The equation of line is y = -4
Given the points:
(x₁, y₁) = (-1, -4)
(x₂, y₂) = ( 3, -4)
The slope-intercept form:
y = mx + b
Where, m is the slope and b is the y-intercept, that is (0, b)
The formula for slope:
m = (y₂ – y₁) / (x₂ – x₁)
We have given
x₁ = -1
x₂ = 3
y₁ = -4
y₂ = -4
So,
m = (-4 – (-4)) / (3 – (-1)) = (-4 + 4) / (3 + 1) = 0/4 = 0
Therefore we have the equation of the line as:
y = mx + b
-4 = 0(x) + b
-4 = 0 + b
b = -4
Therefore, the equation of line y = -4
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Solve for R
60 = -12r
determine whether the following graph represent a function.
1. one to one function
2. function but not one to one
3. not a function
In Δ J L P, m ∠J M P=3 x-6 J K=3 y-2 , and L K=5 y-8 .
Find L K if PK is a median.
In Δ JLP, m ∠ JMP = 3x - 6, JK = 3y - 2, and LK = 5y - 8 then the value of LK = 7.
What is a median?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution. It is sometimes referred to as "the middle" value in a data set.
The middle number is discovered by sorting all data points and selecting the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).
Since [tex]$\overline{P K}$[/tex] is a median, JK = KL.
3y - 2 = 5y - 8
simplifying the above equation, we get
3y - 5y - 2 = 5y - 5y - 8
-2y - 2 = -8
Adding 2 on both sides of the equation
-2y - 2 + 2 = -8 + 2
-2y = -6
y = 3
Substitute the value of y in LK, then we get
LK = 5y - 8
= 5(3) - 8
= 15 - 8
LK = 7
Therefore, the value of LK = 7.
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8x=10x+22
pls show work ty
Answer:
-11
Step-by-step explanation:
step 1
Move the variable to the left-hand side and change its sign
8x-10x=22
step 2
collect like terms
-2x=22
step 3
Divide both sides of the equation by -2
x=-11
For each of the following statistics, determine
whether the value of the statistic is greater for Data
Set 1, equal for both data sets, or greater for Data
Set 2.
Answer:
greater for the data set 1.
simplify this with all the steps
Answer:
[tex]\frac{x}{x+2}[/tex]
Step-by-step explanation:
[tex]\frac{x^2+5x}{x^2+7x+10}[/tex] ← factorise numerator and denominator
= [tex]\frac{x(x+5)}{(x+5)(x+2)}[/tex] ← cancel (x + 5) on numerator / denominator
= [tex]\frac{x}{x+2}[/tex]
What is an equation of each line?
The equation of line is ax + by + c = 0.
A line's equation has the conventional form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.
With the aid of the line's slope and a point on the line, the equation of a line may be created. For a better understanding of how a line's equation is created, let's learn more about the line's slope and the necessary point on the line. The slope of a line is the angle that the line makes with the positive x-axis and can be stated as a numerical integer, fraction, or as the tangent of that angle. The term "point" refers to a coordinate system point with the x and y coordinates.
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Jeff, Gene, and Mike need to eat an entire cake before it goes bad. The cake is cut into 8 pieces.
- Jeff could eat 6 pieces of cake in 2 hours
- Gene can eat 2 pieces of cake in 30 minutes
- Mike can eat 4 pieces of cake in 48 minutes
The pieces can be divided into smaller pieces as necessary - the rates are based on the size of pieces that result when dividing the cake into 8 equal pieces.
Answer these questions below:
1) How many pieces of cake can jeff eat in 1 hour? _________________
2) How many pieces of cake can Gene eat in 1 hour? _____________________
3) How many pieces of cake can Mike eat in 60 minutes? ____________________
4) Will it take Mike, Gene, and Jeff more than 1 hour to each eat the cake, or less that an hour to eat the cake? Explain how you know.
The pieces of cake that Jeff will eat in 1 hour is 3
The pieces of cake that Gene will eat in 1 hour is 4
The pieces of cake that Mike will eat in 1 hour is 5
It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake
How many pieces of cake would they eat in 1 hour?In order to determine the pieces of cake that Jeff can eat in 1 hour, divide 6 by 2.
6/2 = 3 pieces of cake
In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 2 pieces of cake by 2.
2 x 2 = 4 pieces of cake
In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 4 pieces of cake by 60 minutes and divide the result by 48 minutes.
(4 x 60) / 48 = 5 pieces of cake
It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake, because they all eat less than 8 slices of cake in one hour.
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Describe a pair of independent events and a pair of dependent events. Explain your reasoning.
Independent events are the ones whose occurrence is unrelated to any other event.
Dependent events include those that are dependent on previous events.
What is described as independent events?If the probability of an event A occurring is not impacted by the occurring of some other event B, then A & B are referred to as independent events.
Consider the example of a die roll. If A is the event 'the number appearing is odd' and B is the event 'the number showing up is a multiple of 3,'
P(A) = 3/6 = 1/2
P(B) = 2/6 = 1/3
A and B are also the events 'the number showing up is odd & a multiple of 3', implying that;
P(A ∩ B) = 1/6
P(A│B) = P(A ∩ B)/ P(B) = 1/2
Then P(A) = P(AB) = 1/2, implying that the happening of event B has had no effect on the probability of occurring of event A.
What is described as dependent events?Dependent events include those that are dependent on previous events. The outcomes of previous events have an impact on these events. Dependent events are two or maybe more events that are dependent on one another.
When two events, A and B, are interdependent, the probability of their occurrence is:
P(A and B) = P(A) · P(B|A)
Assume we desire to have a queen.
The chances of obtaining a queen on the first draw are 4 from out 52 cards. If we receive a queen in the first draw, we have a 3 out of 51 chance of obtaining a queen in the second draw.
As a result, these are referred to as dependent events because the probability of a second event is determined by the results of the first draw.
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An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $2,600 1.7%
Municipal Bond $3,700 3.2%
Preferred Stock $575 12.9%
Common Stock A $1,225 −5.6%
Using technology, calculate the weighted average ROR of the investments. Round to the nearest tenth of a percent.
2.1%
3.1%
5.9%
7.5%
Based on the investment portfolio given, the weighted average ROR of the investments would be 2.1%
What is the weighted average?First, find the total portfolio value:
= 2,600 + 3,700 + 575 + 1,225
= $8,100
The weighted average Rate of Return (ROR) on the investments is:
= (2,600 / 8,100 x 1.7%) + (3,700 / 8,100 x 3.2%) + (575 / 8,100 x 12.9%) + (1,225 / 8,100 x -5.6%)
= 2.076
= 2.1%
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Answer:
2.1%
Step-by-step explanation:
I got it right.
For every 27 litres of petrol a car
can run for 95 km.
How much petrol do you need
(to 1 DP) to ensure the car has
enough petrol of a trip that is
185 km?
To ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.
We are given that:
For 27 liters of petrol, we can drive a car for 95 km.
SO, by using the unitary method, we get that:
for 1 km of journey, the liters of petrol that we need is = 27 / 95 liters.
1 km = 27 / 95 liters
For 185 km, we get that:
185 km = 27 / 95 × 185 liters
185 km = 52.58 liters.
Therefore, to ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.
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What can I do to get the next 2 marks? Due tmr
The area of the circular shaded area is of 116.113 cm².
What is the area of a circle?The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:
A = πr²
For this problem, the shaded area is the area of the larger circle subtracted by the area of the smaller circle. We have that:
The radius of the larger circle is of 6.5 cm.The radius of the smaller circle is of 2.3 cm.Hence the area of the larger circle is given by:
Al = π(6.5)² = 132.732 cm².
The area of the smaller circle is given by:
As = π(2.3)² = 16.619 cm².
Hence the shaded area is given by:
A = Al - As = 132.732 - 16.619 = 116.113.
The shaded area is of 116.113 cm².
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A women went shopping and spent 2/3 of all the money she had. Then she lost 3/5 of what she had left after shopping. how much money did she have in the begining if she has $10.00 left
Answer:
Total Money = $ 75.00
Step-by-step explanation:
Let X be the Total Money
Amount Spent for Shopping = 2/3 of X = 2X/3
Money Lost = 3/5 of (X -2X/3) = 3/5 of (3X-2X)/3 = 3X/15 = X/5
Balance in hand = $ 10.00
is X - 2X/3 - X/5 = $ 10.00
LCM of 3 and 5 = 15
ie (15X - 10X - 3X)/15 = $ 10.00
(15X - 10X - 3X) = 150.00
2X = $ 150.00
X = $ 150.00/2
X = $ 75.00
Please answer///////////
Answer: the circle is not a function
the square is a function
Step-by-step explanation:
c. Find the exact lengths of the altitudes of triangles B and C.
The length of the altitude of triangle B is
The length of the altitude of triangle C is
The right triangle B and c altitude length are same that is 6.
Given that,
In the given picture there are 2 right triangles.
They are B and C.
2 sides of the triangle B is 3 and [tex]3\sqrt{3}[/tex].
2 sides of the triangle C is 6 and [tex]6\sqrt{2}[/tex].
The angle for both the right triangle B and C is 90°.
We have to find the length of the altitude of right triangles B and C.
By using the Pythagorean theorem we can find the length of the altitude of the right triangle B and C.
The simplest way is to use the Pythagorean theorem if you are aware of two additional right triangle sides:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Where the sides of the right triangle are a, b, and c.
First, We will find for the right triangle B.
Here, a=[tex]3\sqrt{3}[/tex] and b=3
Now, substitute in the formulae
[tex](3\sqrt{3})^{2} +3^{2}=c^{2}[/tex]
[tex]27+9=c^{2}[/tex]
[tex]36=c^{2} \\[/tex]
[tex]c^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{c^{2} } =\sqrt{36}[/tex]
[tex]c=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
Now, We will find for the right triangle C.
Here, b=6 and c=[tex]6\sqrt{2}[/tex]
Now, substitute in the formulae
[tex]a^{2} +6^{2}=(6\sqrt{2}) ^{2}[/tex]
[tex]a^{2} +36=72[/tex]
[tex]a^{2}=72-36 \\[/tex]
[tex]a^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{a^{2} } =\sqrt{36}[/tex]
[tex]a=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
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Add -4 3/8 + 8 6/7 enter your answer
Answer:
Step-by-step explanation:
first you need to make the 3/8 and 6/7 into 21/56 and 48/56 then you take the -4 and 8 then add then together you get 4 then you still have the 21/56 and 48/56 which you need to add so 48 + 21 = 69/56 or 1 and 13/56 you then add the 1 to the 4 which gives you 5 then add the 13/56 to it which gives you your answer of 5 and 13/56
Euler's formula, V − E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. Solve Euler's formula for V
Answer:
V = E - F + 2.
Step-by-step explanation:
V − E + F = 2
Add E to both sides
V + F = E + 2
Subtract F from both sides:
V = E - F + 2.
HELP ASAP!!! WILL MARK BRAINLIEST!!!
What are the coordinates of G after it is rotated 90 degrees clockwise?
Answer:
See below
Step-by-step explanation:
Rotating CLOCK wise would result in -4,3 becoming 3,4 in the first quadrant
given x + y = -2 solve for y
Answer:
what is the value of x? Ans. varies
Step-by-step explanation:
Q is in the interior of
Answer:
...
Step-by-step explanation:
For every x ∈ R and each δ > 0 the interval (x−δ, x δ) carries both rational and irrational numbers. This implies that x can't be an interior factor of Q, and that x is a boundary point of Q. Therefore the indoors of Q is empty and the boundary of Q is R. Thus Q = b(Q) ∪ Q = R ∪ Q = R.
(c) 10y+12-7y-8-3y…..
Answer:
4
Step-by-step explanation:
Hello!
Simplify the expression by combining like terms.
Simplify10y + 12 - 7y - 8 - 3y10y - 7y - 3y + 12 - 8 Collect like terms3y - 3y + 4 Combine like terms4 SimplifyThe simplified expression is 4.
The simplified form of the given expression is 4.
To solve the expression 10y + 12 - 7y - 8 - 3y,
We need to combine like terms and simplify.
Simplify the expression by combining the like terms (the terms that have the same variable and the same exponent).
We have 10y, -7y, and -3y,
Which can be combined to give us a total of 0y.
This means that the variable y has been eliminated from the expression.
Combine the constant terms (the terms that don't have a variable or that have a variable raised to the power of 0).
We have 12 and -8, which can be combined to give us 4.
So, the simplified expression is 4.
We can express this mathematically as follows:
10y + 12 - 7y - 8 - 3y = (10y - 7y - 3y) + (12 - 8)
= 0y + 4 = .
In other words, the expression simplifies to the constant term 4.
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Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha bought is 3/5 of the number of red balloons. The number of green balloons is also 2/3 of the number of yellow balloons.
The number of green and yellow balls is 24 and 36 respectively.
Given that,
Masha bought red, green, and yellow balloons for a party.
red balloons = 40 .
The number of green balloons Masha purchased = 3/5 of the red balloons.
The number of green balloons is again = 2/3 of yellow balloons.
Fraction is described as the number of compositions that comprise the Whole.
Here,
according to the question
Number of red ballons = 40
The number of green balloons Masha bought is 3/5 of the number of red balloons = 40 * 3/5
= 8* 3
= 24
The number of green balloons is also 2/3 of the number of yellow balloons.
= 3/2 * 24
= 36
Thus, the number of green and yellow balls is 24 and 36 respectively.
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Using a calculator, what is the solution of 1080=15³ˣ⁻⁴ ? Round the answer to the nearest hundredth.
The solution of the given equation 1080 = 15³ˣ⁻⁴ is (x = 2.19), round to the nearest hundredth.
What is defined as the logarithmic functions?A logarithmic term represents a number in logarithmic form. A log term is another name for it.
A quantity can also be the sum of two or even more quantities. As a result, a term can consist of the product of two or more quantities, one of which must be in logarithmic form. For such cases, this same terms are known as log terms.
A quantity can also be defined as the quotient of two quantities. But, if a term includes a quotient of quantities, or at least one of the quantities can also be expressed in log form, this same terms are known as log terms.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, consider the given equation given in the question;
1080=15³ˣ⁻⁴
Take log on the both sides;
㏒1080 = ㏒15³ˣ⁻⁴
Using the power rule on the second side of the equation;
㏒1080 = (3x - 4)㏒15
Taking log on one side and other variables on other side.
3x - 4 = ㏒1080/㏒15
Use calculator to find the values of both log.
3x - 4 = 2.57
3x = 6.57
x = 2.19
Therefore, the solution of the given function 1080=15³ˣ⁻⁴ is (x = 2.19), rounded up to nearest hundredth.
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In the equation |x| = b, if b < 0, then how many solutions are there for x?
O One
Ο TWO
O Zero
O Can't be determined without more information
Write a function rule to model the cost per month of a long-distance cell phone calling plan. Then evaluate the function for the given number of minutes.
Monthly service fee: 4.52 Rate: .12 pet minute Minutes used: 250
$34.52 is the function for the given number of minutes.
What is a formula for linear equations?
Y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept, is a straightforward way to write the linear equation formula. Slopes provide information about a line's direction and steepness.The function is
long- distance cell phone calling fee = Monthly service fee + Rate*Minutes used
long- distance cell phone calling fee = $4.52 + $0.12*250 = $34.52
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Refer to ®R .
If SU = 16.2 centimeters, what is RT ?
The diameter of a circle is defined as being twice the length of its radius.
If SU = 16.2 centimeters then the value of RT = 8.1 cm.
What is the difference between the radius and diameter of a circle?The diameter of a circle is defined as being twice the length of its radius. The radius of a circle is measured from the center to one of the circle's endpoints, whereas the diameter is measured from one end of the circle to another end of the circle, passing through the center.
In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.
Here, SU is the diameter and RT is the radius.
Radius of the circle = 1/2 d
Where d = 16.2 then
substitute the value of d in the above equation, and we get
Radius of the circle = 1/2 (16.2)
Radius of the circle = 8.1
Therefore, the value of RT = 8.1 cm.
The complete question is:
If SU = 16.2 centimeters, what is RT?
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The formula for simple interest is I=Prt
a. Solve the formula for t, when r is the simple interest per year.
t=_
b. Use the new formula to find the value of t in the table.
The value of t in the table is _ years
a. The formula solved for t when r is the simple interest per year is t = I/Pr
b. Using the new formula, the value of t in the table is 3 years
Simple InterestFrom the question, we are to solve the given formula for t
The given formula is
I = Prt
To solve for t, we will divide both sides of the equation by Pr
I/Pr = Prt/Pr
I/Pr = t
∴ t = I/Pr
b.
I = $75
P = $500
r = 5% = 0.05
t = 75/(500×0.05)
t = 75/25
t = 3 years
Hence, the value of t in the table is 3 years
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Brooklyn has 3 shelves in her bedroom that have 40 books on each shelf in another room,she has 4 shelves that each contain 20 books if she buys 17 books at a resale shop, how many books does brooklyn have now
Answer:120 plus 80 plus 17 equals 217
Step-by-step explanation:
Answer:
Step-by-step explanation:
217
PLEASE HELP
The Central Islip community has 9,649 homes in it. Smart Boards cost the school district $5,200 each. The HS needs 175, the Reed School needs 150 and the Mulligan school needs 50 new boards. Network Outsource the schools tech company has 12 workers for the HS, 8 for the Reed School and 4 for Mulligan. They all work 8 hours a day. They work 5 days a week, Monday thru Friday. They earn $58 per hour. It will take 45 weeks to finish the job. Find: a) Total Product Cost b) Total Labor Cost c) Total Cost d) Cost per Home e) Cost per Week
Using proportions, the costs are given as follows:
a) Total Labor Cost: $2,505,600.
b) Total Product Cost: $1,950,000.
c) Total Cost = $4,455,600.
d) Cost per home = $461.77.
e) Cost per week = $99,013.33.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item a, the labor cost is found using the earnings of the workers, as follows:
45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)
Hence:
Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.
For item b, the product cost is the cost of the boards, hence:
(175 + 150 + 50 boards) x 5,200
Total Product Cost = 375 x 5,200 = $1,950,000.
For item c, the total cost is the sum of the product cost and the labor cost, hence:
Total Cost = 2,505,600 + 1,950,000 = $4,455,600.
For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:
Cost per home = 4455600/9649 = $461.77.
For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:
Cost per week = 4455600/45 = $99,013.33.
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Find the coordinates of the orthocenter of ΔA B C with vertices A(-3,3), B(-1,7) , and C(3,3)
The orthocenter of the ΔABC is ( -1,5 ).
What is orthocenter?In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.
Given the co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).
To find the orthocenter using below steps:
1. First, we find the equations of AB and BC.
The general form of a line is y = mx + b
where m is the slope and b is the y-intercept.
Using the formula of slope given [tex]$m =\frac{y_2 - y_1}{x_2 - x_1}[/tex] , we will find the slope of AB and BC.
Now, slope of AB is m = (7-3/-1 + 3)
i.e. m = (4/2) = 2
Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,
y = mx + b
1 = 2 × (-1) + b
i.e. b = 3.
So, the equation of AB is y = 2x + 3.
Also, slope of BC is m=(3-7/3+1) i.e. m=-4/4 i.e. m--1
Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,
y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.
So, the equation of BC is y = -x.
2. We will find the slope of line perpendicular to AB and BC.
When two lines are perpendicular, then the product of their slopes is -1.
So, slope of line perpendicular to AB is [tex]m*2=-1[/tex] i.e. m = -1/2
So, slope of line perpendicular to BC is i.e.[tex]m*-1=-1[/tex] i.e. m = 1.
3. We will now find the equations of line perpendicular to AB and BC.
Using the slope of line perpendicular to AB m=-1/2 i.e. and the point opposite to AB
i.e. C(3, 3), we get,
y = mx + b
i.e. [tex]3=-1/2*3+b[/tex]
i.e. b = 9/2
So, the equation of line perpendicular to AB is
[tex]y=-x/2+9/2[/tex]
Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC
i.e. A( -3,3 ), we get,
y = mx + b
i.e. 3 = 1 × -3 + b
i.e. b = 6.
So, the equation of line perpendicular to BC is y = x+6
4. Finally, we will solve the obtained equations to find the value of (x, y).
As, we have y = x + 6 and y = -x/2 + 9/2
This gives, y = -x/2 + 9/2 → x + 6
y = -x/2 + 9/2
simplifying the above equation, we get
2x + 12 = -x + 9
3x = -3
x = -1.
So, y = x + 6
simplifying the above equation, we get
y = -1 + 6
y = 5.
The value of x = -1 and y = 5.
Hence, the orthocenter of the ΔABC is ( -1,5 ).
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