We can say that after answering the offered question Therefore, the proportionality constant of proportionality in this scenario is 11.25.
what is proportionality?Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two remains constant at all values. The diameter and circumference of a circle serve as an example.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
As a result, the proportionality constant in this scenario is 11.25.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
Therefore, the constant of proportionality in this scenario is 11.25.
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A road is5/9 of a mile long. A crew needs to repave 2/3 of the road. How long is the section that needs to be repaved?
The sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.
The length οf the rοad is 5/9 οf a mile.
Tο find the length οf the sectiοn that needs tο be repaved, we can multiply
the length οf the rοad by the fractiοn that represents the fractiοn οf the rοad that needs tο be repaved:
length οf sectiοn tο be repaved = (2/3) * (5/9) mile
Multiplying the numeratοrs and denοminatοrs separately, we get:
length οf sectiοn tο be repaved = (2 * 5) / (3 * 9) mile
Simplifying the fractiοn, we get:
length οf sectiοn tο be repaved = 10/27 mile
Therefοre, the sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.
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Suppose - 2x²-20x-51 ≤ f(x) ≤ 2x²+20x +49 for all x values near -5, except possibly at -5.
Evaluate lim f(x).
X→-5
By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.
What is the squeeze theοrem ?The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.
We have the inequality:
-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49
We can rewrite this inequality as:
-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1
Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.
As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:
-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1
0 ≤ lim f(x) ≤ 1
Therefοre, by the squeeze theοrem, we have:
lim f(x) = 0 as x apprοaches -5.
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a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with garlic rocessed tablet form. Cholesterol levels were measured before and after the treatment. The chan before-after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.1 and a standard devi 16.5. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol afte reatment. What does the confidence interval suggest about the effectiveness of garlic in reducing Cholesterol? Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. E What is the confidence interval estimate of the population mean μ? mg/dL
]Therefore , the solution of the given problem of deviation comes out to be the confidence interval contains both positive and negative values.
Standard deviation : What is it?Statistics uses variance as a gauge of difference. The image of that figure is used to compute the average variance between the collection and the mean. It includes those data points itself into the calculations, unlike many other real measures of variability, by comparing also every figure to the mean.
Here,
Since the population standard deviation is unknown and the sample number is less than 30, we can use a t-distribution to build the confidence interval. The confidence interval's calculation is:
=>CI = x t /2 × (s/n).
Since we need a 99% confidence range, = 0.01 and /2 = 0.005, and (n-1) = (49-1) = 48 is the number of degrees of freedom.
We discover that t/2 = 2.678 using the t-distribution table with 48 degrees of freedom and 0.005 significance level.
When we enter the numbers, we obtain:
=> CI = 3.1 ± 2.678 * (16.5/√49) = 3.1 ± 7.34
The estimated mean net change in LDL cholesterol following treatment, according to the 99% confidence range, is (4.24, 10.44) mg/dL.
We cannot say with 99% certainty that garlic is effective at lowering cholesterol because the confidence interval contains both positive and negative values.
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help with This Math
Answer:
38°
Step-by-step explanation:
this equal to 38° because angle EGD and angle IGJ are corresponding angles
please answer asap for homework
The width of the patio, given the area of the pool and the patio, can be found to be 19. 59 ft
How to find the width ?The area of the pool is said to be equal to the area of the patio which means that to find the width of the patio, you need to find the area of the pool which is :
= 16 ft x 24 ft
= 384 ft ²
The patio is such that the width is the same on every side which makes it a square shaped patio. The width of the patio is therefore:
Width = √ Area of square patio
= √ 384
= 19. 59 ft
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What is the simplified form of the expression the quantity x squared plus 10x plus 21 end quantity divided by 4 times the quantity x plus 7 end quantity?
[tex]\dfrac{x^{2} + 10x + 21}{x + 7} = \dfrac{(x+3)(x+7)}{x + 7} = \bf x + 3[/tex]
___
[tex]x^{2} + 10x + 21 = x^{2} + 3x + 7x + 21 = x(x+3)+7(x+3) = (x+3)(x+7)\\[/tex]
A newspaper editor starts a retirement savings plan in which $275 per month is deposited at the beginning of each month into an account that earns an annual interest rate of 6.4% compounded monthly. Find the value of this investment (in dollars) after 20 years. (Round your answer to the nearest cent.)
Answer:
Step-by-step explanation:
x= 20 (12) =240, Interest%= 6.4, Pv + 0, PMT= 275,temporarily skip FV,P/Y and C/Y= 12,
After 20 years, the value is $133,970.26
The simple interest value of the investment after 20 years is approximately $30,637.45
What do you mean by future value?Future value (FV) is the value of an investment at a future date, based on a series of regular payments (or a lump sum) and assuming a certain interest rate over a period of time. In other words, it's the amount of money an investment will be worth after earning a certain rate of interest over a certain period of time.
What is simple interest?Simple interest is a method of calculating interest on a loan or investment, where interest is only charged on the original principal amount. In other words, the interest is not compounded over time.
In the given question:
We can use the formula for the future value of an annuity:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where: FV = future value
PMT = monthly payment
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values, we have:
FV = 275 x [(1 + 0.064/12)^(12*20) - 1] / (0.064/12)
FV = 275 x (1.00533²⁴⁰ - 1) / 0.00533
FV = 275 x 111.034
FV = 30,637.45
Therefore, the value of the investment after 20 years is approximately $30,637.45.
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i would thank you so much if someone could give me a valid answer please and graph please thank you love
The equation would be y = 0.50x + 10.00, and we have drawn the graph for the same.
What is the graph of the equation?
The graph of an equation is a visual representation of the set of all solutions (points) that satisfy the equation.
To find the equation of the line, we use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
In this case, we are given the slope of the line (0.50) and the y-intercept (10.00), so we can simply substitute these values into the equation:
y = 0.50x + 10.00
This gives us the equation of the line in slope-intercept form. We can use this equation to find the cost of a cab ride for any distance x (in miles) by substituting the value of x into the equation and solving for y (the fare).
Now let's draw the graph of the equation y = 0.50x + 10.00, we get
Hence, the equation would be y = 0.50x + 10.00, and we have drawn the graph for the same.
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WILL GIVE THE BRAINLIEST AND 5 STARS!!!!
The vertices of △ABC are (−6, 2), (−4, 6), and (−2, 2), and the vertices of △DEF are (5,-2), (3, −6), and (1, −2). Which of these sequences of transformations of △ABC exhibit the congruence between the two triangles? Select TWO that apply.
Responses
a rotation of 180° about the origin and a translation of 1 unit left
a rotation of 180° about the origin and a translation of 1 unit left
a reflection across the x-axis and a translation 1 unit right
a reflection across the x-axis and a translation 1 unit right
a rotation of 180° about the origin and a translation of 1 unit right
a rotation of 180° about the origin and a translation of 1 unit right
a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit right
a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit right
a reflection across the y-axis and a translation 1 unit left
a reflection across the y-axis and a translation 1 unit left
a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left
The answer of the given question based on the triangle which is sequences of transformations of △ABC exhibit the congruence between the two triangles the answer is given below,
What is Congruent triangle?Congruent triangles are two or more triangles that have same shape and size. In other words, they have same angles and same side lengths.
The congruence between the two triangles can be exhibited by the following two sequences of transformations:
a) a rotation of 180° about the origin and a translation of 1 unit left
c) a rotation of 180° about the origin and a translation of 1 unit right
Option b) and option e) involve a translation and a reflection that do not preserve orientation, so they do not result in a congruent triangle.
Option d) involves two reflections, which do not commute, so the order matters. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit right, followed by a reflection across the line x = -1, which does not result in a congruent triangle.
Option f) is similar to option d) in that it involves two reflections that do not commute. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit left, followed by a reflection across the line x = 1, which also does not result in a congruent triangle.
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What is the perimeter of △ DEF to the nearest tenth? A. 19.4 B. 20.1 C. 25.3 D. 43.3
Based on the above, the Perimeter of the triangle DEF is 43.3 units
What is an equation?A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, reduction, multiplication, division, exponents, and so forth.
Given the triangle DEF. Using trigonometric ratio:
sin(38) = EF / 18EF = 11.1
Also: cos(38) = DF / 18DF = 14.2
The perimeter of triangle
DEF = DE + EF + DF
= 18 + 11.1 + 14.2 = 43.3 units
Hence, the Perimeter is 43.3 units
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In a certain study, the odds against a car crash on the road are stated as "22:3". What is the probability of a car crash on the road? Enter the probability as a reduced fraction.
Therefore, the likelihood of a vehicle accident just on road is 3/25. The ultimate solution is 3/25 because there is no other way to simplify this fraction.
What is the probability calculation?The probability is typically defined as the proportion of favourable findings to all results inside the poll area. The formula for probability of an event is P(E) = (Number of positive occurrences) (Sample space).
If the odds against a car crash on the road are stated as "22:3", it means that for every 22 unfavorable outcomes (no car crash), there are 3 favorable outcomes (car crash).
The total number of outcomes is 22 + 3 = 25.
Therefore, the probability of a car crash on the road is:
3 favorable outcomes / 25 total outcomes = 3/25
So, the probability of a car crash on the road is 3/25. This fraction cannot be reduced further, so the final answer is 3/25.
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Making Connections: Selecting a Career
Apply Your Knowledge I will double the points if you get this completely done (that means both documents completed with the correct answers)
Top Career Choice: Registered Nurse
Job Description: Registered Nurses (RNs) are responsible for providing and coordinating patient care.
Personal Attributes: Compassionate, Detail-oriented, Patient, Good communication skills, Ability to work under pressure, Physical and emotional stamina
Education: A Bachelor of Science in Nursing (BSN) is the preferred degree for RNs.
Experience: RNs typically gain experience through clinical rotations during their nursing program, as well as through internships or residency programs.
Certification: RNs can earn additional certifications in specialties such as critical care, emergency nursing, or pediatric nursing.
Employment: RNs can work in a variety of settings, including hospitals, clinics, long-term care facilities, and schools.
Why is making a career choice important in one way?Making a career choice opens the door to financial security. The earning potential of an occupation is a major consideration for most people when choosing a suitable career. Choosing the right profession means you will be able to have economic security, which is an important factor in our overall well-being.
Full question "Making Connections: Selecting a Career. Apply Your Knowledge" Top Career Choice, Job Description, Personal Attributes, Education, Experience, Certification, Employment, Job Outlook, Earnings, Work Environment, Related Occupations
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Does anyone know the answer?
Answer:
A
Step-by-step explanation:
Range referes to the smallest and largest values, so the answer you have circles is correct.
Good Job!
Answer: A) Range
Step-by-step explanation:
The range is the difference between the biggest and smallest numbers (or, in this case, folders). If Jack wants to find a notebook that will fit a small and large folder, he will need to find the range.
what 2 distributive property expressions equal to 108
The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The distributive property is given as:
a(b + c) = ab + ac
3(20 + 16) = 3(20) + 3(16) = 60 + 48 = 108
Also:
4(13 + 14) = 4(13) + 4(14) = 52 + 56 = 108
The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108
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James has to fill 40 water bottles for the soccer team. Each bottle holds 1 pint of water.
How many gallons of water does James need in all?
Answer:
James needs 5 gallons of water.
Step-by-step explanation:
1 gallon = 8 pints
40 ÷ 8 = 5
5 gallons
What is the radius of the circle that is centered at (2, −3) and passes through the point (−1, −6)?
Answer:
We can use the distance formula to find the distance between the center of the circle (2, -3) and the point (-1, -6), which should be equal to the radius of the circle.
Step-by-step explanation:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Distance = √[(-1 - 2)² + (-6 - (-3))²]
Distance = √[(-3)² + (-3)²]
Distance = √(18)
So the radius of the circle is equal to √(18) or approximately 4.24.
Need help. My assignment is due in an hour. Will be much appreciated!
The inverse functions and the domains and ranges of the inverse functions can be presented as follows;
A. The inverse function of f(x) is; [tex]f^{-1}(x) = \frac{3-x}{7\cdot x}[/tex]
B. f(g(x)) = [tex]\frac{3}{7\times \frac{(3-x)}{7\cdot x} + 1}[/tex] = x
C. The inverse function reverses the effect of the function. The inverse function is therefore;
x [tex]{}[/tex] y
10[tex]{}[/tex] 5
6[tex]{}[/tex] 8
5[tex]{}[/tex] 9
4[tex]{}[/tex] 13
2) Domain; 10, 6, 5, 4
Range; 5, 8, 9, 13
What is the inverse of a function?An inverse function maps the output, or y-value of a function to the input value or x-value of the function.
2. A. f(x) = 3/(7·x + 1)
The inverse function can be found as follows;
Let f(x) = y
y = 3/(7·x + 1)
(7·x + 1) = 3/y
7·x = (3/y) - 1 = (3 - y)/y
x = (3 - y)/(7·y)
Plugging in x = f⁻¹(x), and y = x, to get;
The inverse of the function; f⁻¹(x) = (3 - x)/(7·x)B. g(x) = (3 - x)/(7·x)
f(x) = 3/(7·x + 1)
f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = 3/(((3 - x)/(x)) + 1) = 3/(3/x - 1 + 1)
3/((3/x - 1 + 1) = 3/(3/x) = 3 × x/3 = x
Therefore; f(g(x)) = 3/(7 × ((3 - x)/(7·x)) + 1) = x
C. The inverse of the function is the function that produces the input of the function from the function's output, therefore, the inverse of the function can be presented as follows;
x [tex]{}[/tex] y
10[tex]{}[/tex] 5
6[tex]{}[/tex] 8
5[tex]{}[/tex] 9
4[tex]{}[/tex] 13
2) The domain is the set of the possible inputs of the function, and the range is the set of the possible outputs of the function.
The domain of the inverse function is; 10, 6, 5, 4The range of the inverse function is; 5. 8. 9. 13Learn more on the inverse of a function here: https://brainly.com/question/9007328
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I need help on this question
Answer: i think the answer is A
Step-by-step explanation:i think bc i is a quadratic function
Answer: D
Step-by-step explanation:
A and B don't make sense, since the maximum value > 0, and the function is more negative than positive. C and D are our remaining answers. C would be incorrect, since if X reaches \infinity , the function isn't infinite. The only way to make C correct, is a sudden spike in the function to infinity. So, the only correct answer is D.
Hope this helps (please respond if I'm wrong)
help asap pls
my assignment is due tonight at midnight
Answer:
See below.
Step-by-step explanation:
We're asked to prove that ΔSTV ≅ ΔTUW.
Let's begin by reviewing what was given to us.
Line Segment SV ≅ & ║ (Congruent and Parallel With) Line Segment TW.∠SVT ≅∠TWU.SV ≅ TW.Because we already have one side and an angle congruent, we need to prove that another angle or side is congruent.
Our goal is to find a Congruency Postulate to prove that ΔSTV ≅ ΔTUW.
As we can see in the diagram, ∠STV ≅ ∠UTV as they're vertical angles. This is possible because Line Segment SV ≅ & ║ Line Segment TW.
We are now able to prove that ΔSTV ≅ ΔTUW with the Angle-Side-Angle Triangle Congruency Postulate (ASA). We proved, and were given 2 angles, and 1 side.
Summary:
∠STV ≅ ∠UTV | Vertical Angles.
ΔSTV ≅ ΔTUW | ASA.
What is a log can kate use to fill remaining 1/3 meters
Answer:
It is not clear what is meant by "a log can Kate use to fill remaining 1/3 meters." However, if we assume that Kate has a gap of 1/3 meters that she needs to fill, she could use a log that is 1/3 meters long to fill the gap. Alternatively, she could use any other object that is 1/3 meters long to fill the gap.
Identify the domain and range of the exponential function.
I am trying to help my son with his math and am about to cry. Lol. May you please help me? Thank you
The domain and range of given graph is Domain: (-∞, ∞) Range: (0, ∞)
What is Function ?
Function can be defined in which it relates an input to output.
The horizontal axis (x-axis) represents the input values, while the vertical axis (y-axis) represents the output values.
To identify the domain and range of this function from the graph, we can look at the values that the function takes on as well as the values that are excluded.
From the graph, we can see that the function appears to be increasing without bound as the input values increase. This means that the domain of the function is all real numbers or (-∞, ∞).
We can also see that the function appears to be taking on only positive values, and never touches or crosses the x-axis. This means that the range of the function is all positive numbers or (0, ∞).
Therefore, The domain and range of given graph is Domain: (-∞, ∞) Range: (0, ∞)
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Find (f.g)(x) for f(x) = 4x - 9 and g(x)=3x^2. Show all work for full credit.
Answer:
The answer is (f.g)(x) = 12x^2 - 9.
Step-by-step explanation:
To find (f.g)(x), we need to apply the composition of functions formula, which is:
(f.g)(x) = f(g(x))
First, we need to find g(x):
g(x) = 3x^2
Now, we need to plug g(x) into f(x) in place of x:
f(g(x)) = 4(g(x)) - 9
= 4(3x^2) - 9
= 12x^2 - 9
Therefore, (f.g)(x) = 12x^2 - 9.
Hope this helps, I'm sorry if it doesn't! If you need more help, ask me! :]
Determine whether a triangle can be formed with the given side lengths.
Question 3and4 pls
Answer:
In question 3 a triangle can be formed however in question 4 it can't be formed
Step-by-step explanation:
there is a theorem that states that two sides of a triangle when added up should be greater than the third one which isn't true in question 4 as
12+9=21 so its equal to the third side but not greater hence a triangle can't be formed
Find the size of the angels labeled with letters. On is the center of the circle
Answer:
Step-by-step explanation:
[tex]i=80[/tex]° (opposite angles in a cyclic quadrilateral are supplementary)
[tex]e=84[/tex]° (An exterior angle of a cyclic quadrilateral is equal to the interior
angle at the opposite vertex.)
The measures of the angles of a triangle are shown in the figure below. Solve for x.
According to the solving Triangle The Value of X in the given figure is 20°
What is Triangle?Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees which is called interior angles.
According to the given information:The three angles are given as ∠1=84°, ∠2=41°, ∠3=2x+15°.
Adding three angles
84° + 41° + 2x + 15° = 180° (sum of interior angle is 180°)
140° + 2x = 180°
2x = 180°-140°
2x = 40°
x = 20°
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trey paid 42 dollars for 2/3 ton of concrete. he wants to know the price of 3 tons of concrete.
Answer:
To find the price of 3 tons of concrete, we need to first figure out how much Trey paid per ton of concrete.
Since Trey paid 42 dollars for 2/3 ton of concrete, we can set up a proportion:
2/3 ton = 42 dollars
1 ton = x dollars
To solve for x, we can cross-multiply:
(2/3) * x = 42 * 1
2x = 126
x = 63
So, Trey paid 63 dollars per ton of concrete.
To find the price of 3 tons of concrete, we can multiply the cost per ton by the number of tons:
3 tons * $63/ton = $189
Therefore, the price of 3 tons of concrete is $189.
For each quadratic function below, use the idea of completing the square to write it in graphing form. Then state the vertex of each parabola. a. f(x)=x² +6x+15 b. y= x^2-4x+9 c. f(x)= x² +8x d. y=x² - 4x+9
please help i don't want answers just somebody to explain this in a way that makes sense help
Note that the graphing form and vertex of each quadratic function are given as follows:
a) for f(x)=x² +6x+15, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).
b) for y= x²-4x+9 the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
c) for f(x)= x² +8x, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).
d) for . y=x² - 4x+9, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
a. To complete the square for the quadratic function f(x)=x² +6x+15, we add and subtract the square of half of the coefficient of x, which is (6/2)² = 9:
f(x) = x² + 6x + 15
= (x² + 6x + 9) + 6
= (x + 3)² + 6
Therefore, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).
b. To complete the square for the quadratic function y= x^2-4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:
y = x^2 - 4x + 9
= (x^2 - 4x + 4) + 5
= (x - 2)² + 5
Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
c. To complete the square for the quadratic function f(x)= x² +8x, we add and subtract the square of half of the coefficient of x, which is (8/2)² = 16:
f(x) = x² + 8x
= (x² + 8x + 16) - 16
= (x + 4)² - 16
Therefore, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).
d. To complete the square for the quadratic function y=x² - 4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:
y = x² - 4x + 9
= (x² - 4x + 4) + 5
= (x - 2)² + 5
Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
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find the value of the expression -x^3+3 x^2-x+20 if x=-1
The value of the expression -x³ + 3x² - x + 20 when x = -1 is 23.
What is the value of the given expression when x = -1?Given the expression in the question;
-x³ + 3x² - x + 20
x = -1To determine the value of the expression,
First, we substitute -1 for x in the expression:
-( -1 )³ + 3( -1 )² − ( -1 )) + 20
Next, we simplify each term using the order of operations (also known as PEMDAS):
-( -1 )³ = -( -1 ) = 1
(recall that the exponent is evaluated first, then the negative sign is applied)
3( -1 )² = 3(1) = 3
(recall that the exponent is evaluated first)
-( -1 ) = 1
(recall that subtracting a negative is the same as adding a positive)
Now, putting these simplified terms back into the original expression, we get:
1 + 3 + 1 + 20
Finally, we add these terms together to get the final answer:
23
Therefore, the value of the expression is 23.
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Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
(1,6)
, (2,10)
, (3,4)
, (4,4)
, (5,8)
, (6,2)
, (7,2)
The Pearson correlation coefficient r for the given points is: 0.191.
How to find the r Pearson correlation coefficient r?We can use the formula for Pearson correlation coefficient r:
r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)²][nΣ(y²) - (Σy)²])
where n is the number of data points, Σ represents the sum, x and y are the variables, and xy, x², and y² represent the products and squares of the variables.
We can first calculate the sums and products:
n = 7
Σx = 28
Σy = 36
Σ(x²) = 140
Σ(y²) = 248
Σ(xy) = 152
Using these values, we can plug them into the formula for r:
r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)² ][nΣ(y²) - (Σy)²])
= [7(152) - (28)(36)] / sqrt([7(140) - (28)^2][7(248) - (36)²])
= 56 / 293
= 0.191
Therefore, the Pearson correlation coefficient r is 0.191.
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to plot the point for a library at (2, - 3) 2 units to