On solving the provided question, the differential equations we obtained are as follows - [tex]\frac{d^3y}{dx^3} - 3\frac{d^2y}{dx^2} + 3\frac{dy}{dx} -y = 0[/tex] And [tex]\frac{d^3y}{dx^3} +\frac{dy}{dx} -10y = 0[/tex]
what is differential equations?
An equation comprising one or more functions and their derivatives is known as a differential equation in mathematics. A function's derivative expresses the rate of change of the function at a specific moment. It is mostly employed in the sciences of physics, engineering, and biology.
Since there are 3 basic function, the order of the differential equation is 3. Since the basic finction e^{x} is repeating thrice, the characteristic roots are 1,1,1,(i.e the characteristic root is 1 with multiplicity 3). Hence the characteristic equation is (D-1)^{3} = 0.
[tex]\frac{d^3y}{dx^3} - 3\frac{d^2y}{dx^2} + 3\frac{dy}{dx} -y = 0[/tex]
Since there are 3 basic function, the order of the differential equation is According to the basic finctions, the characteristic roots are [tex]2,-1[/tex]±[tex]2i.[/tex] Hence the characteristic equation is (D-2)(D^{2}+2D+5) = 0. which means D^{3}+D-10 = 0.
[tex]\frac{d^3y}{dx^3} +\frac{dy}{dx} -10y = 0[/tex]
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Select all of the equations for the line that passes through (5, −2) and (0, 18).
Multiple select question.
A)
y+2=−4(x−5)
B)
x+4y=−12
C)
y−6=−4(x+1)
D)
y=−4x−12
E)
y=−4x+18
F)
4x+y=18
Answer:
Need more info please
Step-by-step explanation:
Given BC over AC congruent to EF over EG
Prove FG=10
Proof:
Let's start of by solving for the length of AC, which is just the sum of lengths AB and BC, which is 10 + 3 = 13 units.
Because of our second given, AC ≅ EG, we know that EG is also 13 units in length. Also, from our first given, BC ≅ EF, we know that EF is 3 units.
We also know that the length of EG is the sum of lengths EF and FG so we can write the equation
EG = EF + FG
13 = 3 + FG
FG = 10 meaning FG is 10 units
Round the answer to the nearest tenth please
Answer:
19.9 m
Step-by-step explanation:
Cone: r= 1m Height= 2m (You will use the radius for the Cylinder)
1/3 x π x 1^2 × 2 = 2.0943951023932
2.0943951023932 x 2 = 4.1887902047864 (Just use the hundreths place if writing down.)
Cylinder: r= 1m Height= 5m
π x 1^2 x 5 = 5π = 15.707963267949
Now add both together then round to tenths.
4.1887902047864 + 15.707963267949 = 19.8967534727354
(Remember use hundreths place if writing down)
19.8967534727354 --> 19.9 m
Find the answers to the following multiplication problems without using a calculator. Reduce the product to their lowest terms and change improper fractions to mixed numbers.
2 / 8 x 15
After reducing the product in the lowest form and changing to mixed fraction , the answer is [tex]3\frac{3}{4}[/tex] .
In the question ,
it is given that ,
the two numbers are 2/8 and 15 ,
we have to find the product without using the calculator and express it in lowest form and then convert the improper fraction in to mixed fraction .
So , the product of 2/8 × 15 = 30/8
in lowest form it is 15/4 .
after converting the improper fraction 15/4 in mixed form ,
we get ,
15/4 = [tex]3\frac{3}{4}[/tex].
Therefore , the product of 2/8 × 15 is [tex]3\frac{3}{4}[/tex] .
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what is a 500 doller diposet for 20 years witha intrest rate of 2%
The value of the amount will be $721.40.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
500 dollar deposit for 20 years with a interest rate of 2%.
Now,
We know that;
The formula for amount is,
⇒ [tex]A = P (1 + r)^n^t[/tex]
Where, A is total amount, P is principle amount, r is interest rate.
Here, We have;
P = $500
t = 20 years
r = 2%
Substitute all the values, we get;
⇒ [tex]A = P (1 + r)^n^t[/tex]
⇒ [tex]A = 500 (1 + 0.02)^2^0[/tex]
⇒ A = 500 × 1.02²⁰
⇒ A = 500 × 1.44
⇒ A = $721.40
Thus, The value of the amount = $721.40
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The quotient of a number and 5 plus 25 is no more than 45. What are the possible values for the number?
All the possible values for the number 'x' will be less than or equal to 1,350.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The remainder of a number and 5 in addition to 25 is something like 45.
Let the number be 'x'. Then the inequality is given as,
x / (5 + 25) ≤ 45
x / 30 ≤ 45
x ≤ 1,350
All the possible values for the number 'x' will be less than or equal to 1,350.
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Jaquan bought an RV for $95,000. He made a down payment of $72,000 and paid $650 monthly for 60 months. What's the total finance charge?
00/1
Vanessa went to the store to pick up some groceries for her family. She brought $20 to the
store. Vanessa's family needed a carton of eggs, which costs $3 and oranges that cost $0.50
each. Let x represent the amount of oranges that she buys. Write an inequality that can be
used to determine the amount of oranges she can buy at the store.
Vanessa can buy a maximum of x oranges, where x is the number of oranges she can buy at the store. We can represent this mathematically as an inequality by letting x represent the number of oranges she can buy and setting it equal to the total amount of money she has minus the cost of the eggs divided by the cost of each orange:
x ≤ ($20 - $3) / $0.50
This inequality tells us that Vanessa can buy at most x oranges as long as the total cost of the oranges (x * $0.50) is less than or equal to the amount of money she has remaining after buying the eggs ($20 - $3).
In other words, Vanessa can buy at most x oranges as long as the total cost of the oranges is less than or equal to $17.50. This means she can buy at most 35 oranges, since 35 * $0.50 = $17.50. Therefore, the inequality that represents the maximum number of oranges Vanessa can buy is:
x ≤ 35.
Hello can someone please help me find x. Im getting stuck. Thanks!
The value of the x is 3.26556.
What is the Intersecting Chord Theorem?
When two chords intersect each other inside a circle, the products of their segments are equal.
We have,
It is a little easier to see this in the diagram, each chord is cut into two segments at the point where they intersect.
One chord is cut into two line segments A(x+10) and B(x+1). The other is into segments C(x) and D(5x+1).
According to Intersecting Chord Theorem:
This theorem states that A×B is always equal to C×D no matter where the chords are.
A.B = C.D
(x+10) * (x+1) = (x) * (5x+1).
x² + x + 10x + 10 = 5x² + x
x² + x + 10x + 10 - 5x² - x = 0
-4x² + 10x + 10 = 0
using the Quadratic Formula where, a = -4, b = 10, and c = 10, we get
x=−0.765564
x = 3.26556
Hence, the value of the x is 3.26556.
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with the given vertices.
4. E(-3, 3), F(1, 3), G (3, -3), H(-5, -3)
Answer:
sorry new don't understand the app
I need the statement and reason. It's difficult for me.
Answer:
DF is congruent to FG
Step-by-step explanation:
segment subractive property means to subract a part of a segment from another if they are equal. If we do this in this situation, we will see that DF is congruent to FG
Statement Reason
CF = EG GivenCD = EF GivenCF = CD + DF Segment additionEG = EF + FG Segment additionEG = CD + FG Substitution propertyCD + DF = CD + FG Substitution propertyDF = FG Subtraction propertyProvedQuestion
Newton's Law of Universal Gravitation: The gravitation attraction, f , between two objects of masses x and y is proportional to the product of the masses and inversely proportional to the square of the distance, d , between the objects.
Write an equation for the constant of variation, k, in terms of f, x, y, and d.
Complete the equation in the space below (do not enter “k=“)
The required equation for the variation of k is given as k = Fd² / xy.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Newton's Law of Universal Gravitation states that the gravitational attraction, f, between two objects with masses x and y is proportional to the product of their masses and inversely proportional to the square of their distance, d.
So,
F ∝ x × y - - - - (1)
And
F ∝ 1 / d² - - - - - (2)
Combining equations 1 and 2
F ∝ xy / d²
Or
F = kxy / d²
Now,
Formulate the above expression with subject to constant k.
K = Fd² / xy
Thus, the required equation for the variation of k is given as k = Fd² / xy.
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The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean ?, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses H0: ? = 115 Ha: ? ? 115. The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students. Based on the P-value computed choose the correct choice. Group of answer choices the data are statistically significant at level ? = .05 and at level ? = .01. the data are not statistically significant at level ? = .05 and not statistically significantat level ? = .01. the data are statistically significant at level ? = .05, but not at level ? = .01 the data are statistically significant at level ? = .01, but not at level ? = .05
The data are statistically significant at level = 0.05, but not at level = 0.01.
Given-
H0: μ = 115
HA: μ ≠ 115
The sample mean = 120
The standard deviation = 25
Standard error of mean 2.5
Solution-
If z = (xbar- μ ) / SE
Then the solution would be
z = (120-115) / 2.5
z = 2
P of the value = 2 P( z > 2) = 2(0.0228) = 0.0456 is the statistically significant level.
Therefore the answer is technically at .05 level of significance.
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Write the following inequality in slope-intercept form.
13x - y < 15
Answer:
y < 13x – 15
Step-by-step explanation:
13x – y < 15
–y < –13x +15
divide both sides by (–)
–(–y) < –(–13)x –(15)
y < 13x – 15
Find f(-2) f(x)= -1/6 (1/4)^x
Answer: 8/3
Step-by-step explanation:
In this equation, x=-2
so
f(-2)=-1/6 (1/4)^(-2)
(1/4)^(-2)=4^2=16
f(-2)=-1/6 16
I am going to assume that it's (1/6)*(1/4)^x meaning:
f(-2)=16/6
=8/3
I hope I assumed correctly.
Answer:
f(-2) = - 8/3---------------------------
Given function:
f(x) = - 1/6 (1/4)ˣFind f(-2), by plugging in the value of x:
f(-2) = - 1/6 (1/4)⁻² = - 1/6 (4²) = - 16/6 = - 8/3Which number completes the
sequence? Type in your answer.
1, 2, 4, 7, 12, 19, 30, ?
The required next term at the end of the sequence is 43.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values are equal.
here,
1, 2, 4, 7, 12, 19, 30,
As
the sequence is the prime addition of the number, as.
1,
1 + 1 = 2
2 + 2 = 4,
4 + 3 = 7
7 + 5 = 12
12 + 7 = 19
19 + 11 = 30
30 + 13 = 43
Thus, At the end of the sequence, the required next term is 43.
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find the 25th, 50th, and 75th percentile from the following list of 32 data. please enter exact answers.
the 25th, 50th, and 75th percentile from the following list of 32 data are 25th percentile: 13 , 50th percentile: 21 , 75th percentile: 29.
To find the 25th percentile:
25th percentile: 25% of 32 = 8th number = 13
Count the total number of values in the data set, which is 32
Calculate 25% of 32, which is 8
Count 8 numbers from the beginning of the list and the 25th percentile is the 8th number, which is 13
To find the 50th percentile:
50th percentile: 50% of 32 = 16th number = 21
Count the total number of values in the data set, which is 32
Calculate 50% of 32, which is 16
Count 16 numbers from the beginning of the list and the 50th percentile is the 16th number, which is 21
To find the 75th percentile:
75th percentile: 75% of 32 = 24th number = 29
Count the total number of values in the data set, which is 32
Calculate 75% of 32, which is 24
Count 24 numbers from the beginning of the list and the 75th percentile is the 24th number, which is 29
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you are measuring a process, and you are given the following information: overall average: 131 population stdev: 5 sample size: 11 determine the upper control limit if your desired confidence interval is 99.73%. enter your answer to one decimal place. it's ok if you get a negative number; in that case, just enter the minus sign in front of it.
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
What is Confidence interval?In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.
Given 131 population
Standard deviation = 5
sample size = 11.
mean = 131/11 = 11.9.
Determine the upper control limit if desired confidence interval is 99.73%
Confidence interval = sample mean ± margin of error
Upper limit = sample mean + margin of error.
Margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex]
Margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].
Value of z* for 99.73% confidence interval is 3.00.
So margin of error = 4.5.
Upper limit = 11.9 + 4.5
Upper limit = 16.4
If we want a confidence level of 99.73%, the top control limit is 16.4.
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Describe and correct the error.
By midpoint segment theorem DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
DE is the midsegment of AB and AC.
AD≅BD and AE≅EC.
The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
DE=1/2BC
5=1/2(10)
5=5
Hence, DE=1/2BC for AD≅BD and AE≅EC of the triangle ABC.
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A rivet is to be inserted into a hole. If the standard deviation of hole diameter exceeds 0.02 mm, there is an unac- ceptably high probability that the rivet will not fit. A random sample of n = 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s = 0.016 mm. (a) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 mm? Calculate a P-value to draw conclusions. State any necessary assumptions about the underlying distribution of the data. (b) Construct a 95% lower confidence bound for o. (c) Use the confidence bound in part (b) to test the hypothesis.
Since our test statistics ( 8.96 ) is less than the critical value ( 29.141 ),
there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
Given that;
H₀ : σ = 0.02
H₁ : σ > 0.02
The test statistics is;
X² = ( n-1 )s² / σ² = ( 15 - 1)(0.016)² / (0.02)²
= 0.003584 / 0.0004
= 8.96
degree of freedom
df = n - 1 = 15 - 1 = 14
For right tailed test, critical value at 0.01 level of significance is 29.141.
Now since our test statistics ( 8.96 ) is less than the critical value (29.141 ),
Therefore, there is no strong evidence to indicate that the standard deviation of hole diameter exceeds 0.02 millimeters.
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Show that the function is increasing and decreasing on the given open intervals. (Enter your answers as a comma-separated list if necessary.)
y = x4 + 7; decreasing on (−[infinity], 0); increasing on (0, [infinity]).
The function y = x⁴ + 7 is decreasing on (-∞ , 0) and increasing on (0 , ∞) .
In the question ,
it is given that ,
the function is y = x⁴ + 7 ,
we have to show that function y is decreasing on (-∞ , 0) and increasing on (0 , ∞) .
differentiating the function y = x⁴ + 7 , with respect to x ,
we get ,
y'(x) = d/dx(x⁴ + 7) = 4x³
putting y'(x) = 0 , then 4x³ = 0 ;
x³ = 0 that means , x = 0 .
thus , the critical number is ⇒ x = 0 .
y'(-1) = 4(-1)³ = -4 So , it is decreasing
y'(1) = 4(1)³ = 4 So , it is increasing .
Therefore , the function y is decreasing in (-∞ , 0) and increasing in (0 , ∞) .
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3.) What is the slope intercept form of the line graphed below?
Superman pro
Step-by-step explanation:
Superman pro
Which of the following represents a nonlinear function?
y=x²
y=x
y=-2 x
y=5 x+7
The equation that represents a non linear function is y = x² , the correct option is (a) .
In the question ,
four functions are given ,
we have to select the option that is non linear ,
we know that ;
A Linear Function is an equation in which the the highest degree of the equation is 1 , and the graph is a straight line . and
A Non Linear Function ,is an equation in which the highest degree of the equation is more than 1 , and the graph is not a straight line .
So , from the given options
we can see that all the options have degree 1 except the equation y = x² which has highest degree 2 .
Therefore , The Non Linear Function is (a) y = x² .
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A drug-testing laboratory produces false negative results 2% of the time and false positive results 5% of the time. Suppose that the laboratory has been hired by a company in which 10% of the employees use drugs.
a) If an employee tests positive for drug use, what is the probability that they actually use drugs?
b) What is the probability that a nondrug user will test positive for drug use twice in a row?
c) What is the probability that someone who tests positive twice in a row is not a drug user?
a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%
b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user is 23%
What is Bayes' theorem in probability?Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.
The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.
The question state that
Pr(D) = 0.10
Pr(D') = 0.90
Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)
Pr(P/D') = 0.05
a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')
⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)
⇒ Pr(D/P) = 0.098/(0.098+0.045)
⇒ Pr(D/P) = 0.098/0.143
⇒ Pr(D/P) ≈ 0.6853
⇒ Pr(D/P) ≈ 69%
b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')
⇒ Pr (P*2/D') = 0.05*0.05
⇒ Pr (P*2/D') = 0.0025
⇒ Pr (P*2/D') = 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)
⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)
⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604
⇒ Pr (D'/P*2) = 0.00225/0.09829
⇒ Pr (D'/P*2) ≈ 0.2289
⇒ Pr (D'/P*2) ≈ 23%
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two events, a and b are independent if and only if . recall that a reorganization of the multiplication rule will yield . suppose for some events a and b, . which of the following statements is true of a and b? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a events a and b are independent since and . b events a and b are not independent, but they are mutually exclusive since . c events a and b are independent since ; however . d events a and b are not independent since and .
The two events a and b are independent if and only if (a) Events a and b are independent .
What are Independent Events ?
Two events A and B are said to be independents if the occurrence of event A does not affect the chance of occurrence of the other event B .
The probability of two independent events can be mathematically represented as P(A and B) = P(A) × P(B) .
So, we can conclude that , Two events, a and b are independent if and only if Events a and b are independent .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
Two events, a and b are independent if and only if
Which of the following statements is true of a and b?
(a) Events a and b are independent
(b) Events a and b are not independent, but they are mutually exclusive
(c) Events a and b are not independent since and .
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A population has a mean of 200 and a standard deviation of 50. Supposed a sample of size 100 is selected and x is used to estimate μ.
What is the probability that the sample mean will be within ±5 of the population mean?
The probability that the sample mean will be within ±5 of the population mean is 0.6826
What is the probability of the sample mean?If the population is normally distributed, the sample means will be normally distributed even with smaller samples. [This is known as the Central Limit Theorem, which states that when a large number of random samples are drawn from a population, the means of these samples will be normally distributed.]
Z=X-μ/σ
Given here, σ = 50 , μ =200 , σₓ = 5 , n = 100 ,
z = 205-200/5 z = 195-200/5
we get z= ±1
From the z table, we get P( z= -1) = 0.1587
From the z table we get P( z= 1) = 0.8413
Thus the final answer is = 0.8413- 0.1587
= 0.6826
Hence, the probability that the sample mean will be within ±5 of the population mean is 0.6826
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Hi, Can anyone help me solve this please?
Ma'am there is nothing to solve...
Emoji::<
Answer:
Step-by-step explanation:
Yes there is literally nothing to solve:(
Armando divided 6 and 258
Answer:
43
Step-by-step explanation:
258 divided by 6 equals 43
Look below
Armando divided 6 and 258
258 is the bigger number, so we will keep that on the right, and then add the dividing symbol. Next, we will add the 6. That should look like this:
258÷6
then just put it on a calculator and you get the answer 43. hope that helps
let c and d be disjoint compact subspaces of the hausdorff space x. then there exist disjoint open sets u and v containing c and d, respectively.
The statement "let c and d be disjoint compact subspaces of the Hausdorff space x and then there exist disjoint open sets u and v containing c and d, respectively." is proved.
Here we have given the let A and B be disjoint compact subspaces of the Hausdorff space X.
And we have to prove the statement.
According to the given question, let us consider that x be an arbitrary coordinate of A and here the points of x isn't in Y because A and B are disjoint.
Then according to Lemma 26.4 disjoint open sets Ux and Vx such that x Î Ux and Ux contain B.
Here the collection {Ux} is a covering of A by sets open in X.
And the finite collection of them {U1, ..,Un} covers A because A is compact.
Here the open set U = U1 U....U Un contains A and it is disjoint from
V = V1 I.....I Vn that contains B because it's the finite intersection of the corresponding open sets containing.
Therefore, here there exists disjoint open sets U and V containing A and B, respectively.
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below are representations of three different linear functions. write an equation for each representation table: x -3, -2, -1, 0. y 9,8,7,6
The representation table given indicates that the function is linear, as the difference between consecutive y-values (9-8, 8-7, and 7-6) is constant. Therefore, we can represent the function with a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the function, we can use the x- and y-values given in the table to solve for m and b. For example, using the x- and y-values (-3,9) and (-2,8), we can solve the equation 9 = m(-3) + b for m and b:
9 = -3m + b
8 = -2m + b
Subtracting the second equation from the first equation gives us:
1 = -m
So the slope of the function is -1. Substituting this value back into either equation gives us:
9 = -3(-1) + b
9 = 3 + b
6 = b
So the y-intercept of the function is 6. Therefore, the equation of the function is y = -1x + 6.
The other two representations can be solved in the same way to find the equations of those functions.