The complete sentence is as follows:
The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.
Given, An amusement park prices tickets at $55 and sells an average of 500 tickets daily. The management finds, over multiple increases in ticket pricing that a $2 increase in the price of a ticket leads to an average of 20 fewer tickets being sold in a day.
Management uses the combined function P to model the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
[tex]P(x) = -40x^2- 100x + 27,500[/tex].
What is the combined function?In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.
We need to use the given information to complete the sentences.
The complete sentence is as follows:
The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increase in the price of a ticket.
The binomial (500 - 20x) is a factor of the polynomial expression and represents the number of tickets sold after x increases of $2 in the price of a ticket.
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The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
An amusement park prices tickets at $55 and sells an average if 500 tickets daily.
The function P(x) represents the daily earning of the amusement part, where x is the number of $2 increases in the price of a ticket.
Plug x = 0
P(0) = 27500
The above value is the constant of the polynomial function.
The constant of the polynomial expression represents the daily earning of the amusement park before any $2 increases in the price of a ticket.
As the x is the number of $2 increases in the price of a ticket.
Then,
= (500 - 20x) is the binomial that represents the number of tickets sold after x increases by $2
Thus, the constant of the polynomial expression represents the daily earning of the amusement park before any $2 increase in the price of a ticket, and (500 - 20x) represents the number of tickets sold after x increases by $2.
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Divide.
6√3 cis(7π/6) ÷ 3√5 cis(π/3)
[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]
[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]
[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]
Answer:
Step-by-step explanation:
Just took the test:
6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=
2sqrt15/5 cis (5pie/6)
In your notebook, set up the following subtraction in a vertical format and select the correct answer.
Find 2p 2 + 3p - 4 less - 2p 2 - 3p + 4.
1. 4p2 + 6p + 8
2. 4p2 - 6p - 8
3. 4p2 + 6p - 8
4. 0
The answer is 4p² + 6p - 8 which is subtraction of one equation from the other in vertical format.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have two polynomial:
2p² + 3p - 4 and -2p² - 3p + 4
Subtraction in a vertical format:
2p² + 3p - 4
- -2p² - 3p + 4
-------------------------
Changin sign of the expression -2p² - 3p + 4:
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
Now adding like terms.
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
4p² + 6p - 8
Thus, the answer is 4p² + 6p - 8 which is the subtraction of one equation from the other in vertical format.
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Which table represents a linear function?
Answer:
The first one (x=1 and y=1/2)
Step-by-step explanation:
The first table is the only one that has a constant rate of change. The x value increases by 1, and the y value increase by 1/2.
Hope this helped :)
Answer:
The first one where x increases by 1 and y increases by 1/2.
Step-by-step explanation:
To find the equation, 1/2=1+b
Solve for b
1/2-1=-0.5
B=-0.5
Now, solve for x
1/2=x-0.5
As you can already see in the table, x increase by 1, so no need to even solve.
The equation would be y=1x-0.5 (I’ll post the graph in the picture to prove it is linear.
A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable yy is 1 and the degree of variable x is 1.
Work out the equation of line B. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms.
Answer:
y = -3x + 1
Step-by-step explanation:
The line crosses the y-axis at 1. This is called the y-intercept. This is the number you fill in for c in the form of the equation given.
You can pick any two points on the line to calculate the slope. But you can actually SEE the slope without having to calculate it when you have the graph to look at. See the line crossing the y-axis at 1. Look for another point (that has nice whole number coordinates) there is one DOWN3 and OVER1. If you notice, the next point is also DOWN3 and OVER1.
DOWN3 and OVER1 is the slope -3/1, which is equal to -3.
Fill in -3 in place of the m in the equation.
y = -3x + 1
Done!
Answer:
y = -3x + 1
Step-by-step explanation:
The equation of a line in slope/intercept form is y = mx + c where m is the slope and c the y-intercept(ie the value of y when x =0)
The slope can be found by taking any two points on the line, (x1, y1) and (x2,y2) and computing (y2-y1)/(x2-x1)
If you look at the line 2 points on the line are P(2,-5) and (0,1)
Slope = (-5-1)/(2-0) = -3
The y-intercept is the y-value at which the line intersects the y-axis ie at x = 0 and you can see that this is 1
Therefore equation is
y = -3x + 1
You can check to see if this is correct by plugging in some other value of x and seeing if the correct y value corresponds to the equation y-value
For example, in the graph we see that at x = 1, y = -2
Indeed -3(1) + 1 = -3 + 1 = -2 also
find the range of the given function y= 8x +1, where x>2
Answer:
infinite or if where using whole numbers
y≥25
Hope This Helps!!!
Friends can you please explain me what is given in this picture, and tell me how to solve this please!..
Thank you
Step-by-step explanation:
the picture and its text explain it actually already.
each block (or square) on each side represents a fraction.
the whole block is 1. the colored parts are the fraction of that whole (1).
we see the example 2/3 × 3/4
the left block with 2 out of 3 strips marked in pink shows us 2/3 (2/3 of the block is pink).
the right block with 3 out of 4 strips marked in purple shows us 3/4 (3/4 of the block is purple).
it is essential for this method to orient the strips in one block to be at a right angle with the strips of the other block.
now, to do the multiplication you overlay the strips of both blocks.
you see this creates a chess board pattern. the total number of little squares or rectangles is the denominator (bottom part) of the result. in this case 12.
the number of little squares or rectangles that are in both original strips is the numerator (the top part) of the result. in this case 6.
so, yes, 2/3 × 3/4 = 6/12, which can then be refined to 1/2.
now, you have to do the same thing with the actual examples (I cannot draw here, sorry) :
1/4 × 3/5 = 3/20
the left block with 4 strips (one in pink, or whatever color you want), the right block with 5 strips (and 3 marked in e.g. purple).
and then the result block with 4 columns and 5 rows creating 20 little squares or rectangles, and 3 of them are in all original strips.
and the same
3/5 × 2/3 = 6/15 = 2/5
1/2 × 2/5 = 2/10 = 1/5
What is another way to write the absolute value inequality p ≤ 12? O-12≤p≤ 12 O-122p≤12 O-12 ≤por p≤ 12 -122P or p≤ 12 958 What is another way to write the absolute value inequality p ≤ 12 ? O - 12≤p≤ 12 O - 122p≤12 O - 12 ≤por p≤ 12 -122P or p≤ 12 958
Answer:
-12 ≤ p ≤ 12
Step-by-step explanation:
If the absolute value inequality is
|p| ≤ 12,
then the answer is
-12 ≤ p ≤ 12
TIMED!! pls
What are the zeros of the quadratic function f(x) = 2x^2 + 16x - 9?
What are the endpoint coordinates for the midsegment of △BCD that is parallel to BC¯¯¯¯¯?
Enter your answer, as a decimal or whole number, in the boxes.
( , ) and ( , )
Answer:
(3,3) (-1,-3), you just have to look at the coordinates
Help me please and thxx
Option C).
Sarah bought snacks for her team's practice. She bought a bag of chips for $1.56 and a 20-pack of juice bottles. The total cost before tax was $33.96. Write and solve an equation which can be used to determine j, how much each bottle of juice cost.
The equation is 1.56 + 20x = 33.96 and the value of x is 1.62.
What is Equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Here, Based on the given conditions, formulate: 1.56 + 20 × x = 33.96
Rearrange unknown terms to the left side of the equation: 20x = 33.96-1.56
Calculate the sum or difference: 20x = 32.4
Divide both sides of the equation by the coefficient of variable: x = 32.4/20
Calculate the product or quotient: x = 1.62
get the result: x = 1.62
Thus, the equation is 1.56 + 20x = 33.96 and the value of x is 1.62.
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Sparky bought a rare Mickey Mantle baseball card for $16,500 that is increasing 8% in value every year. How much will the card be worth in 7 years?
Answer: 28,278.10
Step-by-step explanation:
[tex]a_{7} =16500(1.08)^7[/tex]
[tex]a_{7} =28278.1[/tex]
Consider the equation. Which graph shows a line that is perpendicular to the line defined by the given equation? A. In a linear graph line diagram, A line passes through (minus 4, minus 2) and (2, minus 0.5) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. B. In a linear graph line diagram, A line passes through (2, 0.5) and (minus 4, 2) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. C. In a linear graph line diagram, A line passes through (2, 4) and (0.5, minus 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units. D. In a linear graph line diagram, A line passes through (2, minus 4) and (0.5, 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units.
option (B) is correct the graph second represents the line that is perpendicular to the line y = 4x - 2
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The question is incomplete:
The complete question is:
Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?
Please refer to the attached picture.
The given line:
y = 4x - 2
The slope of the line M = 4
The slope of the line which is perpendicular to the above line:
m = -1/4 = -0.25
The graph second has a slope of -0.25
[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]
y - 2 = -0.25x - 1
y = -0.25x + 1
m = -0.25
Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.
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Answer: C
Step-by-step explanation:
please help asap Part of the proceeds from a garage sale was $540 worth of $5 and $20 bills If there were 3 more bills $5 bills than $20 bills, find the number of each denomination.
Answer:
15 ($20 dollar bills) and 19 ($10 dollar bills) ! Pretty sure this is correct, if wrong let me know and i'll make a question for you to give your points back, i dont know if i can do that but i can try!! Have a good day.
Simplify -3/2÷9/6
○-4
O-1
04
01
Answer:
-1
Step-by-step explanation:
the answer snis negative One
Find the length of x. Assume the triangles are similar.
Triangles are similar and only differ in size meaning they are dilated
So first we have to find the scale factor of dilation (by how much the smaller triangle got bigger)
Find scale factor:
2.4a=4.8
z=2
Find x:
we multiply the original side of the small side with the scale factor of 2
2.8(2)=x
5.6=x
So, x=5.6
A sales manager sets sales goals for each of his employees. The manager increases the goals of his salespeople by 5% each month. If Maria’s sales goal was initially 95 units for the month, what is her sales goal after 6 months?
Answer:
Her sales after 6 months are = 127units
Step-by-step explanation:
Percentage increase:- The degree to which a value increases expressed in percent form is known as percentage increase.
formula for % increase = (final value - initial value)/initial value(100)
Here in the question,
percentage increase after every month is = 5%
initial value = 95 units
therefore by applying above formula :-
[(x-95)/95]×100 = 5 [where x is the value of her sales goals after 1 month]
x = (5/100)×95+ 95
x = 99.75
Now this x will be the initial value for the next month
x₂ = (5/100)99.75+ 99.75 [ x₂ = sales goal after 2 months]
x₂ = (5/100)×99.75+ 99.75
x₂ = 104.73
similarly,
(x₃-104.73/104.73)100 = 5 [x₃ = sales after 3 months]
x₃ = 109.96
similarly for 4th month,
(x₄ -109.96/109.96)100 = 5 [x₄ = sales after 4 months]
x₄ = 115.45
for 5th month,
(x₅ -115.45/115.45)100 = 5 [x₅ = sales after 5 months]
x₅ = 121.22
finally for the 6th month
(x₆-121.22/121.22)100 = 5 [x₆ = sales after 6 months]
x₆ = 127.28
therefore,
her sales after 6 months are = 127.28 units or 127 units by rounding off
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Estimate the sum
6 13/28 + 8 3/32
Answer:
14 will be the answer...
Step-by-step explanation:
6 13/28 = 6
8 3/32 = 8
6 + 8 = 14
A car travels at an average speed of 50 km/h for 1.5 hours. How far did the car travel in km?
Answer:
75 km
Step-by-step explanation:
(50km/h)(1.5h) = 75km
At an amusement park, 40 percent of the tickets were sold in the first hour. If 800 tickets were sold in the first hour, which equation can be used to find the total number of tickets sold for the entire day?
StartFraction 800 divided by 40 Over 40 divided by 40 EndFraction = StartFraction 20 Over 1 EndFraction
StartFraction 100 divided by 4 Over 800 divided by 4 EndFraction = StartFraction 25 Over 200 EndFraction
StartFraction 40 times 20 Over 800 times 20 EndFraction = StartFraction 800 divided by 16,000 EndFraction
Answer:
2000 tickets were sold
Step-by-step explanation:
40% can also be written as 0.40
800/ 0.40 = 2000 total tickets
Graphs of tinear Relationships: Mastery Test
Select the correct answer from each drop-down menu.
The graphs below show the average temperature of a city, y, in "F, for the first 8 months of last year. Both graphs show the same information.
Change in Temperature
Change in Temperature
Y
60
40
20
2
Month
Graph A
Month
Graph B
Bejaron is preparing a report and wants to emphasize that the temperature increased greatly over the first 3 months
Complete the forowing sentences
To me the
should
crease in temperature, it would be best for Benjamin to usa
us this graph for his presentation because the temperature
Temperature (°F)
150
120
BO
Temperature ("F)
To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph
How to determine the appropriate graph?The graphs that complete the question are added as an attachment
From the attached graph, we have the following highlights:
The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....The above means that graph B is a misleading graph
Hence, Benjamin should use graph A for his report
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How do you factor a^2-b
Answer:
a
2
−
b
2
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
a
and
b
=
b
.
The graph of g(x) is the result of translating the graph of f(x) = 3 ^ x six units to the rightWhat is the equation of g(x)
Answer: [tex]g(x) = 3^{x-6}[/tex]
Step-by-step explanation:
Think about it like doing
x - 6 = 0
x = 6
That is how you know that it will be shifted 6 units right (how you can tell the difference between right and left shift)
How do you find inverse functions?
will give brainliest to first helpful response
Answer:
swap x and y
Step-by-step explanation:
You can find an inverse function by replacing "x" and "y"
for example:
y = mx + b
becomes
x = my + b
if your equation is:
f(x) = 3(x²) - 3
{remember, f(x) means the same thing as y}
y = 3(x²) - 3
inverse:
x = 3(y²) - 3
this is it, hope this is helpful!!
Answer:
make every (x) a (y)
12. Allison is buying some boxes of frozen treats: popsicles, p, ice cream bars, b, and ice cream
sandwiches, s. All three items cost $2.25 for each box. Write two equivalent expressions to
determine how much Allison will spend on all the frozen treats.
Answer:
One possible answer is: 2.25p + 2.25b + 2.25s
Another possible answer: 2.25(p + b + s)
==========================================================
Explanation:
p = number of popsiclesb = number of ice cream barss = number of ice cream sandwichesEach item costs $2.25 per box, so,
2.25p = cost of just the popsicles only2.25b = cost of just the ice cream bars only2.25s = cost of just the ice cream sandwiches onlyAdd up those subtotals to get the grand total
2.25p + 2.25b + 2.25s
is one possible answer
What we can do is factor out the common 2.25 using the distributive rule in reverse.
Another possible answer is: 2.25(p + b + s)
100 POINTS! Write a system of three linear equations with three variables each that has the unique solution (1,2,-1). Write your equation in standard form. Use the variables x,y, and z with non-zero coefficients
Answer:
Three linear equations that has a unique solution (1,2,-1) are:-
x+ y+ z =2
2x + y + 3z = 1
x+ 2y+ z = 4
Step-by-step explanation:
Linear equations in three variables:-
If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0)
then ax + by + cz = r is called a linear equation in three variables. (The
“three variables” are the x, the y, and the z.)
The numbers a, b, and c are called the coefficients of the equation. The
number r is called the constant of the equation.
so from from above explanation we can write 3 linear equations with three variables as.
x+ y+ z =2
2x + y + 3z = 1
x+ 2y+ z = 4
Now to check if the given point (1,2,-1) is solution or not these equations must satisfy this point,
x+ y+ z =2
1+ 2- 1 = 2
2= 2
2x + y + 3z = 1
2×1 +2 - 3×1 = 1
1=1
x+ 2y+ z = 4,
1+ 2×2 -1 = 4
4=4
therefore all three equations satisfies the given point
hence these are the three linear equation having point (1,2, -1) as the unique solution
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answer:
2nd and third option
Step-by-step explanation:
The second option just combines the 6.5p and the 0.01p on the right side to obtain 6.49p. The third option just multiplies both sides by 100.
what is the vertex of the graph of y = -4x(x + 2)^2 + 5
Answer:
The vertex is the point of coordinates (-2 , 5)
Step-by-step explanation:
we notice that the equation of the parabola is given in vertex form :
y = -4(x + 2)² + 5
then
y = -4(x − (-2))² + 5
Therefore
The vertex of the graph is the point (-2 , 5)
answer must be in simplest form
The trigonometric ratios shows that the cos M is 4/5.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex]hypothenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin [tex]\alpha[/tex], cos [tex]\alpha[/tex] and tan [tex]\alpha[/tex], where:
[tex]sin \alpha =\frac{opposite\;leg}{hypotenuse} \\ \\ cos \alpha =\frac{adjacent\;leg}{hypotenuse} \\ \\ tan \alpha =\frac{opposite\;leg}{adjacent\;leg}[/tex]
For finding the cos M, firstly, you should find the side MN from Pythagorean Theorem.
[tex]hypothenuse^2=(leg_1)^2+(leg_2)^2\\ \\\ 30^2=18^2+(MN)^2\\ \\ 900=324+(MN)^2\\ \\(MN)}^2=900-324\\ \\ (MN)^2=576\\ \\ MN=24[/tex]
If MN=24, the cos M will be
[tex]cosM =\frac{adjacent\;leg}{hypotenuse} =\frac{24}{30} =\frac{4}{5}[/tex]
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PQRS is a parralelogram. the position vector of Q R and S are 5i +7j, -3i-8j and -4i-6j. find the position vector of P
The value of the variable x = 6 and y = 5. Then the position vector of P will be 6i + 5j.
What is the equation of a line passing through two points?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
PQRS is a parallelogram. the position vector of Q R and S are 5i +7j, -3i-8j and -4i-6j.
Then the point of Q, R, and S will be (5, 7), (-3, -8), and (-4, -6).
Let the point P be (x, y).
We know that the slope of the line QS and PQ will be same and line is passing through (-3, -8).
y = 1.444x + C
-8 = 1.444 (-3) + C
C = -3.667
Then the equation will be
y = 1.444x – 3.667 …1
The slope of the line PQ and RS will be same and line is passing through (5, 7).
y = -2x + D
7 = -2 (5) + D
D = 17
Then the equation will be
y = -2x + 17 …2
By solving equation 1 and 2, we have
x = 6 and y = 5
Then the position vector of P will be
⇒ 6i + 5j
The graph is given below.
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