Can a rectangular piece of wrapping paper with an area of 81 square inches have a perimeter of 60? (Hint: Let length=30-w.) algebra 1
Answers
We find this by looking at the factors of 81.
3 and 27 are factors and if using the formula given we see that length = 30-3 = 27.
Using these factors of 81, the parameter would be 27 + 27 + 3 + 3 which results in 60.
Related Questions
5 scapulae (3 right and 2 left)
Answers
Axillary is 3 skulls.The remainder goes to the appendix.
Which of the bones in the collection belong to the axial skeleton?The bones could potentially represent up to 22 different people.This is due to the possibility that each bone comes from a different person.
There were only 3 skulls, leading some to first believe there would only be 3 persons. However, there were 4 right femurs, indicating that there is a missing skull to correspond with one of the right femurs.
In light of this, you can only conclude, until further proof, that each bone belongs to a different person.
Axillary =3 skulls.
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Compare investing $1500 at 9% compounded monthly for 11 years with investing $1500 at 14% compounded monthly for 11 years.
Answers
Answer:
Final amount after 11 years = $4021.97
Step-by-step explanation:
We will use the formula to get the final amount after t years,
Final amount = \(a(1+\frac{r}{n})^{nt}\)
here a = Initial amount
r = Rate of interest
n = Number of compounding in a year
For Initial amount 'a' = $1500
r = 9%
t = 11 years
n = 12 [Compounded monthly]
F = \(1500(1+\frac{9}{12})^{12\times 11}\)
= $4021.97
A circle of radius 1 rolls along the x-axis until it comes in contact with the functionf(x) = x^2. Find the location of the center of this circle.
Answers
2 squared is 4 times 2 is 8 the answer is 8 because 1 times 8 is 8
Which of the following continuous functions are uniformly continuous on the specified set? Justify your answers. Use any theorems you wish. (a) f(x) = x17 sin x – em cos 3x on [0, ], (b) f(x) = x3 on [0, 1], (c) f(x) = x3 on (0,1), (d) f(x) = x3 on R, (e) f(x) = on (0,1], (f) f (x) = sin on (0,1), (g) f(x) = x2 sin on (0,1).
Answers
(a) The function f(x) = x^17 sin(x) - e^(-m) cos(3x) is uniformly continuous on the interval [0, ∞).
This can be justified by noting that the function is a composition of continuous functions, and the product, sum, and composition of continuous functions result in a continuous function. Since the interval [0, ∞) is a closed and bounded set, and the function is continuous, it follows that f(x) is uniformly continuous on [0, ∞).
(b) The function f(x) = x^3 is uniformly continuous on the interval [0, 1]. This can be justified by considering the fact that f(x) is a polynomial function, and all polynomial functions are uniformly continuous on any closed and bounded interval.
(c) The function f(x) = x^3 is not uniformly continuous on the interval (0, 1). This can be shown by considering the limit as x approaches 0 and 1. The function exhibits unbounded slopes as x approaches these endpoints, violating the condition for uniform continuity.
(d) The function f(x) = x^3 is not uniformly continuous on the set of real numbers, R. This can be shown by considering the behavior of the function as x approaches positive and negative infinity. The function does not exhibit bounded slopes at these extremes, violating the condition for uniform continuity.
(e) The function f(x) = 1 is uniformly continuous on the interval (0, 1]. Since the function is a constant, it has a constant slope of zero, satisfying the condition for uniform continuity.
(f) The function f(x) = sin(x) is uniformly continuous on the interval (0, 1). This can be justified by the fact that sin(x) is a periodic function with bounded slopes, and hence, it is uniformly continuous on any bounded interval.
(g) The function f(x) = x^2 sin(x) is not uniformly continuous on the interval (0, 1). This can be shown by considering the behavior of the function as x approaches zero. The product of x^2 and sin(x) leads to unbounded slopes near zero, violating the condition for uniform continuity.
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a researcher is interested comparing quality of sleep between people who work overnight shifts and people who work day shifts. a sample of 50 day shift workers and 50 night shift workers are asked to complete a quality of sleep measure, which the researcher will treat as an interval scale measure. the researcher will compare the mean levels of each group to see if there is a statistically significant difference between the groups. which analysis would be acceptable to use?
Answers
The correct analysis would be 3 option
Describe statistics using an example.
A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.
The right response is selection 3. To compare the means of two independent groups, use the independent samples t test. to determine whether there is a substantial difference between the means of the two groups. In this instance, we are comparing two different groups of people: those who work the night shift and those who work the day shift. By definition, these two groups of persons would differ, therefore neither a matched sample test nor a one-sample test would be appropriate. Furthermore, we are not interested in person's r, which is a measure of linear correlation between two variables.
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A basket of fruit holds 12 apples, 24 pears, and 16 oranges. Find the ratio of apples, pears, and oranges in the basket.
Answers
Answer:
3:6:4
Step-by-step explanation:
We are given that
Number of apples in the basket=12
Number of pears in the basket=24
Number of oranges in the basket=16
We have to find the ratio of apples, pears and oranges in the basket.
\(12=4\times 3\)
\(24=4\times 3\times 2\)
\(16=4\times 2\times 2\)
HCF (12,24,16)=4
Now, divide each number by HCF
Then, we get
3:6:4
Therefore, the ratio of apples, pears and oranges in the basket.
3:6:4
Which of the following could be an example of a function with a domain
(-∞0,00) and a range (-∞,4)? Check all that apply.
A. V = -(0.25)* - 4
-
□ B. V = − (0.25)*+4
c. V = (3)* +4
□ D. V = − (3)* — 4
-
Answers
The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4
A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.
From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.
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Jaxon and drake share a bag of tootsie rolls. Jaxton eats 3/5 of the bag and drake eats 5/12 of the bag. Use benchmark fractions to estimate the fraction of the bag of tootsie rolls jackson and drake ate
Answers
Answer:
\(\frac{49}{60}\)
We can conclude that, both of them have eaten almost the complete bag of Tootsie rolls
Step-by-step explanation:
Given that:
Fraction of Tootsie rolls eaten by Jaxton = \(\frac{3}{5}\)
Fraction of Tootsie rolls eaten by Drake = \(\frac{5}{12}\)
Here, we have to use the Benchmark fractions to estimate what fraction of tootsie roll bags was eaten by Jaxton and Drake.
First of all, let us add the given two fractions to find the total amount of Tootsie rolls eaten by both of them together.
Total Tootsie rolls eaten by both of them =
\(\dfrac{3}{5} + \dfrac{5}{12}\\\\\text{Taking LCM of denominator i.e. 5 and 12 = 60}\\\Rightarrow \dfrac{3\times 12 + 5\times 5}{60}\\\Rightarrow \dfrac{49}{60}\)
The most commonly used benchmark fractions are 0, \(\frac{1}{2}\) and 1.
Here, with the fraction we can write our benchmark fractions as:
\(\dfrac{0}{60}, \dfrac{30}{60}, \dfrac{60}{60}\)
We can see that, \(\frac{49}{60}\) is near to \(\frac{60}{60}\).
Therefore, we can conclude that, both of them have eaten almost the complete bag of Tootsie rolls.
The specificheat of a human is approximately 3.47 J/8 ∘
C. Use this information to answer the following questions. (a) If a 1601lb man eats a candy bar containing 287 Cal, how much will his body temperature increase if all of the calories from the candy bar are converted into heat energy? Remember that a food calorie (Cal) is equal to 1kcal, 6
C GOTutorial (b) If a 160lb man eats a roll of candy containing 41.9Cal, how much will his body temperature increase if all of the calories from the candy are converted into heat energy? ∘
C
Answers
(a)the body temperature of the 1601 lb man will increase by approximately 3.0 °C.(b)the body temperature of the 160 lb man will increase by approximately 2.4 °C.
The specific heat of a human is given as 3.47 J/°C. Using this information, we can calculate the increase in body temperature when a certain number of calories are converted into heat energy. In the first scenario, a 1601 lb man consumes a candy bar containing 287 Cal. In the second scenario, a 160 lb man consumes a roll of candy containing 41.9 Cal. We will calculate the increase in body temperature for each case.
(a) To calculate the increase in body temperature for a 1601 lb man who consumes a candy bar containing 287 Cal, we need to convert calories to joules. Since 1 Calorie (Cal) is equal to 4184 joules, we have:
Energy = 287 Cal × 4184 J/Cal = 1.2 × \(10^6\) J
Now, using the specific heat formula Q = mcΔT, where Q is the energy, m is the mass, c is the specific heat, and ΔT is the change in temperature, we can rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
Assuming the mass of the man is converted to kilograms, we have:
ΔT = (1.2 × \(10^6\) J) / (1601 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 3.0 °C
Therefore, the body temperature of the 1601 lb man will increase by approximately 3.0 °C.
(b) For a 160 lb man who consumes a roll of candy containing 41.9 Cal, we repeat the same calculation:
Energy = 41.9 Cal × 4184 J/Cal = 1.75 × \(10^5\) J
ΔT = (1.75 × \(10^5\) J) / (160 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 2.4 °C
Thus, the body temperature of the 160 lb man will increase by approximately 2.4 °C.
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differentiate. f(x) = qx + r/sx + t, where q
,
r
,
s
,
t
are constants.
Answers
To differentiate the function f(x) = qx + r/sx + t, where q, r, s, and t are constants, the derivative is given by f'(x) = q - (r/s) * (1/x^2).
To differentiate the given function, we need to apply the rules of differentiation. Let's break down the steps:
1. Differentiate qx with respect to x: Since q is a constant, the derivative of qx is simply q.
2. Differentiate r/sx with respect to x: We can rewrite r/sx as r * (s * x)^(-1). Applying the power rule of differentiation, the derivative of (s * x)^(-1) is (-1) * (s * x)^(-1 - 1) * s = -s/x^2.
3. Differentiate t with respect to x: Since t is a constant, the derivative of t with respect to x is 0.
4. Combining the derivatives obtained from the previous steps, we have f'(x) = q - (r/s) * (1/x^2).
Therefore, the derivative of the given function f(x) = qx + r/sx + t, where q, r, s, and t are constants, is f'(x) = q - (r/s) * (1/x^2).
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Rotate the point (1,2) 90°
(-4,4)
(0,2)
(2,0)
(-2,1)
Answers
Answer: (-2,1)
Step-by-step explanation:
The point (1,2) is in quadrant 1.
When rotated 90 degrees counter clockwise, it moves to quadrant 2.
The new point becomes (-2,1)
renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten. according to recent statistics, the chances of renata being ready to complete kindergarten tasks when she enters school are about:
Answers
The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.
What is probability?
To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.
We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.
The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.
So, there are equal chances of both.
Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.
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What is the intersection of y = 3x +4 and y = -2x +1
Answers
Both linear functions will intersect at the same point, meaning, the x y coordinates are the same. So you have to equate both equations and clear the value of x:
\(\begin{gathered} 3x+4=-2x+1 \\ 3x+2x=1-4 \\ 5x=-3 \\ x=\frac{-3}{5} \end{gathered}\)Now using either function you have to calculate the value of the corresponding y-coordinate, for explanation purposes I'll do it with both:
\(\begin{gathered} y=3x+4 \\ y=3\cdot(\frac{-3}{5})+4=\frac{11}{5} \end{gathered}\)\(\begin{gathered} y=-2x+1 \\ y=-2(\frac{-3}{5})+1=\frac{11}{5} \end{gathered}\)As you see, using either function to calculate the y-coordinate is the same.
The functions intersect in point (-3/5, 11/5)
to examine the effectiveness of two types of interventions for anxiety, researchers randomly assigned participants to a 12-week course of cognitive-behavioral therapy, a 12-week mindfulness-based stress reduction program, or a waitlist control group. the researchers administered a standardized measure of anxiety to participants before and after the interventions or waitlist period. in this experiment, what is the dependent variable?
Answers
The dependent variable in this experiment is the level of anxiety as measured by a standardized measure of anxiety before and after the interventions or waitlist period.
What is the dependent variable about?The dependent variable in this experiment is the standardized measure of anxiety that was administered to participants before and after the interventions or waitlist period.
The dependent variable is what is being measured or observed to determine the effectiveness of the two interventions (cognitive-behavioral therapy and mindfulness-based stress reduction program) for anxiety.
Therefore, The researchers are trying to find out how the interventions affect anxiety, so anxiety levels are the outcome or result of the intervention and therefore the dependent variable.
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Mr Wiggins buys 100 bags of candy for $5. What is the cost per bag?
Answers
Answer:
Step-by-step explanation:
$5= 500cents
500÷100=5
5 cents per bag of candy
find the x and y intercepts of the line calculator
Answers
The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3).
To determine the x-intercept, let y = 0 and solve for x in the equation y = 3x - 1.
Substitute 0 for y in the equation.0 = 3x - 1
Add 1 to both sides1 = 3x
Divide both sides by 3x = 1/3
The x-intercept of the line is (1/3, 0).
To find the y-intercept, let x = 0 and solve for y in the equation y = 3x - 1.
Substitute 0 for x in the equation.y = 3(0) - 1y = -1
The y-intercept of the line is (0, -1).
Therefore, the x-intercept is (1/3, 0), and the y-intercept is (0, -1).
Therefore, The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3). The calculation above supports the conclusion.
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Triangle ABC has angle measures as shown below. Using the information in the diagram, find the value of x. Be sure to write your answer down on a piece of paper - you will need it for Question 4.Find x and measure of Angle C
Answers
Solution:
Given the triangle ABC;
The sum of interior angles of a triangle is 180 degrees. Thus;
\(\angle A+\operatorname{\angle}B+\operatorname{\angle}C=180^o\)We have;
\(\begin{gathered} 35^o+52^o+3(x+2)^o=180^o \\ \\ 87^o+3x^+6^o=180^o \\ \\ 3x=180^o-93^o \\ \\ 3x=87^o \\ \\ x=\frac{87}{3} \\ \\ x=29 \end{gathered}\)Thus, the measure of angle C is;
\(\begin{gathered} m\angle C=3(x+2)^o \\ \\ m\angle C=3(29+2)^o \\ \\ m\angle C=3(31)^o \\ \\ m\angle C=93^o \end{gathered}\)
"In the formula, P3 = Dx/(R − g), the dividend is for period:
a. four.
b. two.
c. one.
d. five.
e. three."
Answers
The dividend in the formula P3 = Dx/(R - g) is for period e. three.
In the given formula P3 = Dx/(R - g), the dividend, Dx, refers to the cash flow or payment made during a specific period. The subscript "3" in P3 indicates the period of time for which the dividend is associated.
In the given formula, P3 = Dx/(R - g), the subscript 3 represents the period of time for which we are calculating the dividend.
The dividend, Dx, represents the cashflow or payment made during a specific period. In this case, the dividend is associated with period 3.
Therefore, the dividend in the formula corresponds to period e. three.
The dividend in the formula P3 = Dx/(R - g) is for period e. three
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Please I BEG you to help...
Answers
36x^8
Explanation:
Use the rules of exponents
Answer:
36x^8
Step-by-step explanation:
You distribute the exponent (2) to the the coefficient (6) and the other exponent (4). When you distribute 2 to 6 you are squaring the 6.
6^2 = 6•6 = 36
Because of the power rule, you just multiply both the exponents together.
4•2 = 8
so when you put it together it looks like this: 36x^8
FV of $600 each 6 month for 4 year at a nominal rate of 8%, compounded emiannually. Do not round intermediate calculation. Round your anwer to the nearet cent
Answers
The future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.
The formula to use in this case is FV = PV(1 + r/n)^nt, where FV is the future value, PV is the present value, r is the nominal interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Given the information in the problem, we know that:
PV = $600 (the present value)
r = 0.08 (the nominal interest rate as a decimal)
n = 2 (the interest is compounded semi-annually)
t = 4 (the number of years)
Plugging these values into the formula, we get:
FV = $600(1 + 0.08/2)^(2*4)
To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)
= (1.04)^8
=2.2824
FV = $600*2.2824
FV = $1369.44
Thus, the future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.
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PV = $600 (the present value)
r = 0.08 (the nominal interest rate as a decimal)
n = 2 (the interest is compounded semi-annually)
t = 4 (the number of years)
Plugging these values into the formula, we get:
FV = $600(1 + 0.08/2)^(2*4)
To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)
= (1.04)^8
=2.2824
FV = $600*2.2824
FV = $1369.44
Sample size in factor analysis/ PCA
Answers
Factor analysis and Principal Component Analysis (PCA) are statistical techniques used to reduce the dimensionality of data sets, identify underlying patterns, and simplify data interpretation. In both methods, sample size plays a critical role in determining the accuracy and reliability of the results.
An appropriate sample size is essential for several reasons:
1. Adequate Representation: A larger sample size helps ensure that the data is representative of the population, capturing a wide range of variability and improving the generalizability of the results.
2. Statistical Power: Larger sample sizes increase the statistical power of the analysis, enabling the detection of smaller effects and providing more reliable estimates of the underlying factors or components.
3. Stability: In factor analysis and PCA, larger sample sizes lead to more stable factor structures or component loadings, increasing the likelihood that the results are replicable in different samples or across time.
4. Error Minimization: A sufficient sample size helps minimize errors and distortions in the analysis, reducing the chance of overfitting the data or extracting spurious factors or components.
While there is no one-size-fits-all rule for determining an optimal sample size, some guidelines can help. A widely cited rule of thumb is a minimum of 10 to 20 observations per variable, with more complex models or data structures requiring larger sample sizes. Another approach is to perform a power analysis or Monte Carlo simulation, considering the desired level of statistical power, effect size, and specific model parameters.
In summary, selecting an appropriate sample size for factor analysis or PCA is crucial to ensure accurate, reliable, and generalizable results. Following guidelines and considering the context of the data and research question can help make informed decisions about sample size.
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How many solutions does 7(x - 2) + 5 = 3 (2x - 1) + 1 have?
Answers
Answer:
one, x = 7
Step-by-step explanation:
7(x - 2) + 5 = 3 (2x - 1) + 1
reduce:
7x - 14 + 5 = 6x - 3 + 1
x = 7
Jonathan is having a party at the trampoline park. The party costs $110 plus $5 per person who attends. Which expression can Jonathan use to figure out the total amount of dollars he owes at the end of the party?
Answers
Answer:
110 + 5x
Step-by-step explanation:
The base price is 110 dollars. The amount of people who attended the party is defined by x. Each person that joins the party adds 5 dollars to the total.
Use the zero product property to find the solutions to the equation x2 + 12 = 7x.
x = –4 or x = 3
x = –4 or x = –3
x = –3 or x = 4
x = 3 or x = 4
Answers
Answer:
x= 4, 3
The choose (d)
Step-by-step explanation:
x²+12=7x
x²-7x+12=0
(x-3)(x-4)=0
x=3
or x=4
Answer:
D
Step-by-step explanation:
on edge
if v=5 x=38 and y=-7 find w
Answers
Answer:
incomplete question friend
PLEASE HELP NO LINKS OKAY!!
Answers
A coffee shop owner wants to examine the number of customers who pass in front of his store in the morning from 7:00am to 7:30am. Suppose that the mean number of customers during this time window is 200. What is the probability that more than 210 people will pass in front of his store
Answers
The probability that more than 210 people will pass in front of his store is 0.2272.
In the question, we are given that a coffee shop owner wants to examine the number of customers who pass in front of his store in the morning from 7:00 A.M to 7:30 A.M.
We are asked to find the probability that more than 210 people will pass in front of his store if the mean number of customers during this time is 210.
This experiment follows a Poisson Distribution with a mean (λ) = 200, and the random variable X = 210.
To find the probability that more than 210 people will pass in front of his store, we will find P(X > 200).
P(X > 200) = 1 - P(X ≤ 210).
Now, P(X ≤ 210) can be calculated using the function poissoncdf(200,210) on the calculator.
As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).
The value of poissoncdf(200,210) = 0.77271.
Thus, the value of P(X > 210) = 1 - 0.77271 = 0.22729.
Thus, the probability that more than 210 people will pass in front of his store is 0.2272.
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find all missing variables and measures of each angle
Answers
I hope this is helpful
The Hormel Corporation has an annual dividend rate of $1.04. If you owned 5,000 shares of
Hormel, how much would you receive annually in dividends?
$4,900
$5,000
$5,100
$5,200
Answers
Answer:
$4,900
Step-by-step explanation:
\(\frac{\mbox{number of shares}}{\mbox{annual dividend}} = \frac{5,000}{1.04}\)
This simplifies to 4807.7, which you can round to $4,900.
Given the following three points, find by hand the quadratic function they represent.
(-1,-8), (0, -1),(1,2)
(1 point)
O f() = -5x2 + 8x - 1
Of(x) = -222 +50 - 1
O f(x) = -3.x2 + 4.0 – 1
O f() = -3x2 + 10x - 1
Answers
Answer:
The equation is;
f(x) = -2·x² + 5·x - 1
Step-by-step explanation:
The general form of a quadratic equation or function f(x) is, f(x) = y = a·x² + b·x + c
Given that the points representing the quadratic function are;
(-1, -8), (0, -1), (1, 2) which are of the form (x, y)
When x = -1, f(x) = y = -8
Plugging in the above values into the general form of a quadratic function, we have;
-8 = a·(-1)² + b·(-1) + c = a - b + c
-8 = a - b + c.........................(1)
When x = 0, y = -1, we have;
-1 = a·(0)² + b·(0) + c = c
c = -1.......................................(2)
When x = 1, y = 2, which gives;
2 = a·(1)² + b·(1) + c = a + b + c
2 = a + b + c........................(3)
Adding equation (1) to equation (3), we have;
-8 + 2 = a - b + c + a + b + c
-8 + 2 = 2·a + 2·c
From equation (2) c = -1, we get;
-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)
-6 = 2·a - 2
-4 = 2·a
a = -2
From equation (3), we have
2 = a + b + c
Substituting the values of a, and c gives;
2 = -2 + b - 1
b = 2 + 2 + 1 = 5
b = 5
The equation is therefore;
f(x) = -2·x² + 5·x - 1.
Answer:
b
Step-by-step explanation: