Given the number pattern:
20; 18: 14; 8;
a) Determine the nth term of this number pattern.
b) Determine the value of T12 in this number pattern.
c) Which term in this number pattern will have a value of - 36?
A quadratic number pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to - 14.
a) Calculate the second difference of this quadratic number pattern.
b) Hence, or otherwise, calculate the first term of this number pattern.
Answers
Answer:
\(\textsf{a)} \quad T_n=-n^2+n+20\)
\(\textsf{b)} \quad T_{12}=-112\)
\(\textsf{c)} \quad \sf 8th\;term\)
a) Second difference is 2.
b) First term is 10.
Step-by-step explanation:
The given number pattern is:
20, 18, 14, 8, ...To determine the type of sequence, begin by calculating the first differences between consecutive terms:
\(20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8\)
As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):
\(-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6\)
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of the n² term is half of the second difference.
As the second difference is -2, the coefficient of the n² term is -1.
Now we need to compare -n² with the given sequence (where n is the position of the term in the sequence).
\(\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}\)
We can see that the algebraic operation that takes -n² to the terms of the sequence is to add (n + 20).
\(\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}\)
Therefore, the expression to find the the nth term of the given quadratic sequence is:
\(\boxed{T_n=-n^2+n+20}\)
To find the value of T₁₂, substitute n = 12 into the nth term equation:
\(\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}\)
Therefore, the 12th term of the number pattern is -112.
To find the position of the term that has a value of -36, substitute Tₙ = -36 into the nth term equation and solve for n:
\(\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}\)
As the position of the term cannot be negative, the term that has a value of -36 is the 8th term.
\(\hrulefill\)
Given terms of a quadratic number pattern:
T₂ = 1T₃ = -6T₅ = -14We know the first differences are negative, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:
\(T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14\)
From this we can create three equations:
\(T_1-a=1\)
\(-6-b=T_4\)
\(T_4-c=-14\)
The second differences are the same in a quadratic sequence. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).
\(-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c\)
From this we can create three equations:
\(-a+x=-7\)
\(-7+x=-b\)
\(-b+x=-c\)
Substitute the equation for -b into the equation for -c to create an equation for -c in terms of x:
\(-c=(-7+x)+x\)
\(-c=2x-7\)
Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create two equations for T₄ in terms of x:
\(\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}\)
\(\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}\)
Solve for x by equating the two equations for T₄:
\(\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}\)
Therefore, the second difference is 2.
Substitute the found value of x into the equations for -a, -b and -c to find the first differences:
\(-a+2=-7 \implies -a=-9\)
\(-7+2=-b \implies -b=-5\)
\(-5+2=-c \implies -c=-3\)
Therefore, the first differences are:
\(T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14\)
Finally, calculate the first term:
\(\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}\)
Therefore, the first term in the number pattern is 10.
\(10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14\)
Note: The equation for the nth term is:
\(\boxed{T_n=n^2-12n+21}\)
Related Questions
Please look at the photo. Thank you!
Answers
The value of f(5) is positive
At f(x) = 0, the value of x is 1
For the interval f(x) ≤ 0, the values of x are [-2, 1]
How to determine the values of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
f(5) = 1
This means that f(5) is positive
Also, we have
When f(x) = 0, the value of x is 1
For the interval f(x) ≤ 0, we have the values of x to be
-2 ≤ x ≤ 1
When represented as an interval, we have
[-2, 1]
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A gain of seven yards in football is represented by 7. What number represents a loss of
seven yards?
A 0
B. 7
C. -(-7)
D. -7
Answers
Answer:
D. -7
Step-by-step explanation:
Since positive 7 represents a gain of seven yards, a loss would be represented by a negative number.
So, a loss of seven yards will be represented by -7.
So, the correct answer is D. -7
Find the volume of the following figure
Answers
so it would be 6 x 4 x 2 so the answer is 48
If a new car is valued at $19200 and 8 years later it is valued at $8000, then what is the average rate of change of its value during those 8 years?
Answers
Answer: $1400 / year
Step-by-step explanation:
Let's start by finding the difference in the new car and the price 8 years later:
$19200 - $8000 = $11200
This means the car depreciated by $11200 over 8 years. We divide this by the 8 years:
$11200 / 8 years = $1400.
This means the car changed by an average of $1400 each year.
Which expression is equivalent to 6x+7-12*2-(3 to the power 2 +3)-x
Answers
Step-by-step explanation:
Questions about equivalent expressions usually feature both simple expressions and complex expressions. To check which complex expression is equivalent to the simple expression:
Distribute any coefficients: a(bx\pm c)=abx\pm aca(bx±c)=abx±aca, left parenthesis, b, x, plus minus, c, right parenthesis, equals, a, b, x, plus minus, a, c.
Combine any like terms on each side of the equation: xxx-terms with xxx-terms and constants with constants.
Arrange the terms in the same order, usually xxx-term before constants.
If all of the terms in the two expressions are identical, then the two expressions are equivalent.
Example
How do we solve for unknown coefficients?
Some questions will present us with an equation with algebraic expressions on both sides. On one side, there will be an unknown coeffient, and the question will ask us to find its value.
For the equation to be true for all values of the variable, the two expressions on each side of the equation must be equivalent. For example, if ax+b=cx+dax+b=cx+da, x, plus, b, equals, c, x, plus, d for all values of xxx, then:
aaa must equal ccc.
bbb must equal ddd.
To find the value of unknown coefficients:
Distribute any coefficients on each side of the equation.
Combine any like terms on each side of the equation.
Set the coefficients on each side of the equation equal to each other.
Solve for the unknown coefficient.
Example
How do we rearrange formulas?
Formulas are equations that contain 222 or more variables; they describe relationships and help us solve problems in geometry, physics, etc.
Since a formula contains multiple variables, sometimes we're interested in writing a specific variable in terms of the others. For example, the formula for the area, AAA, for a rectangle with length lll and width www is A=lwA=lwA, equals, l, w. It's easy to calculate AAA using the formula if we know lll and www. However, if we know AAA and www and want to calculate lll, the formula that best helps us with that is an equation in which lll is in terms of AAA and www, or l=\dfrac{A}{w}l=
w
A
l, equals, start fraction, A, divided by, w, end fraction.
Just as we can add, subtract, multiply, and divide constants, we can do so with variables. To isolate a specific variable, perform the same operations on both sides of the equation until the variable is isolated. The new equation is equivalent to the original equation.
The value of equivalent expression is,
⇒ 5x - 29
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 6x + 7 - 12 × 2 - (3² + 3) - x
Now, We can simplify as;
⇒ 6x + 7 - 12 × 2 - (3² + 3) - x
⇒ 6x + 7 - 24 - (9 + 3) - x
⇒ 6x + 7 - 24 - 12 - x
⇒ 5x - 29
Thus, The value of equivalent expression is,
⇒ 5x - 29
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2. A(n) is NOT an example of an agreement. (1 point)
O lease
O month-to-month
O annual
O fine print
Answers
An Annual is not an example of an agreement.
Can you solve this i will give 10 points
Answers
Answer:
2
Step-by-step explanation:
Area = length * width * height
4/5 * 3/2 * 5/3
= 60/30
= 2
a study was conducted that resulted in the following relative frequency histogram. determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.
Answers
If the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
What is Histogram?Histogram a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
Given is relative frequency histogram.
The histogram is not given, so will discussion the property that tells whether the histogram indicates a normal distribution or not.If the bars roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.Therefore, if the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
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The sum of the measures of the angles is 180. The sum of the measures of the second and third angles is two times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
Answer:
(60,47,73)
Step-by-step explanation:
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2 ≤ x ≤ 6.
Answers
To find the average rate of change over an interval we need to calculate how much the function has changed over that interval by subtracting the final value by the initial one and dividing by the lenght of the interval. With this in mind we have:
\(\begin{gathered} \text{rate}=\frac{19-13}{6-2} \\ \text{rate}=\frac{6}{4} \\ \text{rate}=1.5 \end{gathered}\)The average rate of change for this interval is 1.5
bridge is raised so that it forms a 15° angle with the ground. It is then raised some more so that it forms a 43° angle with the ground. How many degrees was the draw bridge raised from its first position to its second position?
Answers
Answer: If you minus it the answer is -0.488692191 rad
I think
Step-by-step explanation:
How do you find the second of an angle?
The whole part of the measure of an angle in decimal degrees is the whole number of degrees. Multiplying the decimal part by 60 gives the number of minutes. If this number of minutes has a decimal part, then multiplying this decimal part by 60 gives the number of seconds.
These are my opinion
The correct way to solve an expression is to work the problem from left to right. True or False?
Answers
Answer:
true
Step-by-step explanation:
The statement 'The correct way to solve an expression is to work the problem from left to right.' is True.
What is an expression?"It is a combination of numbers, variables and mathematical operations."
What is order of operations?"It is a rule that states the sequence in which the multiple operations in an expression should be solved."
For given question,
To solve an expression we use PEMDAS ordering.
This means, first we solve parentheses, then solve exponents, then perform all multiplications and divisions from left to right and lastly perform addition and subtraction, from left to right.
This means, to solve an expression work the problem from left to right.
Therefore the statement 'The correct way to solve an expression is to work the problem from left to right.' is True.
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e = radians. Identify the terminal point and tan e.O A. Terminal point: (33) tan = 13B. Terminal point: (1, 1); tan 6 = 73(1,1)tan 0 = 2C. Terminal point:; tane3D. Terminal point:
Answers
The correct answer is Option D
This following are the steps to take:
Step1: Convert the angle from radians to degrees
\(\begin{gathered} 1\pi radians=180^o \\ \text{Thus }\frac{\pi}{6}\text{ radians = }\frac{180^o}{6} \\ \text{ }\frac{\pi}{6}\text{ radians =}30^o \end{gathered}\)Step 2: Draw a unit circle (with a radius of 1 unit), and show the line which forms angle 30 degrees with the x -axis
Step 3: Compute the values of the terminal points:
\(\begin{gathered} Th\text{e x-coordinate of the terminal point = 1 }\times cos30^0\text{ = }\frac{\sqrt[]{3}}{2} \\ Th\text{e y-coordinate of the terminal point = 1 }\times\sin 30^0\text{ = }\frac{1}{2} \\ \text{Thus the coordinates of ther terminal point = }(x,y)\text{ = (}\frac{\sqrt[]{3}}{2},\text{ }\frac{1}{2}\text{)} \end{gathered}\)Step 4: Compute the values of the tangent of the angle:
\(\begin{gathered} \tan 30^0\text{ = }\frac{y}{x}=\frac{\frac{1}{2}}{\frac{\sqrt[]{3}}{2}}=\frac{1}{\sqrt[]{3}}\text{ } \\ \\ \tan 30^o=\frac{1}{\sqrt[]{3}}\text{ }\times\frac{\sqrt[]{3}}{\sqrt[]{3}}\text{ =}\frac{\sqrt[]{3}}{3} \\ \\ \tan 30^{o\text{ }}=\text{ }\frac{\sqrt[]{3}}{3} \end{gathered}\)
A line contains the point (4, 5) and has a slope of -2.
Which point is also on the line?
(5,7)
(6,2)
(5,3)
(4.1)
Answers
Answer: (5,3)
Step-by-step explanation:
Substituting into point-slope form, the equation of the line is
\(y-5=-2(x-4)\)
Which rearranges as follows:
\(y-5=-2x+8\\\\y=-2x+13\)
To determine if a point lies on a line, you can see if its coordinates satisfy the equation.
Of all the options, only (5,3) works.
Look at ZVSW and ZTSW in the image below.
W
Which of the following is the best description for this pair of angles?
O acute
O complementary
Osupplementary
O straight
Answers
VSW and TSW are supplementary angles.
What is supplementary angle?
Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, and you add them together, the result will be a straight line.
What is complementary angle?
Complementary angles are two angles whose sum is equal to 90 degrees (a right angle). In other words, when two angles are complementary, they "complete" a right angle when added together.
According to given information:In geometry, an angle is formed when two lines or rays intersect. Angles are measured in degrees and are classified based on their measures.
The pair of angles VSW and TSW in the image can be classified as supplementary angles.
Two angles are supplementary if their measures add up to 180 degrees.
In this case, angle VSW and angle TSW are adjacent angles that together form a straight angle, which measures 180 degrees. Therefore, VSW and TSW are supplementary angles.
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Consider that AQRS is similar to ALMN and the measure of ZN is 42°. What is the measure of 2S?
A)
42°
B)
48°
56
D)
589
Answers
Answer:
A
Step-by-step explanation:
Solve the equation. Show all your steps0.5x + 4.2 = 0.7x
Answers
To solve the equation
\(0.5x+4.2=0.7x\)You have to isolate the x-term on one side of the equal sign, for this, pass the term 0.5x to the right side of the equation by applying the opposite operation to both sides of it:
\(\begin{gathered} 0.5x-0.5x+4.2=0.7x-0.5x \\ 4.2=0.2x \end{gathered}\)Next, the x term is being multiplied by 0.2, to cancel the said multiplication you have to divide the term by 0.2. And you keep the equality valid, what is done to one side of the equation has to be done to the other side, so you have to divide 4.2 by 0.2 too:
\(\begin{gathered} \frac{4.2}{0.2}=\frac{0.2x}{0.2} \\ 21=x \end{gathered}\)The value of x is 21
(k^8+8k^2+10k+21) / (k+7)
Answers
Answer:
Step-by-step explanation:
\(\frac{k^8+8k^2+10k+21}{k+7}\) is already simplified.
Suppose that 35% of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 30 students from the population of 750 students at the school and finds that 40% of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this.
Let ^p represent the proportion of a sample of 30 students in the school who can sing their national anthem correctly.
What are the mean and standard deviation of the sampling distribution of ^p?
Answers
Answer:
m^p = 0.35
o^p = \(\sqrt\frac{0.35(1-0.35}{30}\)
Step-by-step explanation:
2x-7y=-56 and 7x+2y=8 are they parallel perpendiculare or neither
Answers
Answer:
They are perpendicular
Step-by-step explanation:
2/7 for the first
-7/2 for the second
Because they are the same lines duh
what is 2x³/x+5 divided by x-5/3x-1
Answers
\(\cfrac{2x^3}{x+5}\div \cfrac{x-5}{3x-1}\implies \underset{\textit{difference of squares}}{\cfrac{2x^3}{x+5}\cdot \cfrac{3x-1}{x-5}}\implies \cfrac{6x^4-2x^3}{x^2 - 5^2}\implies \cfrac{6x^4-2x^3}{x^2 - 25}\)
6. In case of short
circuit............current will flow in
that circuit. *
Answers
Answer:
As suggested in the name itself:
a short circuit makes the circuit 'short' which causes the resistance of the circuit to be close to none
When the resistance is decreased, the amount of current flowing in the circuit increases (ohm's law: R ∝ 1/ I)
Therefore, in case of a short-circuit. More current will flow in the circuit
Solve the equation: x²-2x=8
Show all the Steps with explanation.
Answers
Answer:
x = 4, -2
Step-by-step explanation:
x^2-2x=8
Move the constant term to the right side of the equation.
x^2 - 2x = 8
Take half of the coefficient of x and square it.
(-2/2)^2 = 1
Add the square to both sides of the equation.
x^2 - 2x + 1 = 8 + 1
Factor the perfect square trinomial.
(x - 1)^2 = 9
Take the square root of both sides of the equation.
x-1=\(\sqrt{9}\)
x-1=±3
Isolate x to find the solutions.
Taking positive
x=3+1=4
x=4
Taking negative
x=-3+1
x=-2
The solutions are:
x = 4, -2
Answer:
\(x = -2,\;\;x=4\)
Step-by-step explanation:
To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:
\(x^2-2x-8=8-8\)
\(x^2-2x-8=0\)
Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.
The two numbers whose product is -8 and sum is -2 are -4 and 2.
Rewrite the coefficient of the middle term as the sum of these two numbers:
\(x^2-4x+2x-8=0\)
Factor the first two terms and the last two terms separately:
\(x(x-4)+2(x-4)=0\)
Factor out the common term (x - 4):
\((x+2)(x-4)=0\)
Apply the zero-product property:
\(x+2=0 \implies x=-2\)
\(x-4=0 \implies x=4\)
Therefore, the solutions to the given quadratic equation are:
\(\boxed{x = -2,\;\;x=4}\)
identify an equation in point slope form for the line parallel to y=-2/3x+8 that passes throygh (4,-5)
Answers
Answer:
The equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through the point (4, -5) is:
y - (-5) = (-2/3)(x - 4)
Simplifying, we get:
y + 5 = (-2/3)x + 8/3
y = (-2/3)x - 7/3
Therefore, the equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y = (-2/3)x - 7/3.
Step-by-step explanation:
Suppose you travel 300 miles on a highway for 6 hours.At what rate did you travel?use the distance formula d=rt and solve for r.
Answers
Answer:
50 mph
Step-by-step explanation:
y=3(2-1)2+1
Solución
Answers
Answer:
y = 7
Step-by-step explanation:
y = 3(2-1) 2 + 1
y = 3(1)(2) + 1
y = 6 + 1
y = 7
7 1 /4 x − x =9 3/ 8
Answers
Answer:
1.5 is the correct answer
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
Answers
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
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PLEASE HELP MEEE, I'M FALLING IN MY CLASS
Answers
The average rate of change of the function graphed is -4.
What is average rate of change?
The average rate at which one item is changing in relation to another is known as the average rate of change.
The function y = f(x) is graphed.
We have to find the average rate of change of the function on the interval
2 ≤ x ≤ 4.
The average rate of change is defined as,
Average rate of change = \(\frac{f(b)-f(a)}{b-a} = \frac{f(4)-f(2)}{4-2}\)
From graph,
f(4) = -4, f(2) = 4
So,
Average rate of change = \(\frac{-4-4}{4-2} = \frac{-8}{2} = -4\).
Therefore, for the given graphed function, the average rate of change is, -4.
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The table represents a linear relationship
X—2 0 4
Y-4 3 1
Which equation represents the table
Y=1/2x+5
y=-1/2x+3
Y=2x-3
Y=-4x+2
Answers
The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.
To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.
Given the table:
X: 2 0 4
Y: -4 3 1
We can plot these points on a graph and see that they form a straight line.
Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.
Based on the given options, we can now evaluate each equation to see which one represents the line:
Y = 1/2x + 5
When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.
Y = -1/2x + 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.
Y = 2x - 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.
Y = -4x + 2
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.
In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.
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