Based on the line and the points that it goes through, the equation with the same proportional relationship as the graph is y = three-fifths x.
How to find the relationship of the graph?To find the relationship of the points on the line in the coordinate plane, you need to find the slope of the line. The slope can be found by the formula:
= Change in y / Change in x
Solving for the slope gives:
= (3 - 0) / (5 - 0)
= 3 / 5
For equations to be proportional, they need to have the same slope. With the slope of the line being 3/5, the equation that would have the same proportional relationship is:
y = 3/5x
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the volume of the ice cream cone is increasing at the rate of 10 units3/sec and its radius is increasing at the rate of 1 14 units/sec when the radius r and height h are (r, h)
The rate of change for the height of the ice cream is [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
What is the rate of change of the height of a cone?
The volume of an ice cream cone (V), in cubic units, is described by the following formula:
V = (1 / 3) · (π · r²) · h (1)
Where:
r - Radius of the cone, in units.h - Height of the cone, in units.The rate of change for the height of the cone is derived from differentiating (1) with respect to time:
V' = (1 / 3) · (2π · r) · h · r' + (1 / 3) · (π · r²) · h'
V' = (2π / 3) · h · r' + (π / 3) · r² · h'
h' = [V' - (2π / 3) · h · r'] / [(π / 3) · r²]
Where:
h' - Rate of change of the height, in units per second.V' - Rate of change of the volume, in cubic units per second.If we know that V' = 10 and r' = 1 / 14, then the rate of change for the height of the cone is:
h' = [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²]
The height of the ice cream cone changes at a rate of [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
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Carlos is moving to a new city and looking for a new job. He wants to rent an apartment, and he is willing to use half of his monthly paycheck for rent and apartment-related fees that he knows will be 200$. He doesn’t know exactly how much he’ll make at his new job yet, but he knows it will be somewhere between $3000 and $4000. Write an inequality and solve an inequality to show the price range David’s apartment will have to be in.
Answer: The price of the apartment lies in the range of $1300 to $1800
Step-by-step explanation: Because Carlos doesn't exactly know how much he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.
Let the rent on the new apartment = r
let monthly pay of Carlos = x
Given, apartment related fees = 200$
Given he is willing to use half of his monthly pay for rent and apartment related fees combined.
∴rent + apartment related fees = Monthly pay / 2
⇒[tex]r + 200 = \frac{x}{2}[/tex]
⇒[tex]x=2*(r+200)[/tex]
⇒[tex]x=2r+400[/tex] (1)
Given Carlos' monthly pay is in the range of $3000 to $4000
∴[tex]3000\leq x\leq 4000[/tex]
⇒[tex]3000\leq (2r+400)\leq 4000[/tex] (from equation (1))
⇒[tex]3000-400\leq 2r+400-400\leq 4000-400[/tex] (subtracting 400)
⇒[tex]2600\leq 2r\leq 3600[/tex]
⇒[tex]\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}[/tex] (dividing by 2)
⇒[tex]1300\leq r\leq 1800[/tex] (2)
ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)
here is a problem solved using inequality
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Solve the system by graphing.check your solution
3x-y=3
-3x-y=-9
The equation intercept at (2,3) in the graph given in the question.
solve ?
Given two equations are ,
3 x - y = 3
-3 x - y = -9
to solve the equations, substract both equations ,
(3 x - y = 3) - (-3x -y = -9)
we get, 6x =12
x = 2
by substituting value of x in any of the equation we get ,
3 x 2 -y =3
6 -y =3
-y = -3
y = 3
so x = 2 , y = 3
the points on the graph is (2,3)
Both equations are in slope intercept form.
The graph of y = mx +b, where m is the slope and b is the y intercept, is shown below.
They have the same y intercept, so they cross at (2,3).
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Given that f(x)=−2x2+4x and g(x)=3x+3, find the functions below.
Simplify answers completely.
The expression of (f+g)(x) from the functions f(x)=−2x2+4x and g(x)=3x+3 is (f+g)(x) = (-2x^3+7x^2 +3x ).
How can the expression of the function be simplified?From the question we were given the functions that is expected to be simplified as :
f(x)=−2x^2+4x
g(x)=3x+3
And we were told to find the function (f+g)(x) which can be written as :
(f+g)(x) = [(−2x^2+4x )+(3x+3)]x
This can be further expressed as :
(f+g)(x) = (-2x^2+4x +3x+3 )x
This can be further simplified as :
(f+g)(x) = (-2x^2+7x+3 )x
This can be further simplified as :
(f+g)(x) = (-2x^3+7x^2 +3x )
Therefore, the expression of the function (f+g)(x) is (f+g)(x) = (-2x^3+7x^2 +3x ).
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The missing part:
Find (f+g)(x).
Drag each object to show whether distance is proportional to time in the situation represented.
The table with the situations that represent or not proportional relationships of distance and time is given at the end of the answer.
Which situation models a proportional relationship?A situation represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
One example, in the context of this problem, is the relation between velocity, distance and time, as velocity is distance divided by time, hence:
v = d/t.
The relation between distance and time is given as follows:
distance = velocity x time
distance = v x t.
Hence it will only be proportional if the velocity is constant, that is, if the acceleration is of zero.
Examples of non-proportional situations in the context of this problem are:
A touchdown, as when the play starts the player is stopped then he accelerates and the velocity is not constant.The horse running around the race track, same logic, different velocities.The distance and time table (4 - 15, 8 - 30, 12 - 45) does not show enough information, we need to know if the initial point was of (0,0).
What is the missing information?The objects are missing, and have been dragged to their correct situation on the table.
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Show the relationship between -5/6 and -7/10. Use an inequality symbol
[repost]
The rational numbers - 5 / 6 and - 7 / 10 are equivalent to - 25 / 30 and - 21 / 30, respectively. Then, the relationship is that - 5 / 6 is the less than - 7 / 10 as - 25 < - 21.
What is the relationship between two rational numbers?
Rational numbers are real numbers of the form m / n, where m and n are integers and n is not zero. In this problem we need to determine the relationship between two rational numbers, this can be done by amplifying the two rational numbers to a form with the same denominator and then compare the two numerators.
First, find the least common multiple of the two denominators:
6 = 2 × 3
10 = 2 × 5
L.C.M. = 2 × 3 × 5 = 30
Second, amplify each rational number:
- (5 × 5) / (6 × 5) = - 25 / 30
- (7 × 3) / (10 × 3) = - 21 / 30
Third, compare the numerators of the fraction found in the previous step:
Since - 25 < - 21, then - 5 / 6 < - 7 / 10.
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g(x) = 15 - 4x
3
h(x) = x+8
Write g(h(x)) as an expression in terms of x.
g(h(x)) =
Answer:
[tex]g(h(x))=−6x−17
[/tex]
Step-by-step explanation:
given:
[tex] g(x) = 15 - 4x \\ h(x) = \frac{3}{2 } x + 8[/tex]
To find g(h(x)) substitute h(x) instead of every x in g(x)
therefore:
[tex]g(h(x)) = 15 - 4( \frac{3}{2} x + 8) \\ [/tex]
simplify
[tex]g(h(x)) = 15 - 6x - 32 \\ g(h(x)) = - 6x - 17[/tex]
|-2+2|-2
Wouldn’t this be -2
Answer:
yes correct ^ ^
Step-by-step explanation:
This question is a bit confusing
Shelley buys a volleyball and kneepads to get ready for her season. The volleyball was discounted 30%. The kneepads cost half the original price of the volleyball. She spent a total of $64.08 including $4.08 in tax.
Select all the true statements, where x is the original price of the volleyball.
An equation to model this situation is 0.7x+0.5x+4.08=64.08.
An equation to model this situation is 0.3x+0.5x+4.08=64.08.
The original price of the volleyball was $50.
An equation to model this situation is 0.7x−0.5x+4.08=64.08.
The original price of the volleyball was $75.00.
9.
Katy fills some gift boxes.
Each gift box will contain one toy and one keyring.
Katy buys toys in bags of 8.
Katy buys keyrings in bags of 14.
She wants to use all the toys and all the keyrings she buys.
What is the smallest number of gift boxes Katy can fill?
Anyone
The most appropriate choice for LCM will be given by
Smallest number of gift boxes Katy can fill is 56
What is LCM?
Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.
Here,
Katy buys toys in bags of 8.
Katy buys keyrings in bags of 14.
Each gift box will contain one toy and one keyring.
Number of gift boxes Katy can fill has to be a common multiple of 8 and 14
Smallest number of gift boxes Katy can fill is the least common multiple of 8 and 14
Now,
8 = 2 x 2 x 2
14 = 2 x 7
LCM of 8 and 14 = 2 x 2 x 2 x 7
= 56
Smallest number of gift boxes Katy can fill is 56
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Make sure you ans
1. A cell phone company offers two texting plans. People who use plan A pay 20 cents for each text sent or received. People who
use plan B pay 14 dollars per month, and then pay an additional 8 cents for each text sent or received.
question
a. Write an inequality to represent the fact that it is cheaper for someone to use plan A than plan B. Use x to represent the number
of texts they send.
b. Solve the inequality.
hey you man what are you going here go to there
could i get some help
last one got deleted
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 4^{\frac{2}{5}} \right)^{\frac{1}{4}}\implies 4^{\frac{2}{5}\cdot \frac{1}{4}}\implies 4^{\frac{1}{10}}\implies \sqrt[10]{4^1}\implies {\Large \begin{array}{llll} \sqrt[10]{4} \end{array}}[/tex]
The data show the number of pieces of mail delivered to a single home address each day for three weeks.
4, 0, 2, 6, 1, 0, 3, 4, 0, 2, 4, 1, 5, 2, 3, 1, 1, 2
Which statement is true about a graph representing the data? Select two options.
The number line of a dot plot would start at 1.
A dot plot would show 7 points for numbers greater than 2.
The intervals on a histogram should be 0 to 2, 3 to 4, and 5 to 6.
A histogram would have a maximum of 7 bars.
A histogram should not show a bar that includes 0 pieces of mail
For the above question, statement 2 and 4 are true for the given data and after plotting the dot plot and histogram.
As per the question statement, data is showing the number of pieces of mail delivered to a single home address each day for three weeks.
Which is as follows: 4, 0, 2, 6, 1, 0, 3, 4, 0, 2, 4, 1, 5, 2, 3, 1, 1, 2
10 for 3 days, 1 for 4 days, 2 for 4 days, 3 for 2 days, 4 for 3 days, 5 for 1 day and 6 for 1 day.
Statement 1: False because the number line of a dot plot would start at 0.
Statement 2: True
Statement 3: False as it should be 0, 1, 2, 3, 4, 5 and 6
Statement 4: True
Statement 5: False as it should show 3 bars at 0 in histogram
Dot plot: An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)Histogram: A histogram is a graph that use rectangles to display the frequency of numerical data.To learn more about dot plot and histogram, click on the link given below:
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Answer:
b,d
Step-by-step explanation:
Complete the table by classifying the polynomials by degree and number of terms. binomial quadratic monomial Polynominal 2002 3x 55 -3x²2 - 6x + 9 constant exponential Name Using Degree linear Name Using Number of Terms trinomial
The given expression -3x²-6x+9 is quadratic expression and it is trinomial.
Classification of polynomials are given below:
A) 2x²
Degree = 2, so it is quadratic expression
Name using number of terms=monomial
B) -2
Degree = 0, it is constant
Name using number of terms=monomial
3) 3x-9
Degree = 1, so it is linear expression
Name using number of terms=monomial
4) -3x²-6x+9
Degree = 2, so it is quadratic expression
Name using number of terms=trinomial
Therefore, the given expression -3x²-6x+9 is quadratic expression and it is trinomial.
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phyllis invested 9,500, a portion earning a simple interest rate of 91/5% per year and the rest earning a rate of 9% per year. After one year the total interest earned on these investments was 870.00. how much money did she invest at each rate?
Answer:
See below
Step-by-step explanation:
x = amount at 9.2 % interest = .092 x
(9500 -x) = amount at 9% interest = .09 ( 9500-x) summed, they = 870
.092x + .09 ( 9500-x) = 870
x = 7500 then the other amount at 9 % is 2000
(EASY POINTS)
After reviewing the image I know its an expansion and that the top negative answers are incorrect. Its either C or D
Answer:
Its C
Step-by-step explanation:
write the equation in slope intercept form of the line that passes through the points (-4,8) and (4,6)
The equation of the line in the slope-intercept form is y = -1/4x + 9
Equation of a lineFrom the question, we are to determine the equation of the line that passes through the given points.
The given points are (-4, 8) and (4, 6)
Using the formula,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
x₁ = -4
y₁ = 8
x₂ = 4
y₂ = 6
Thus,
(y - 8)/(x - -4) = (6 - 8)/(4 - -4)
(y - 8)/(x + 4) = -2 / (4 + 4)
(y - 8)/(x + 4) = -2 / 8
(y - 8)/(x + 4) = -1/4
4(y - 8) = -1(x + 4)
4(y - 8) = -x + 4
y - 8 = -1/4x + 1
y = -1/4x + 1 + 8
y = -1/4x + 9
Therefore,
The equation is y = -1/4x + 9
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A 45 foot ladder is set up against the side of a house so that it raches up 27 feet. if latanya grabs the ladder at its base and pulls it 3 feet farther from the house how far up will the side of the ladder reach now
Using Pythagorean theorem, the side of the ladder will reach 22.45 ft far up now.
Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.
c² = a² + b²
If a 45 foot ladder is set up against the side of a house so that it reaches up 27 feet, then the distance between the base of the ladder and the base of the side of the house is the difference between the square of the two values.
c = 45 ft
a = 27 ft
b² = c² - a²
b² = (45 ft)² - (27 ft)²
b² = 2025 - 729
b² = = 1296
b = 36 ft
If Latanya grabs the ladder at its base and pulls it 3 feet farther from the house, then the distance becomes b + 3 = 39 ft.
Using Pythagorean theorem, determine how far up the ladder is on the side of the house.
c = 45 ft
b = 39 ft
a² = c² - b²
a² = (45 ft)² - (39 ft)²
a² = 2025 - 1521
a² = 504
a = 6√14
a = 22.45 ft
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What is the slope of the line that passes through the points (-4, 6) and
(-4, 18)?
The slope of the line passing from the two points is found as infinity.
What is meant by slope of the line?The slope of the line is a measurement of its steepness and direction. Any 2 separate points on a line can be used to calculate the slope of that line. The slope of the a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.For the given question;
The two passing points of the line is given as;
(x1, y1) = (-4, 6)
(x2, y2) = (-4, 18)
The formula for calculating the slope is;
Slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (18 - 6)/ (- 4 + 4)
m = 12/0
m = ∞
It means, the line is parallel to the x axis.
Thus, the slope of the line passing from the two points is found as infinity.
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HELP PLS I NEED THIS TODAY
What are the similarities and differences between number 1 and 3?
What similarities do you see between 3 and 4
For example:
Similar: both arithmetic/linear/common difference
Different: #1 is discrete #3 is continuous
WILL GIVE BRAIN
Once a large pink ribbon, the sign of the fight against breast cancer, was erected out of pink post-it notes on a billboard. If the area of the rectangular billboard covered by the ribbon was approximately
3705 square feet, and the width of the billboard was approximately 57 feet, what was the height of this billboard?
Answer:
65 feet
Step-by-step explanation:
[tex]3705=57h \\ \\ h=\frac{3705}{57}=65[/tex]
2y + k = 6y - ky; y please solve this
Answer:
[tex]y=-\frac{k}{-4+k}; k \neq 4[/tex]
Step-by-step explanation:
2y + k = 6y - ky; solve for y
2y = 6y - ky - k (Subtraction Property of Equality)
2y - (6y - ky) = 6y - ky - k - (6y - ky) (Subtraction Property of Equality)
-4y + ky = -k (Simplify)
y(-4 + k) = -k (Factor)
[tex]\frac{y(-4+k)}{-4+k}=\frac{-k}{-4+k}: k\neq 4[/tex] (Division Property of Equality)
[tex]y=-\frac{k}{-4+k}; k \neq 4[/tex] (Simplify)
The value of y is k/ (4- k).
What is algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to different addition, subtraction, multiplication, and division arithmetic operations.
Given:
2y + k = 6y - ky
Now, solving for y
2y -6y + ky = -k
-4y + ky= -k
y( k-4) = -k
y = -k/(k -4)
y= k/ (4- k)
Hence, the value of y is k/ (4- k).
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Avery is the oldest of four siblings whose ages are consecutive odd integers. If the sum of their ages is 112, find Avery's age.
Four siblings whose ages are consecutive odd integers. If the sum of their ages is 112 then The eldest sibling is 31, followed by siblings 29, 27, and 25.
What is consecutive integers ?
Consecutive means in order. Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.
Let x = the 1st sibling
Let x -2 = the second sibling
Let x -4 = the third sibling
Let x-6 = the fourth sibling.
If you add the four siblings together they equal 112
(x) +(x-2)+(x-4)+(x-6) = 112 Combine like terms
4x - 12 = 112
add 12 from both sides
4x - 12 + 12 = 112 + 12
4x = 124
divide 4 both side :
x = 31
The eldest sibling is 31, followed by siblings 29, 27 and 25
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WILL GIVE BRAINLIEST
Write an equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4).
y equals negative one-fourth times x minus 7
y equals negative one-fourth times x plus 2
y = 4x + 24
y = 4x + 36
Answer:
[tex]y=-\frac{1}{4}x+2[/tex]
Step-by-step explanation:
Perpendicular lines have slopes thst are negative reciprocals, so the slope of the line to be found is -1/4.
Substituting into point-slope form, the equation is [tex]y-4=-\frac{1}{4}(x+8)[/tex].
Rearranging into slope-intercept form,
[tex]y-4=-\frac{1}{4}(x+8) \\ \\ y-4=-\frac{1}{4}x-2 \\ \\ y=-\frac{1}{4}x+2[/tex]
Select Correct or Incorrect for each equation.
Equation
-1+1/-1=1
-1/1=-1
Answer:
first equation: Incorrect
second equation: Correct
Step-by-step explanation:
first equation:
[tex]-1 + (\frac{1}{-1}) = 1[/tex]
[tex]-1 + (-1) = 1[/tex]
[tex]-2 = 1[/tex]
negative 2 isn't the same as positive 1 which isn't true so the answer is incorrect.
second equation:
[tex](\frac{-1}{1} ) = -1[/tex]
[tex](-1) = -1[/tex]
negative 1 is the same as negative 1 so the answer is correct
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the difference.
9832 - 6199 =
3633 is the difference of these numbers.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.
Subtraction can be applied in a variety of real-world situations. Assume you had five apples and your friend had three. We may calculate the quantity of remaining apples by subtracting: 5 - 3 = 2.
Given Data
9832 - 6199
Subtracting,
= 9832 - 6199
= 3633
3633 is the difference of these numbers.
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Bronze is an alloy made of copper and tin. the ratio of copper to tin is 23 to 2, if a bronze statue weighs 50kg what is the mass of copper in the statue
STEP BY STEP AND URGENT
Answer:46kg
Step-by-step explanation:
23+2=25
50/25=2
2x23=46kg
Answer:
46 kg
Step-by-step explanation:
Ratio of copper to tin in the bronze alloy is 23:2
That means, as a ratio of the entire brass mass, the copper content is in the ratio of 23/(23 + 2) = 23/25
Since the mass of the bronze statue is 50 kg, the mass of copper in it must be 50 x 23/25 = 46 kg
The remaining kg (2/25 of 50 kg) is tin
translate to an inequality. he runs at least 1.8 hours per day. question content area bottom part 1 let r represent the number of hours of running per day.
g ≥ 1.8 is the number of hours of running per day in inequality .
What are the mathematical inequalities?
An inequality in mathematics depicts the relationship between two values in an unbalanced algebraic expression. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.Income gap, gender inequality, access to health care, and social class are some of the most prominent instances of social inequality. Some people receive better and more skilled care in the medical field than others. Additionally, they must pay more for these services.Atleast means the number would be greater than or equal to given number.
g ≥ 1.8
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The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
Which graph could be the graph of f(x)?l
The graph could be the graph of f(x) which is the correct answer would be option (B).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We are given the degree of the polynomial function f(x) to be 3; and
the roots of the equation f(x) to be 0 are -1, 0, and 4.
So we will put these values in the polynomial function of degree 3 to get:
f(x) = (x -(-1))(x-0)(x-4)
f(x) = (x + 1)x(x-4) = x³ - 3x² - 4x
According to this, the x-intercepts of this function on the graph will be:
(0, 0)
(-1, 0)
(4, 0)
So we will look for a graph that intercepts the x-axis at these points.
Therefore, the graph of the option (B) at the bottom right satisfies the conditions and is the graph of f(x).
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Pretty please help. I'm going to be grounded if I dont get this answered