y) = 53, sum(xy) = 286, sum(x^2) = 214, sum(y^2) = 506
r = [n(sum(xy)) - sum(x)sum(y)] / sqrt{ [n(sum(x^2)) - sum(x)^2][n(sum(y^2)) - sum(y)^2] }
r = [10(286) - (40)(53)] / sqrt{ [10(214) - (40)^2][10(506) - (53)^2] }
r = 0.832 (rounded to 3 decimal places)
2. The critical value (rcrit) for a 2-tailed test with a 0.05 alpha level and 8 degrees of freedom is 0.632 (using a t-distribution table or calculator).
3. The calculated correlation coefficient (r = 0.832) is greater than the critical value (rcrit = 0.632), which means that the correlation is statistically significant. We would reject the null hypothesis and conclude that there is a significant positive correlation between client expectations and satisfaction with therapy sessions.
The sum of four consecutive integers is 250. What is the greatest of these integers?
The greatest of the given integers is 64.
Given that, the sum of four consecutive integers is 250. We need to find what is the greatest of these integers.
Let the consecutive integers be = x, x+1, x+2, x+3
Therefore,
x + x+1 + x+2 + x+3 = 250
4x + 6 = 250
2x + 3 = 125
2x = 122
x = 61
Therefore, the greatest integer = 61 + 3 = 64
Hence, the greatest of the given integers is 64.
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For the ordered stem-and-leaf plot given, find:
a. the minimum value
b. the maximum value
c. the number of data with values greater than 25.
d. the number of data with values of at least 40.
e. the percentage of the data with value less than 15.
From a stem-and-leaf plot,
1. The minimum value = 13
2. The maximum value = 62
3. The number of data with values greater than 25 = 16
4. The number of data with values of at least 40 = 4
5. The percentage of the data with value less than 15 = 6.25%
We know that on a stem and leaf plot, the minimum is the first value and the maximum is the last value.
From the stem-and-leaf plot,
a) the minimum value is 13
b) the maximum value is 62
c) the number of data with values greater than 25:
26, 27, 28, 28, 31, 31, 32, 34, 34, 35, 38, 39, 42, 43, 47, 62
So, the number of data with values greater than 25 = 16
d) the number of data with values of at least 40:
42, 43, 47, 62
So, the required number = 4
e) the percentage of the data with value less than 15:
the data with values less than 15 are: 13, 14
So, the number of the data with values less than 15 are: 2
The total number of data values = 32
So, the required percentage would be,
P = (2/32) × 100
P = 6.25%
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If the recommended adult dosage for a drug is D (in mg), then to determine the appropriate dosage e for a child of age a, pharmacists use the equation c = 0.0417D(a + 1).
Suppose the dosage for an adult is 150 mg.
(a) Find the slope of the graph of e. (Round your answer to two decimal places.)
P
What does it represent?
The slope represents the Select of the dosage for a child for each change of 1 year in age.
(b) What is the dosage for a newborn? (Round your answer to two decimal places.)
ma
a) The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.
b) The dose for newborn baby is: 6.225 mg
How to interpret the slope?The equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
(a) Let a be an age of an child in years. Then:
c = 0.0417Da + 0.0417D
Where D is a constant
Since D = 150 mg, then we have:
The slope of the graph = 0.0417(150)
= 6.225 mg/year
The slope shows that the appropriate dose c for an older child increases by 6.225 mg if the child is one year older.
(b) Newborn baby: a=0
Thus:
c(0) = 0 + 6.225
= 6.225 mg
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Select the correct answer.
What is √81y6 in simplest form?
A. 3√/9y
B. 9y^4
C.3 √9y^2
D.9y^3
I called at 11:45 pm been on the phone for 1 hour 24 minutes what time did that person hang up
Answer:
If you called at 11:45 pm and were on the phone for 1 hour 24 minutes, the call would have ended at 1:09 am.
A swimming pool is shaped like the figure below. Each end is a semicircle, and the length and width of the rectangle are 60 feet and 30 feet, respectively.
The area of the border is 105.53 feet².
We have,
The swimming pool is a combination of two shapes.
Rectangle:
Length = 60 feet
Width = 30 feet
Area = 60 x 30 = 1800 feet²
Semicircle:
Diameter = 30 feet
Radius = 15 feet
Area = π/2 r² = 1/2 x 3.14 x 15 x 15 = 353.25 feet².
Now,
The area of the swimming pool.
= 1800 + 353.25
= 2153.25 feet²
Now,
Without the border.
Area of the swimming pool.
= rectangle area + semicircle area
= 60 x (30 - 1) + 1/2 x π x (15 - 1)²
= 60 x 29 + 1/2 x 3.14 x 14 x 14
= 1740 + 307.72
= 2047.72 feet²
Now,
The area of the border.
= 2153.25 - 2047.72
= 105.53 feet²
Thus,
The area of the border is 105.53 feet².
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Part B
What do the slope and y-intercept represent?
To change a temperature in degrees Celsius, C, to a temperature in degrees
Fahrenheit, F, the equation F=2C+32 can be used.
Part A
Explain how you know the equation represents a linear function.
The slope represents that: a Fahrenheit degree change is equivalent to a Celsius change of 2 degrees.
The y-intercept of 32 represents that: It is the melting point of water on the Fahrenheit scale.
How to Interpret Linear Functions?The general form of expression of Linear functions in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
Now, the equation is given as:
F = 2C + 32
Thus:
Slope = 2
y-intercept = 32
The slope is 2. This means that a Fahrenheit degree change is equivalent to a Celsius change of 2 degrees.
The y-intercept is 32. This is the melting point of water on the Fahrenheit scale.
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Identify the rule for the function table
y =12 - x
y = x - 12
y = x ÷ 2
y = 2 ÷ x
The rule of the function table is,
⇒ y = 1/2x
Now, We have to given that;
Table is shown in image.
Let two points on the table is, (24, 12) and (12, 6)
Hence, We get;
The equation for table is,
y - 12 = (6 - 12) / (12 - 24) (x - 24)
y - 12 = - 6/-12 (x - 24)
y - 12 = 1/2 (x - 24)
y - 12 = 1/2x - 12
y = 1/2x
Thus, The rule of the function table is,
⇒ y = 1/2x
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The principal P is borrowed at a simple interest rate r for a period of time t. Find the loans future value A or the total amount due at time t
P= 5000
r=4.5%
t = 6 months
The future value or the total amount due at time t for the loan is $5112.50.
To find the future value or the total amount due at time t for a loan with a principal P, a simple interest rate r, and a period of time t, we can use the formula for calculating simple interest;
A=P + (P × r × t)
where; A = future value or total amount due at time t
P = principal amount
r = simple interest rate
t = time period (in years)
Given the values; P = $5000
r = 4.5% (or 0.045 as a decimal)
t = 6 months (or 0.5 years)
We can substitute these values into the formula and calculate the future value;
A = 5000 + (5000 × 0.045 × 0.5)
A = 5000 + 112.5
A = $5112.50
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Few families can survive on a single salary.
Please select the best answer from the choices provided
T
F
Few families can survive on a single salary is true statement
Many families rely on dual incomes to make ends meet, especially in areas with high living costs.
However, there are still many families that rely on a single salary to support themselves.
While it may be challenging to make ends meet on a single salary, it is still possible for families to survive and even thrive in these circumstances.
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Give me the domain and range
Tell me if the graph is a function or not
The domain and range of the graph are domain = [-2, 5] and range is [-6, 2] and the graph is not a function
Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the x values to be
x = -2 to 5
On the graph, we have the y values to be
y = -6 to 2
This means that domain = [-2, 5] and range is [-6, 2]
If the graph is a function or notThe graph is the graph of a circle
A circle does not represent a function
Hence, the graph is not a function
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click on the region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2
Answer: The region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2 is the area bounded by the two lines and the x-axis.
Step-by-step explanation:
The function f(x) = 1.85x^2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answer:
I helped you last time so I'll help you again.
Step-by-step explanation:
We can find the average rate of change of f(x) over the interval [10, 20] using the formula:
average rate of change = (f(b) - f(a))/(b - a)
where a = 10 and b = 20.
So, we have:
f(a) = f(10) = 1.85(10)^2 = 185
f(b) = f(20) = 1.85(20)^2 = 740
average rate of change = (740 - 185)/(20 - 10) ≈ 55.5
Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.
What is the slope of the line that passes through
the points (2,-4) and (2, 4)?
A. -3 B.0. C.8. D. Undefined
The line is a vertical line, then the correct option is D, the slope is undefined.
How to find the slope of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope, b is the y-intercept, and x is the variable.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the two points are (2, -4) and (2, 4)
Replacing that we would have a problem, that is because we have the same x-value in both points.
Then we have a vertical line at x = 2.
That line has no defined slope, thus, the correct option is D.
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in a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win.
The calculated value of the probability of winning is 3.06501854e-7
Calculating the probability of winningFrom the question, we have the following parameters that can be used in our computation:
Select 6 numbers out of 39 to win
This means that when a number is selected, the number is returned and the total numbers reduces by 1
i.e. P(Current) = n/(39 - n)
Using the above as a guide, we have the following:
P(Win) = 6/39 * 5/38 * 4/37 * 3/36 * 2/35 * 1/34
Evaluate the product of tthe expressions
So, we have
P(Win) = 3.06501854e-7
Hence, the probability of winning is 3.06501854e-7
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Complete question
In a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win You purchase one lottery ticket What is the probability that you will win?
The probability of winning is
Find the missing side of the triangle . leave your answer in simplest radical form
Answer: B: [tex]\sqrt{65}[/tex]
Step-by-step explanation:
The figure indicates this is a right triangle. As such, we can use the pythagorean theorem:
a^2 + b^2 = c^2
16 + 49 = x^2
sqrt(65) = x
.: x = [tex]\sqrt{65}[/tex]
Circle A has a circumference of 8π/x+2 units and Circle B has a circumference of 4π/x+2 units. What is a simplified expression for the difference in the areas of Circle A and B
The simplified expression for the difference in the area of circle A and B is 12π/(x+2)²
What is area of a circle?A circle is simply a round shape that has no corners or line segments. The area of a circle is expressed as;
A = πr²
The circumference of a circle = 2πr
for circle A;
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
area = πr² = (4/x+2)²π
for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
area =( 2/2x+2)²π
difference = (4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1252 with a standard deviation of 39 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.
(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between
and
A.D.
(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between
and
A.D.
(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between
and
A.D.
a) The range of years centered about the mean in which about 68% of the data in between 1291 or 1213.
b) The range of years centered about the mean in which about 95% of the data in between 1330 or 1174.
c) The range of years centered about the mean in which about 95% of the data in between 1369 or 1135.
We have,
Mean= 1252
Standard deviation= 39
a) The range of years centered about the mean in which about 68% of the data
= 1252 ±39
= 1252 + 39 or 1252 -39
= 1291 or 1213
b) The range of years centered about the mean in which about 95% of the data
= 1252 ± 2(39)
= 1252 + 78 or 1252- 78
= 1330 or 1174
c) The range of years centered about the mean in which about 95% of the data
= 1252 ± 3(39)
= 1252 + 117 or 1252- 117
= 1369 or 1135
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The two tables show the number of copies of album x y and z sold in outlets A , B C and D of w company.
Which outlet sold the greatest amount of copies of album x in July and august
Suppose x, y, z > 1 and integers, let :
p(x, y): x is a factor of y,
q(x, y, z): z = GCF(x, y), and
r(x): x is prime.
Check if the following argument is valid or not.
(∀x)(∃y)(p(x, y) ⇒ r(x)), (∀x)(∀y)(∀z)(¬q(x, y, z)), (∃x)(∀y)(p(x, y) ∨ r(x)).
Therefore, (∀y)(∃z)(∃x)q(x, y, z).
Yes, The argument is valid.
Now, We have;
(∀x) (∃y) (p(x, y) ⇒ r(x))
Means that for any integer x, there exists an integer y such that if x is a factor of y, then x is prime.
(∀x)(∀y)(∀z)(¬q(x, y, z)) means that for any integers x, y, and z, the greatest common factor of x and y is not z.
(∃x)(∀y)(p(x, y) ∨ r(x)) means that there exists an integer x such that for any integer y, either x is a factor of y or x is prime.
Therefore, (∀y)(∃z)(∃x)q(x, y, z) means that for any integer y, there exists integers z and x such that the greatest common factor of x and y is z.
To see why this conclusion follows, consider that if (∀y)(∃z)(∃x)q(x, y, z) were false, then there would be some integer y such that for all integers z and x, the greatest common factor of x and y is not z.
However, this would contradict (∀x)(∀y)(∀z)(¬q(x, y, z)), which states that for any integers x, y, and z, the greatest common factor of x and y is not z.
Therefore, the argument is valid.
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Two forces F₁ and F₂ act on a particle P. The force F₁ is given by F₁ = (-i + 2j) N and F₂ acts in the direction of the vector (i + j). The resultant of F₁ and F₂ acts in the direction of the vector (i + 3j). The acceleration of Pis (3i + 9j) ms 2. At time t = 0, the velocity of Pis (31 -22j) m s´¯¹. Find the speed of P when t = 3 seconds. (4 marks)
The evaluated speed of P is 54.5 m s¯¹, under the condition that two forces F₁ and F₂ act on a particle P. The force F₁ is given by F₁ = (-i + 2j) N and F₂ acts in the direction of the vector (i + j).
To evaluate the speed of particle P when t = 3 seconds, we can apply the equations of motion formulas to calculate the velocity if the acceleration and initial velocity values are already given.
The formula can be derived :
v = u + at
Here,
v = final velocity of the particle,
u = initial velocity of the particle,
a = acceleration acting on the particle
t = time taken.
It is known to us that the acceleration of P is (3i + 9j) ms² and at time t = 0, the velocity of P is (31 -22j) m s¯¹. We can evaluate the initial velocity u by taking the magnitude of (31 -22j) that is
√(31² + (-22)²)
= 39.051 m s¯¹.
Now we can staging all values into the formula
v = u + at
v = 39.051 + (3i + 9j) × 3
v = 39.051 + (9i + 27j)
v = (39.051 + 9)i + (27)j
v = 48.051i + 27j
Then, when t = 3 seconds, the speed of particle P is √(48.051² + 27²)
= 54.5 m s¯¹.
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Define your variables, write a system of equations, use your calculator to solve the system of equations and answer the problem.
A grocer sells milk chocolate at $2.60 per pound, dark chocolate at $4.80 per pound, and dark chocolate with almonds at $5.50 per pound. He wants to make a mixture of 50 pounds of mixed chocolates to sell at $4.71 per pound. The mixture is to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined. How many pounds of each type must he use in this mixture?
10 pounds of milk chocolate, 15 pounds of dark chocolate, and 25 pounds of almond chocolate.
We have,
A grocer sells milk chocolate at $2.60 per pound, dark chocolate at $4.80 per pound, and dark chocolate with almonds at $5.50 per pound.
Let x be the pounds of milk chocolate and y is the number of pounds of of dark chocolate.
So, x + y + (x+y)= 50
2(x+y)= 50
x+y = 25
x = 25 - y
Now, 2.6x + 4.8y + 5.5(x+y)= 50(4.71)
2.6x + 5.5x + 4.8y + 5.5y = 235.5
8.1x+ 10.3y = 235.5
8.1(25-y) + 10.3y = 235.5
202.5 - 8.1y + 10.3y = 235.5
2.2y = 33
y = 15
and, x = 10
Thus, 10 pounds of milk chocolate, 15 pounds of dark chocolate, and 25 pounds of almond chocolate.
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I REALLY NEED HELP LIKE ASAP PLS PLS I HAVE A LOT OF HOMEWORK TO DO PLS ANSWER
5(3n+4n+3) = -125
solve for the value of n pls.
Answer:
n=-4
Step-by-step explanation:
5(3n+4n+3) = -125
First, combine like terms:
5(7n+3) = -125
Then, distribute the 5:
35n+15 = -125
Then, get n by itself:
35n= -140
Then, divide by 35 to get n by itself:
n = -140/35
Simplify
n = -4
о
What are three things that your
personality test can tell you?
Choose three answers.
How you prefer to interact with
others
How to break up with a partner
What you might enjoy in a career
1/3
How you rocharge your onoray
The three things that a personality test can tell you are:
A. How you prefer to interact with others.
C. What you might enjoy in a career.
D. How you recharge your energy.
What is personality test?A personality test is a tool used to assess and measure an individual's traits, characteristics, and patterns of behavior.
It may be a series of questions or statements that the individual must respond to.
The results are used to determine the person's strengths and weaknesses, their communication and social interaction (like if they are extrovert or introvert), how they process information and decision-making, etc.
They can also tell of an individual's preferred methods of finding balance in their lives, like spending time alone or with friends and families, being in nature, etc.
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Consider the quadratic function f (x) = 2x² - 16x + 24. Complete the square to rewrite the function in the form
f(x)= a(x-h)² + k.
f(x) =
The quadratic function f(x) = 2x² - 16x + 24 can be rewritten in the vertex form f(x) = 2(x - 4)² + 4.
What is the vertex form of the given function?Given the function in the question:
f(x) = 2x² - 16x + 24
To determine the vertex form f(x) = a(x-h)² + k, we need to complete the square.
Factor out the leading coefficient of 2:
f(x) = 2x² - 16x + 24
f(x) = 2(x² - 8x + 12)
To complete the square, we need to add and subtract the square of half of the coefficient of x:
f(x) = 2[(x² - 8x + 16) - 4] + 8
Since (x² - 8x + 16) is a perfect square trinomial, we factored as (x - 4)².
f(x) = 2[(x - 4)² - 4] + 8
Now we can simplify and rewrite in the desired form:
f(x) = 2(x - 4)² - 4 + 8
f(x) = 2(x - 4)² + 4
Therefore, the vertex form is f(x) = 2(x - 4)² + 4.
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