Describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
Transformation #1
Transformation #2
Write an ordered-pair rule for each transformation in the sequence.
Transformation #1
Transformation #2
Answers
Answer: The required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒ (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).
Step-by-step explanation: We are given to describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
From the figure, we note that
the co-ordinates of the vertices of triangle ABC are A(0, 4), B(0, 0) and C(2, 3).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(-2, -3), B'(2, -3) and C'(-1, -1).
We see that if triangle ABC is rotated 90 degrees in anticlockwise direction about the origin, then its co-ordinates changes according to the following rule :
(x, y) ⇒ (-y, x).
That is
A(0, 4) ⇒ (-4, 0),
B(0, 0) ⇒ (0, 0),
C(2, 3) ⇒ (-3, 2).
Now, if the vertices of the rotated triangle are translated 2 units right and 3 units down, then
(x, y) ⇒ (x+2, y-3).
That is, the final co-ordinates after rotation and translation will be
(-4, 0) ⇒ (-4+2, 0-3) = (-2, -3),
(0, 0) ⇒ (0+2, 0-3) = (2, -3),
(-3, 2) ⇒ (-3+2, 2-3) = (-1, -1).
We see that the final co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.
Thus, the required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒ (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).
Related Questions
Fatima is shading this model to show 0.08x3 . shade the correct amount of boxes that will show the product
Answers
In total that's 24 hundreths to shade
For more help, please upload a picture
Hope this helps!!
Shade 0.08 3 times
In total that's 24 hundreths to shade
all im doing is trying to get points Lol
What is the standard form of the equation of a parabola that opens left or right
Answers
Answer:
The equation of the parabola which opens left or right is [tex]x=ay^2+by+c[/tex].
Step-by-step explanation:
We know that,
If in the equation of the parabola,
1. If x is squared, then the parabola opens upwards or downwards.
2. If y is squared, then the parabola opens towards left or right.
Since, we want the equation of the parabola which opens left or right.
So, we get that,
The variable 'y' is being squared in the equation of the given parabola (from 1).
Thus, the equation of the parabola which opens left or right is [tex]x=ay^2+by+c[/tex].Answer:
x = ay^2 + by + c
Step-by-step explanation:
it was correct for me
You and your friend are selling raffle tickets for a new laptop. you sell 14 more then your friend sells. Together you and your friend sell 58 tickets. Write a system of linear equations that represent this situation. How many did each of you sell?
Answers
You sold 36 tickets and your friend sold 22 tickets.
Explanation:Let's represent the number of tickets you sell as x and the number of tickets your friend sells as y.
We know that you sell 14 more tickets than your friend, so we have the equation:
x = y + 14
We also know that together you and your friend sell 58 tickets, so the equation becomes:
x + y = 58
Now we can solve these two equations simultaneously to find the values of x and y.
Substitute the value of x from the first equation into the second equation:(y + 14) + y = 58
Combine like terms:2y + 14 = 58
Subtract 14 from both sides to isolate the variable:2y = 44
Divide both sides by 2 to solve for y:y = 22
Now substitute the value of y back into one of the original equations to solve for x:x = 22 + 14
Simplify:x = 36
Therefore, you sold 36 tickets and your friend sold 22 tickets.
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The system of equations representing the problem is y = x + 14 and x + y = 58. Solving this system we get x = 22 (friend's sold tickets) and y = 36 (your sold tickets).
Explanation:We'll use a system of linear equations to model this situation. Let's define x as the number of tickets your friend sells, and y as the number of tickets you sell. From the problem, we know two things:
1. You sell 14 more tickets than your friend: y = x + 14.
2. Together, you and your friend sell 58 tickets: x + y = 58.
To solve this system, we can substitute y in the second equation with x + 14 from the first equation. This gives us:
x + (x + 14) = 58.
Solving this we get x = 22 and substituting x into the first equation gives: y = 22 + 14 = 36.
So, your friend sold 22 tickets, and you sold 36 tickets.
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Simplify 6 - 4[x + 1 - (y + 3)] + 5y.
Answers
2x+2-6y+5y
2x+2-y
-y+2x+2
25xy4 + 60xy3 5xy 5xy3 + 12xy2 5y2 + 12 5xy + 12y 5y3 + 12y2
Answers
the simplified expression is 25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12
To simplify the given expression, we first need to combine like terms. Like terms are those that have the same variables raised to the same powers. In this case, we have terms with x and y raised to different powers.
The expression is:
25xy^4 + 60xy^3 + 5xy^3 + 5xy + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2
Now, let's combine the like terms:
Combine the terms with xy^4: 25xy^4
Combine the terms with xy^3: 60xy^3 + 5xy^3 = 65xy^3
Combine the terms with xy^2: 12xy^2
Combine the terms with xy: 5xy + 5xy + 12xy = 22xy
Combine the terms with y^2: 5y^2 + 12
Combine the terms with y: 12y + 5y + 12y^2 = 18y + 12y^2
Combine the terms with y^3: 5y^3 + 5y^3 = 10y^3
Now, let's put all the combined like terms together:
25xy^4 + 65xy^3 + 22xy + 12xy^2 + 18y + 12y^2 + 5y^3 + 12
This is the simplified expression.
The probable question maybe:
simplify the given expression [tex]\(25xy^4 + 60xy^3 + 5xy + 5xy^3 + 12xy^2 + 5y^2 + 12 + 5xy + 12y + 5y^3 + 12y^2\)[/tex]
I Reaally Need Help If You Wamt Ill Eve Go Over 100 Points
Answers
(b) (1,5), (3,3); y = 3x + 3 5 = m1 + b, 3 = m3 + b
(c) coincident i believe, because it is not independent or inconsistent
(d) 2x + 3 = 3x + 3
(-2x)(-3) (-2x)(- 3)
0 = -2x
x = 0
hope this helps
side walk 1
slope = (7-3)/(2-0) = 4/2 = 2
b = 3
slope intercept form
y = 2x + 3
b)
sidewalk 2
slope = (3-5)/(3-1) = -2/2 = -1
point slope form equation
y - 5 = -1(x - 1)
slope intercept form
y - 5 = -1(x - 1)
y - 5 = -x + 1
y = -x + 4 ....slope intercept form
c)
sidewalk1 : y = 2x + 3
sidewalk2: y = -x + 4
2x + 3 = -x + 4
3x = 1
x = 1/3
y = 2(1/3) + 3
y = 2/3 + 3
y = 3 2/3
solution x = 1/3 and y = 3 2/3
A system of two linear equations can have one solution so it's consistent and exactly 1 solution so it is independent
d) you can use this from c)
x = 1/3 and y = 3 2/3
The length of the hypotenuse of a right triangle is 13 cm. the length of one leg is 5 cm. find the length of the other leg. (1 point) 14 cm 144 cm 8 cm 12 cm
Answers
Answer: 12
Step-by-step explanation:
A wedge is cut out of a circular cylinder of radius 10 by two planes. one plane is perpendicular to the axis of the cylinder. the other intersects the first at an angle of 30° along a diameter of the cylinder. find the volume v of the wedge, taking rectangular cross-sections to be parallel to the line of intersection of the two planes, which is the x-axis. (let r = 10.)
Answers
[tex]r^2=x^2+y^2 \\ \\ \Rightarrow y=\sqrt{10^2-x^2}=\sqrt{100-x^2}[/tex]
The wedge makes a shape whose cross-section perpendicular to the x -axis at distance x from the origin is a triangle whose base is is given by: [tex]y=\sqrt{100-x^2}[/tex]
The height of the wedge is given by:
[tex]y\tan30^o= \frac{\sqrt{100-x^2}}{\sqrt{3}} [/tex]
The cross sectional area of the wedge is given by:
[tex]A(x)= \frac{1}{2} bh \\ \\ = \frac{\sqrt{100-x^2}}{2} \cdot\frac{\sqrt{100-x^2}}{\sqrt{3}} \\ \\ = \frac{100-x^2}{2\sqrt{3}} [/tex]
The volume is given by:
[tex]V= \int\limits^{10}_{-10} {A(x)} \, dx \\ \\ = \int\limits^{10}_{-10} {\frac{100-x^2}{2\sqrt{3}}} \, dx =2\int\limits^{10}_{0} {\frac{100-x^2}{2\sqrt{3}}} \, dx \\ \\ =\int\limits^{10}_{0} {\frac{100-x^2}{\sqrt{3}}} \, dx=\frac{1}{\sqrt{3}}\left[100x-\frac{x^3}{3}\right]^{10}_0 \\ \\ =\frac{1}{\sqrt{3}}\left[100(10)-\frac{(10)^3}{3}\right]=\frac{1}{\sqrt{3}}\left[1000-\frac{1000}{3}\right] \\ \\ =\frac{1}{\sqrt{3}}\left[\frac{2000}{3}\right]=\frac{2000}{3\sqrt{3}}[/tex]
The volume of the wedge is 50π/3 - 25√3.
Explanation:To find the volume of the wedge, we need to calculate the volume of the cylindrical segment between the two intersecting planes. The formula for the volume of a cylindrical segment is V = h((R^2θ)/2 - (R^2sinθ)/2), where h is the height of the segment, R is the radius of the cylinder, and θ is the angle of the intersection between the planes. In this case, h is 10 and θ is 30°, so the formula becomes V = 10((10^2 * π/6)/2 - (10^2 * sin(π/6))/2). Simplifying the equation gives V = 50π/3 - 25√3.
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explain using complete sentences whether or not this is the most appropriate format for representing data and why if it is not the best format explain which format should have been used instead
Answers
The most appropriate format for representing data depends on the intended audience, data type, and presentation purpose. Adherence to professional formatting guidelines is critical, and while figures can make data accessible, they should not duplicate table data. The effectiveness of formats such as complete sentences, tweets, Prezi, and visual figures varies based on the context.
When choosing the most appropriate format for representing data, several factors need to be considered such as the intended audience, the type of data, and the purpose of the data presentation. Complete sentences, Prezi presentations, 140 character tweets, and drawn pictures each have their own strengths in conveying information effectively and engagingly depending on these factors.
For professional or academic reports, complete sentences and structured paragraphs provide in-depth analysis and explanation. However, for social media platforms, 140 character tweets can quickly capture attention and convey key points. A Prezi can be highly engaging and visually appealing for presentations, making complex information accessible. Conversely, when displaying detailed findings, sometimes a well-illustrated figure or a clear table can speak volumes more efficiently.
Nonetheless, adhering to formatting guidelines is crucial in a professional context, as non-compliance could lead to the rejection of the report. It's also important to note that while figures are useful for making data accessible, they should not duplicate data presented in tables. When using figures, they must be clearly titled, referenced in the text, and situated conveniently in the report. If the figures are too dense, they can be relegated to an appendix.
In summary, there is no one-size-fits-all format for data presentation. Preference may vary depending on personal comfort with certain formats or the requirements of a specific assignment. Reflecting on the exercise of presenting information in various formats can elucidate which is most effective for your specific needs and audience.
By definition a simple random sample of size n is any sample
Answers
Arithmetic sequence find the next next term in the sequence 44, 51, 58, 65
Answers
Hii!
_________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
72
[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]
To find the next term in the arithmetic sequence, we should first find the common difference.
The common difference is the amount we add or subtract to obtain the next term. In the given sequence we add 7.
So, let's find the next term.
[tex]\twoheadrightarrow\sf65+7[/tex]
[tex]\bullet[/tex] Add 7
[tex]\twoheadrightarrow\sf72[/tex]
[tex]\bullet[/tex] Great job! We found the next term
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
Give an example of a rational function that has a horizontal asymptote of y = 2/9.
Answers
The only solution of the equation x^2 +bc+16=0 is x=4 why is the value of b
Answers
If it has only a solution of x = 4, then you must have
(x - 4)(x - 4) = 0
x^2 - 8x + 16 = 0
-8x = bx
b = -8
Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)
2x-2y=12
-2x-3y=-22
2x-6y=10
x+8y=5
3x-y=-5
x+4y=7
x+y=2
2x+y=13
Answers
-2x - 3y = -22
solution could be (x,2)
===============
2x - 6y = 10
x + 8y = 5
solution could be : (5,y)
==============
3x - y = -5
x + 4y = 7
solution could be : (x,2)
=============
x + y = 2
2x + y = 13
solution could be : neither....is this one written correctly ?
Answer: system 2 (5,0) and system 3 (-1 2)
2x-6y=10 3x-y=-5
x+8y=5 x+4y=7
Step-by-step explanation:
Solve each system. Then drag each one to the column headed by a point which could be its solution. (5,y) or (x,2)
system 1
2x - 2y =12
-2x-3y = -22
solve simultaneous equation
2x - 2y =12
-2x-3y = -22
add the equations gives
2x +(-2x) =0
-2y+(-3y) =-5y
12+ (-22) = -10
-5y =-10
y =2
2x -2(2) =12
2x-4 =12
2x = 12+4
x= 16/2 =8 x=8 and y =2 = (8,2)
system 2
2x-6y=10 *(-1) = -2x + 6y =-10
x+8y=5 *(2) = 2x + 16y =10 add the equations
22y =0 y =0
x : 2x - 6(0) =10
x = 10/2 = 5
(5, 0)
system 3
3x-y=-5 *(-1) = -3x + y =5
x+4y=7 * (3) = 3x + 12y = 21
add the equations = 13y = 26 y = 2
3x -2 =-5 = 3x = -3 =x =-1
(-1 2) answer
system 4
x+y=2 *(-2) = -2x -2y = -4
2x+y=13 *(1) = 2x +y = 13
add the two equations = -y =9
y = -9
substitute 2x-9= 13= 2x =22 x =11
(11 -9)
What value of n would make point A the circumcenter?
1. 2
2. 3
3. 4
4. 5
Answers
Answer:
The correct option is 2. The value of n is 3.
Step-by-step explanation:
Circumcenter is the point, where the perpendicular bisectors of a triangle intersect each other.
Circumcenter is also known as the center of the triangle. The distance from circumcenter to each vertex are same.
In triangle DEF, if A is the circumcenter.
[tex]AE=AD[/tex]
[tex]10=2n+4[/tex]
Subtract 4 from both sides.
[tex]10-4=2n[/tex]
[tex]6=2n[/tex]
Divide both sides by 2.
[tex]3=n[/tex]
Therefore the value of n is 3 and option 2 is correct.
Answer:
Option 2 is true
Step-by-step explanation:
We have to find the value of n for which point A becomes circumcenter.
Circumcenter: It is that point where perpendicular bisectors of triangle intersects.
The circumcenter is also knows as center of triangle.
Circumcenter is at equal distance from each vertex of triangle.
If point A is circumcenter then
AE=AD
We have AE=10 units
AD=2n+4
Substitute the value
10=2n+4
[tex]2n=10-4[/tex]
By subtraction property of equality
[tex]2n=6[/tex]
[tex]n=\frac{6}{2}=3[/tex]
Hence, the value of n is 3 would make point A the circumcenter.
What is the slope below
Answers
(3, -2) and (2, -4)
m = (y2 - y1)/(x2 - x1) = (-4 - (-2))/(2 - 3) (-4 + 2)/(-1) = -2/(-1) = 2
Ou work as a cashier for a grocery store and earn $5 per hour. you also mow lawns and earn $10 per hour. you want to earn at least $50 per week, but would like to work no more than 10 hours per week. which system of inequalities, along with y ≥ 0 and x ≥ 0, would you use to solve the real-world problem?
Answers
The problem can be represented by two inequalities: one to ensure earning at least $50 per week (5x + 10y >= 50) and another to restrict working to no more than 10 hours per week (x + y <= 10), alongside x >= 0 and y >= 0 to indicate non-negative hours worked for each job.
To determine the system of inequalities to solve the problem, we need to define variables for the number of hours spent on each job. Let's use x to represent the number of hours working as a cashier at the grocery store, and y to represent the number of hours mowing lawns. The student earns $5 per hour at the grocery store and $10 per hour mowing lawns. They want to earn at least $50 per week and work no more than 10 hours in total.
From this information, we can establish the following inequalities:
5x + 10y >= 50 (To ensure earning at least $50 per week)
x + y = 10 (To ensure working no more than 10 hours per week)
Additionally, we include y >= 0 and x >= 0 to represent that the number of hours worked at either job cannot be negative.
What is the height of an equilateral triangle with sides that are 12 cm long? Round to the nearest tenth. (1 point)
Answers
Answer:
10.4 cm
Step-by-step explanation:
Looking at the triangle in the attached pic, we can see that the right, smaller triangle is a right triangle on which we can apply the pythagorean theorem to solve for the height, h.
Pythagorean theorem tells us [tex]c^2=a^2+b^2[/tex] where c is the hypotenuse (12 in our case) and a & b are the two legs (6 and h are the respective lengths).
So let's solve for h:
[tex]c^2=a^2+b^2\\12^2=6^2+h^2\\144=36+h^2\\144-35=h^2\\108=h^2\\h=\sqrt{108} \\h=10.4[/tex]
How to find the length and width of a rectangle when given the area and perimeter?
Answers
Which canadian island has a population density that ranges from under 2 people to as many as 250 people per square mile?
Answers
Prince Edward Island in Canada has a population density that can range from less than 2 people to as many as 250 people per square mile. This is due to various factors including climate, farmland, and job opportunities.
Explanation:The Canadian island with a population density that ranges from under 2 people to as many as 250 people per square mile is Prince Edward Island. This island is one of the three Maritime Provinces in Canada and is the smallest in both land area and population. But, when it comes to population density, it has a higher range than many other islands in Canada. This is due to its favorable climate, good farmland, and the job opportunities, mainly in farming and tourism, which attract a decent population.
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If applying 6 newtons of force to an object results in 42 joules of work, what distance (in meters) would the object travel?
Answers
Answer:
The object would travel 7 meters.
Step-by-step explanation:
The distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
If applying 6 newtons of force to an object results in 42 joules of work
We know,
Work = Force x Distance
42 = 6xDistance
Distance = 7 meters
Thus, the distance the object would travel is 7 meters if applying 6 newtons of force to an object results in 42 joules of work.
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A cone has a radius of five feet and a height of 18 feet. If the radius of the cone is tripled but the volume but the volume remains unchanged, what will be the new height of the cone
Answers
v=(1/3)pi*5*5*18=(1/3)pi815*15*h
h=2
If 8 times a number is decreased by 20,the result is the same as 3 times the number increased by 80
Answers
Final answer:
The algebraic expression for the problem is '8n - 20 = 3n + 80', which simplifies to 'n = 20'. Therefore, the number in question is 20.
Explanation:
The question presents a classic algebra problem where we have to find the value of a variable that satisfies a given condition. Specifically, this problem states:
"If 8 times a number is decreased by 20, the result is the same as 3 times the number increased by 80."
To solve this, we'll convert the words into an algebraic equation and solve for the number. Let's use 'n' to represent the number:
8n - 20 = 3n + 80This equation tells us that when you multiply the number by 8 and subtract 20, it's equal to the result of multiplying the number by 3 and adding 80. To find 'n', we combine like terms and solve:
8n - 3n = 80 + 205n = 100n = 100 / 5n = 20Thus, the number we're looking for is 20.
PLZ HELP ASAP!!!
1. Give me an example of irrational number (other than pi).
Be prepared to explain how you know its irrational.
2. How do you simplify x8 / x3?
3. Estimate square root of 39 without a calculator.
Be prepared to explain.
4. Write the following number in scientific notation: 402000.
Answers
An irrational number is something that cant be expressed as a ratio. For ex:the square root of 2. Hope this helps.
What's the probability of getting an even number and a head when rolling a die and then tossing a coin?
Answers
Answer: 1/4
Step-by-step explanation:
NEED HELP FAST PLEASE!!!
What is the equation of this line?
y = -3/2x
y = 2/3x
y = -2/3x
y = 3/2x
Answers
The slope is rise/run = 2/3 meaning we go up 2 and over to the right 3. For instance, moving from (0,0) to (3,2) has us move up 2 and over to the right 3.
Alternatively you can use the slope formula m = (y2-y1)/(x2-x1) to get the same result of 2/3.
so slope = (2 + 2)/(3+3) = 4/6 = 2/3
y = mx + b
b = y - mx
b = -2 - (2/3)(-3)
b = -2 + 2
b = 0
equation
y = 2/3x
answer
B. y = 2/3x
Find cotθ if θ terminates in Quadrant III and secθ = - 2.
Answers
If you know your sine/cosine values you know that when:
cos(x) = 1/2 , sin(x) = √(3)/2
The fact that theta, or "x" as I've been using... terminates in Quadrant III means both cosine and sine will be negative and then cotangent will be positive.
cot(x) = cos(x) / sin(x)
cot(x) = (-1/2) / (-√(3)/2)
cot(x) = (1/2) * (2/√(3))
cot(x) = 1/√(3)
or rationalized as √(3)/3
If a box measures 1.2m by 3.4m by 0.50m, what is its volume in liter
Answers
1.2(100cm/1m) = 120 cm
3.4(100cm/1m) = 340 cm
0.5(100cm/1m) = 50 cm
the volume of a box is equal to (length)(width)(height)
that is
V = (120cm)(340cm)(50cm)
V = (6000 cm^2)(340cm)
V = 2040000 cm^3
now 1 cm^3 is equal to one mL and 1000 mL is 1 Liter
V =2040000 mL multiply by (1 Liter/1000 mL)
V = 2040 L
That's 2,040 liters.
Hope this helps :)
1.2m * 3.4m * 0.5m = volume
2.04m^3 = volume
Now we need to convert that in liters
1 cubic meter = 1000 liters
So 2.04 cubic meters = 2040 liters
The number of years that Brad has been on the soccer team is 2 less than five times a number of years Scott has in total the boys have been on the soccer team for about 10 years how long has Brad been on the soccer team
Answers
A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts.
Which points did the group leader label?
(0, 8) and (16, 0)
(0, 30) and (15, 0)
(0, 15) and (30, 0)
(0, 16) and (8, 0)
Answers
Total amount of spaghetti sauce - 240 oz.
Small jar capacity - 8 oz
Large jar capacity - 16 oz
Points:
(0, 8) and (16, 0)
(0, 30) and (15, 0)
(0, 15) and (30, 0)
(0, 16) and (8, 0)
*Solution
The only points that would be labeled by the leader would be those points that would correspond to a total amount of 240 oz of spaghetti sauce. Thus, each point should be evaluated using the following expression:
8x + 16y (EXPRESSION 1)
8x + 16y = 240 (EQUATION 1)
The expression and the equation was set up based on the condition that the x-axis corresponds to the number of small (8 oz) jars and the y-axis corresponds to the number of (16 oz) large jars.
Since pairs of intercepts are given, both points should be evaluated using the given expression and each of the results should give an answer of 240. Thus, Equation 1 must be satisfied.
Testing out each pair one by one:
1. (0,8) and (16,0)
8(0) + 16(8) = 128
8(16) + 16(0) = 128
This does not satisfy the condition set by Equation 1 because the result of the evaluation of each of the intercepts using Expression 1 is not 240. Therefore, these are not the intercepts of the line to be plotted.
2. (0,30) and (15,0)
8(0) + 16(30) = 480
8(15) + 16(0) = 120
This does not satisfy the condition set by Equation 1 because the result of the evaluation of each of the intercepts using Expression 1 is not 240. Therefore, these are not the intercepts of the line to be plotted.
3. (0,15) and (30,0)
8(0) + 16(15) = 240
8(30) + 16(0) = 240
This satisfies the condition set by Equation 1 as each of the intercepts, when evaluated using Expression 1, gives an answer of 240.
4. (0,16) and (8,0)
8(0) + 16(16) = 256
8(8) + 16(0) = 64
This does not satisfy the condition set by Equation 1 because the result of the evaluation of each of the intercepts using Expression 1 is not 240. Therefore, these are not the intercepts of the line to be plotted.
Thus, the points that the leader will be plotting on the graph are the intercepts (0,15) and (30,0).