Answer:
Hello,
Step-by-step explanation:
1. We must decompose the conic into 2 lines.
[tex]f(x,y)=x^2-5xy+y^2+5x-2y+1=0\\\\We\ are\ going\ to\ find\ the\ center\\\\\left\{\begin{array}{ccc}\dfrac{ \partial{f} }{\partial{x} }&=&12x-5y+5=0\\\\\dfrac{ \partial{f} }{\partial{y} }&=&-5x+2y-2=0\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x=0\\y=1\\\end {array} \right.\\\\We\ must\ find\ an\ other\ point\ of\ f(x,y).\\\\if\ y=0\ then\ x=\dfrac{-1}{2} \ or\ x=\dfrac{-1}{3}[/tex]
The 2 lines are: 2x-y+1=0 and 3x-y+1=0
Paralleles are y=2x and y=3x
Perpendiculars are x+2y=0 and x+3x=0
Simplify 9 – 3(4x – 18) + 6x
The expression is simplified to 7(-x + 9)
What are algebraic expressions?
Algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.
They are also made up of mathematical or arithmetic operations
Given the expression;
9 – 3(4x – 18) + 6x
expand the bracket
9 - 12x + 54 + 6x
collect like terms, we have;
-12x + 5x + 54 + 9
Add or subtract like terms
-7x + 63
Factor out 7
7(-x + 9)
Thus, the expression is simplified to 7(-x + 9)
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for a given non-zero vector v in r 3 there is a unique unit vector parallel to it. is it true or false? explain your answer.
The given statement is true that for a given non-zero vector v in r³ there is a unique unit vector parallel to it.
A vector is defined by its length and direction. If two vectors have the same direction, they are parallel. The length is irrelevant.If the length of a vector is one, it is a unit vector. The direction is irrelevant.So, in order to locate a unit vector parallel to another vector, it must point in the same direction and be of length 1.For a given non-zero vector, there are an infinite number of parallel vectors to it but with different magnitudes. There is only one vector which is not only parallel to the given non-zero vector but also has a magnitude of 1, i.e., the unit vector parallel to it.Thus, it is true that for a given non-zero vector v in r³ there is a unique unit vector parallel to it.To learn more about vectors, visit :
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697x82=________x________=________
The answer is most probably to round the the numbers to nearest 10 digits and multiply
697x82 = 56,154
700 x 80 = 56000
What is rounded numbers?A rounded number is less precise but roughly equal to the original number in value.
To the closest hundred, 341 is equivalent to 300. This is due to the fact that 341 is more similar in value to 300 than to 400. Because $1.89 is closer to $2.00 than to $1.00, when rounded off to the nearest dollar, it becomes $2.00.
The standard rounding rule is as follows:
Round up if the number you are rounding is followed by a 5, 6, 7, 8, or 9. For instance, 38 rounded up to the nearest ten is 40.Round down if the number you are rounding is followed by a 0, 1, 2, 3, or 4. Example: 30 when 33 is rounded to the nearest ten.Learn more about rounded number
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Full questionRound to nearest 10 digits and multiply
697x82=________x________=________
connie walks from her home to the bicycle repair shop at 6mk/h and then bikes home at 20km/h. if her total traveling time is 39 minutes, how far is her home from the bicylce repair shop
Her home is 3km far from the bicycle repair shop;
Her avg speed = 2*6*20/(6+20) = 60/13 km/h
d = r*t = (60/13)*(39/60)
d = 3 km;
What is Avg Speed?
In normal use and in kinematics, the speed (normally known as v) of an object is the significance of the change of its position over time or the value of the change of its role consistent with unit of time; it is for this reason a scalar amount.
The common speed of an item in an c programming language of time is the distance travelled by using the item divided by the length of the c program languageperiod
the instant pace is the restriction of the common speed because the length of the time c program languageperiod methods 0. velocity isn't similar to pace.
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How do I remember my timetables easily? Any advice?
Answer:
Study a Times Tables map each day if you can soon you will get the hang of it
how do I determine whether each linear relationship is a direct variation and if so how do I state the constant of proportionality.
Pictures, x 3
Profit, y 24
By using the given pair of values we can see that the constant of proportionality is 8, and the proportional relation is:
y = 8*x
How to determine the proportional relation?A proportional relation is a linear relation with an y-intercept of 0, so these are written as:
y = a*x
Where a is the constant of proportionality.
By knowing a pair of values x and y, we can find the value of a. In this case we can see that when x = 3, y = 24, replacing that in the general equation we get:
24 = a*3
24/3 = a = 8
Then the constant of proportionality is 8, and the proportional relation is:
y = 8*x
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Please help me with this page
Answer:
a) A = 1, C = 0, and D > 0 --> Graph B
b) A = 1, C = 0, and D < 0 --> Graph C
c) A > 1, C > 0, and D > 0 --> Graph D
d) 0 < A < 1, C < 0, and D < 0 --> Graph A
the length of a rectangle is four less than twice it’s width. If the width is 6 inches what is the length of the rectangle ?
Answer:
The question states four less than twice its width so we first find twice the width. The width is 6 and twice that is 12. Note that it says four less than, so four less than 12 is 8. so the length of the triangle is 8.
Step-by-step explanation:
Hope it helps! =D
Simplify:(4x^2 - 2x) - (-5x^2 - 8x)
aye could yall help a brother out?
Answer: 9x^2+6x
Step-by-step explanation:
(4x^2 - 2x) - (-5x^2 - 8x)=
4x^2 - 2x +5x^2 + 8x=
4x^2+5x^2 - 2x + 8x=9x^2+6x
What is the answer for 10x=4x + 5
I don't see why my answer got deleted from last time as nothing was wrong with it, but your answer is: x = 5/6.
--------------------------------------------------------
Hope this helps!
Have a great day and God bless! :)
i need help with this question asap
Answer:
x² + y² = z²
Step-by-step explanation:
(a)
Using the right triangle altitude theorem,
x/z = p/x
x² = pz
(b)
y/z = q/y
y² = qz
(c)
x² + y² = pz + qz
x² + y² = z(p + q)
z = p + q
x² + y² = z × z
x² + y² = z²
evaluate the polynomial function at x=-2 using direct and synthetic substitution f(x)=3x⁵-x³+6x²-x+1
Answer:
-61
by both methods
Step-by-step explanation:
Let's first see what the terms direct substitution and synthetic substitution mean.
Direct Substitution
In direct substitution, to find the value of a polynomial f(x) at any point x = k. we simply substitute the value of k into the polynomial function and solve for f(k)
Synthetic Substitution
In synthetic substitution we make use of the Remainder Theorem..
The Remainder Theorem states that when we divide a polynomial [tex]f(x)[/tex] by [tex]x-c[/tex], the remainder [tex]R[/tex] equals [tex]f(c)[/tex]
Solving using direct substitution
The given polynomial is
[tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex]
and we are asked to evaluate this function at [tex]x = - 2[/tex]
Using Direct Substitution,
[tex]f(-2) = =3\left(-2\right)^5-\left(-2\right)^3+6\left(-2\right)^2-\left(-2\right)+1\\\\=3\left(-32\right)-\left(-8\right)+6\left(-2\right)^2-\left(-2\right)+1\\\\=- -96 + 8 + 6(4) + 2 + 1\\=-96 + 8 + 24 + 2 + 1\\\\= -61\\\\[/tex]
Using direct substitution we get [tex]\bold{f(-2)= -61}[/tex]
Using Synthetic Substitution
Since the remainder when [tex]f(x)[/tex] is divided by [tex]x - c[/tex] is [tex]f(c)[/tex] , we will divide the polynomial [tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex] by [tex]x -(-2) = x + 2[/tex] and find out the remainder which will give f(-2)
This is the technique used in synthetic division
Step 1. Write only the coefficients of [tex]x[/tex] in the dividend inside an upside-down division symbol. Write -2 as the divisor on the left of this row
[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 2
Carry down the leading coefficient as is to below the division symbol
[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\;\;\;\;3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 3
Multiply the above carry-down value by -2 and carry that result to the next column:
[tex]3\left(-2\right)=-6[/tex]
[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 4
Add down the column
[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 5
Multiply the above carry-down value by -2 and carry that result to the next column:
(-6)(-2) = 12
2 | 3 0 -1 6 -1 1
| -6 12
-------------------------------------------------
3 -6
Step 6
Add down the column
-1 + 12 = 11
2 | 3 0 -1 6 -1 1
| -6 12
-------------------------------------------------
3 -6 11
Repeat this process for the other two coefficients
The final result is
2 | 3 0 -1 6 -1 1
| -6 12 -22 32 -62
-------------------------------------------------
3 -6 11 -16 31 -61
The last carry-down value s the remainder and the value of f(-2) = - 61
Two friends are planning for a gathering. The food budget is modeled by one half times the absolute value of the quantity x minus 110 end quantity equals 6 comma where x is the amount spent on food. What are the least and greatest amounts that the two friends could spend on food?
A. $98, $122
B. $104, $116
C. $107, $113
D. $110, $122
The least and the greatest amounts are $98 and $112
How to determine the least and the greatest amounts?The food budget is modeled by 0.5|x - 110| = 6
So, we have:
0.5|x - 110| = 6
Divide both sides by 0.5
|x - 110| = 12
Remove the absolute bracket
x - 110 = 12 and x - 110 = -12
Add 110 to both sides
x = 112 and x = 98
Hence, the least and the greatest amounts are $98 and $112
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Factorise x^2+4x+3=0
Mooberry Creamery uses 2 cups of ice cream in each milkshake. How many milkshakes can they make with 1 gallon of ice cream?
ANSWER
8 milkshakes
Step-by-step explanation
16 cups in a gallon. 2 cups per milkshake. 8 milkshakes are the answer
Answer:
8 milkshakes
Step-by-step explanation:
16 cups in a gallon. 2 cups per milkshake.
16/2=8
Factor
completely 3x^4 30x^3 + 75x^2
PLS HELP!
The factors of the expression is 3x²(x+5)(x+5) .
Factors of a number are defined as the numbers which divide the given number completely.
For an algebraic expression the factors of the expression are smaller polynomials which divide the given expression completely.
Factors of algebraic expression can be calculated by the following methods:
Middle-term factorizationcompletion of squareUsing factor theoremThe given polynomial is of the form:
3x⁴ + 30x³ + 75x²
Taking 3x² common from all the terms we get:
3x² (x² + 10x + 25)
Now we use middle- term factorization method to factor (x² + 10x + 25)
3x² (x² + 5x + 5x + 25)
or, ( 3x² ){x ( x + 5 ) + 5 ( x + 5 )}
or, 3x² (x + 5) (x + 5)
or, 3x² (x + 5)²
Hence the factors of the expressions are: 3x² (x + 5)²
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Disclaimer: The complete question is :
Factor completely: 3x⁴ + 30x³ + 75x²
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5. [0/1 Points]
Find a mathematical model that represents the statement. (Determine the constant of proportionality.)
y varies inversely as x. (y 6 when x = 28.)
DETAILS
Submit Answer
PREVIOUS ANSWERS
x
Check which variable(s) should be in your answer.
Need Help? Read It
LARPCALCLIMSHS 1.10.051.
( b ) = 2/3 Please help me solve this equation
Answer:
b=2/3
Step-by-step explanation:
Let's solve the equation step by step
( b ) = 2/3
Remove bracket
b=2/3
Find the equation of the linear function represented below in the slope intercept form.
to get the equation of any straight line, we simply need two points off of it, let's use those two points off the table in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-22}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-40}{6 +4} \implies \cfrac{ -40 }{ 10 }\implies -4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{-4}(x-\stackrel{x_1}{(-4)})\implies y-18=-4(x+4) \\\\\\ y-18=-4x-16\implies y=-4x+2[/tex]
help, i’ll give you brain list sh or wtv if it’s correct. !!
the combinations that work are "A" and "B" as they both equal to 80
Use the picture below to solve for the missing information, given PQ = 2x + 8, QR = x + 11, and PR = 5x - 3.
Someone please help, BE SPECIFIC on the answers & how you got them, with a explanation. (please fill in all the blanks, thank you)
NO TROLLING. please.
(For geometry class by the way, we're learning about segments).
Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.
What are the numerical values of x, segment PQ, QR and PR?Given the data in the question;
Q is a point between P and RSegment PR = 5x - 3Segment PQ = 2x + 8Segment QR = x + 11Numerical value of x, segment PQ, QR and PR = ?Since Q is a point between P and R.
PR = PQ + QR
Plug in the given values and solve for x.
5x - 3 = ( 2x + 8 ) + ( x + 11 )
5x - 3 = 2x + 8 + x + 11
5x - 3 = 3x + 19
5x - 3x = 19 + 3
2x = 22
x = 22/2
x = 11
Numerical value of segment PQ when x = 11 will be;
PQ = 2x + 8 = 2(11) + 8 = 30
Numerical value of segment QR when x = 11 will be;
QR = x + 11 = (11) + 11 = 22
Numerical value of segment PR when x = 11 will be;
PR = 5x - 3 = 5(11) - 3 = 52
Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.
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the measure of an angle is 26.5 what is the measure of its complementary angle
Answer: 63.5
Step-by-step explanation:
90 - 26.5 = 63.5
find the equivalent fractionsss with large denominatorsss
Answer: 24/54
Step-by-step explanation:
[tex]\displaystyle\\\frac{4}{9}=\\\\ \frac{4}{9}*1=\\\\ \frac{4}{9}*\frac{6}{6} =\\\\\frac{4*6}{9*6} =\\\\\frac{24}{54}[/tex]
14. Equation Editor Ryan downloaded a video
game to his computer. The size of the file
was 2.4 x 10 (5 th power) kilobytes. After the game was
installed, he downloaded a patch file for the
game that was 48,000 kilobytes in size.
(Lesson 6)
A. What is the size of the game in standard
form?
B. how many times larger was the game than the patch file
Part a: The size of the game in standard form is 240000 kilobytes
Part b: The game was 5 times larger than the patch file
Part A:
Size of the game downloaded by Ryan on his computer = 2.4 * 10^5
Size of the patch file for the game = 48000 kilobytes
Therefore, converting the size of the game into the standard form:
Size of the game = 2.4 * 10^5
= 2.4 * 100000
= 240000 kilobytes
Therefore, the size of the game is 240000 kilobytes in standard form
Part B:
Size of the game = 240000 kilobytes
Size of the patch file = 48000 kilobytes
Computing the size of the game with respect to the patch file we get:
=240000/48000
= 5
Hence, the game was 5 times larger than the patch file
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1
T
school 1 H
school 2
2
✓
✓
468 10 12 14 16 18
hours in the weight room
The two box plots summarize the number of hours
spent in the weight room for all the players on the
football team for two different high schools. Determine
whether the following statements are true or false.
d) School 1 had the player that spent the most time
in the weight room.
M
True
O
False
Sep 16
3:00
true!!!
school 1 spent 13 hours in the weight room whereas school 2 spent 11 hours in the weight room
estimate the slope of the tangent line at p by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to p.
The secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.Point P: (15, 1257)
(a) The secant lines' slopes PQ.
The points are as follows:
Q = {(5, 3410), ( 10, 2210), (20, 550), (25, 145), (30, 0)}The slope (m) is calculated using:
Therefore, the secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.The slope (m) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So far, we have:
The slope of the secant line for Q = (5,3410) is:
[tex]\begin{aligned}m_1 &=\frac{1275-3410}{15-5} \\m_1 &=\frac{-2135}{10} \\m_1 &=-213.5\end{aligned}[/tex]
The slope of the secant line for Q = (10, 2210) is:
[tex]\begin{aligned}&m_2=\frac{1275-2210}{15-10} \\&m_2=\frac{-935}{5} \\&m_2=-187\end{aligned}[/tex]
The slope of the secant line for Q = (20, 550) is:
[tex]\begin{aligned}&m_3=\frac{1275-550}{15-20} \\&m_3=\frac{725}{-5} \\&m_3=-145\end{aligned}[/tex]
The slope of the secant line for Q = (25, 145) is:
[tex]\begin{aligned}&m_4=\frac{1275-140}{15-25} \\&m_4=\frac{1135}{-10} \\&m_4=-113.5\end{aligned}[/tex]
The slope of the secant line for Q = (30, 0) is:
[tex]\begin{aligned}&m_5=\frac{1275-0}{15-30} \\&m_5=\frac{1275}{-15} \\&m_5=-85\end{aligned}[/tex]
(b) The average slope of the tangent.
The secant lines that are closest to tangent P are:
Q = {( 10, 2210), (20, 550)}This is because point P (15, 1275) is located between the two previous points.
The slopes of secant lines at Q = {( 10, 2210), (20, 550)} are:
[tex]\begin{aligned}&m_2=-187 \\&m_3=-145\end{aligned}[/tex]
The average slope (m) is as follows:
[tex]\begin{aligned}&m=\frac{m_2+m_3}{2} \\&m=\frac{-187-145}{2} \\&m=\frac{-332}{2} \\&m=-166\end{aligned}[/tex]
Hence, the average slope is -166.
Therefore, the secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.Know more about slopes here:
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The complete question is given below:
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).
(8x-4)+(4x-90)
also simplify
Answer:
12x-94
---------------------
Hope this helps!
Have a great day and God bless! :)
the angle of elevation to the top of a very tall building is found to be 11° from the ground at a distance of 1 mi from the base of the building. using this information, find the height of the building. (round your answer to the nearest foot.)
The height of the building = 1026.328ft
Given the angle of elevation = 11°
The angle of elevation is the angle formed between the horizontal distance to the base of the building and the line of sight to the top of the building.
We know that tan x = opposite side/adjacent side.
Here the opposite side gives the height of the building and the adjacent side is the distance to the base of the building on the ground.
Distance to the base of the building on the ground = 1 mile = 5280 ft.
So tan 11° = h/5280
⇒ h= tan 11° x 5280 = 0.194 x 5280 = 1026.328 ft
So the height of the building = 1026.328 ft
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On a number line, point A is at 5, and point B is at -10. Point C is on AB such that the ratio of AC to CB is 1: 3. Find D on BC such that the ratio of BD to DC is 3:5.
The location of point D on the number line is -5.15625
How to determine the location of point D?The given parameters are:
A = 5
B = -10
AC : CB = 1 : 3
This means that
C = AC/(AC + AB) * (A - B)
This gives
C = 1/4 * (5 + 10)
Evaluate
C = 3.75
Also, we have:
BD : DC = 3 : 5
So, we have:
D = BD/(BD + DC) * (B - C)
This gives
D = 3/8 * (-10 - 3.75)
Evaluate
D = -5.15625
Hence, the location of point D on the number line is -5.15625
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Find an equation of the line. Write the equation using function notation. Through ;(6,-7) perpendicular to 2y=x-4
The equation of the line in function notation is y.=-2x + 5
Equation of alineThe standard equation of a line is expressed as y = mx + b
where
m is the slope
b is the y-intercept
Given the equation
2y=x-4
y = 1/2x - 2
The slope perpendicular will be -2
Substitute into y-y₁ = m(x-x₁)
y-(-7) = -2(x-6)
y+7 = -2x +12
y = -2x + 5
Hence the equation of the line in function notation is y.=-2x + 5
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