The point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
What is equation of line?
The algebraic form of representing set of points is known as the equation of line.
The point slope form is as follows:
[tex]y-y_{1}=m(x-x_{1})[/tex] ... (1)
Here, [tex]y_{1}[/tex] is [tex]y[/tex] co-ordinates, [tex]x_{1}[/tex] is [tex]x[/tex] co-ordinates, and [tex]m[/tex] is the slope.
Also, slope is given by the following expression:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Hence, equation (1) can be written as follows:
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})[/tex] ... (2)
Consider the following points:
[tex](g(x_{1}),x_{1})=(1250,0)\\(g(x_{2}),x_{2})=(750,5)[/tex]
substitute values in equation (2).
[tex]y-1250=\frac{750-1250}{5-0}(x-0)\\y-1250=-100x[/tex]
On comparing the above equation with equation (1), the value of slope [tex]m=-100[/tex]
Now, calculate the slope intercept form.
The following form is known as the slope intercept form:
[tex]y=mx+c[/tex]
Here, [tex]c[/tex] is the [tex]y[/tex] intercept that the value of [tex]y[/tex] when [tex]x=0[/tex] .
Substitute the value of slope that is -100 and value of g(x) when x =0 that is 1250 for [tex]c[/tex] in the above equation.
[tex]y=-100x+1250[/tex] ... (3)
Standered form of a line is as follows:
[tex]Ax+By=C[/tex]
Here, A,B, and C are integeres.
Rearrange equation (3) as follows:
[tex]y=-100x+1250\\100x+y=1250[/tex]
Hence, the point slope form is [tex]y-1250=-100x[/tex]. The slope intercept form is [tex]y=-100x+1250[/tex]. The standered form of line is [tex]100x+y=1250[/tex].
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Answer:
Step-by-step explanation:
What is the regression equation for the given data?
The regression equation for the given data is y = -35.575 + 24.774 x.
Let x be the guests and y be the cost.
From the given table:
mean of x = ∑x / n
= 3+4+4+6+6+7+8+8 / 8
= 46/8
= 5.75
∑[tex]x^{2}[/tex] = 290
mean of y = ∑y/n
= 30+60+88+90+115+160+150+162 / 8
= 106.875
a = mean of y - mean of x * b
[tex]b = \frac{s_{xy} }{s_{xx} }[/tex]
[tex]s_{xx} \\[/tex] = ∑[tex]x^{2}[/tex] - (∑[tex]x)^{2}[/tex]/n
= 290 - 46*46/8
= 25.5
[tex]s_{xy} =[/tex] ∑xy - ∑x∑y / n
= 5548 - 46*855/8
= 631.75
a = 106.875 - 5.75*b
b = 631.75/25.5
b = 24.774
a = -35.575
Therefore the regression equation y = -35.575 + 24.774 x.
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Gabrielle is 15 years older than Milkhail. The sum of there ages is 95 what is Milhails age
The age of Milkhail is 40 years .
In the question ,
it is given that
the the sum of ages of Gabrielle and Milkhail is = 95
let the age of Milkhail be "m" .
given that Gabrielle is 15 years older than Milkhail
So, the age of Gabrielle is = m + 15
the equation representing the sum of ages is given by
total age = age of Milkhail + age of Gabrielle
95 = m + m + 15
adding the like terms ,
we get
95 = 2m + 15
subtracting 15 from both the sides
2m = 95 - 15
2m = 80
dividing both sides by 2
m = 80/2
m = 40
Therefore , the age of Milkhail is 40 years .
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8 - Arrange from LEAST to GREATEST without the use of a calculator
Given the numbers:
[tex]3^{\frac{1}{3}},\text{ }4^{\frac{1}{2}},\text{ }\sqrt[3]{9},\text{ 1}^8,\text{ \lparen-}\frac{1}{2})^{-2}[/tex]Let's arrange the numbers from the least to the greatest without the use of a calculator.
Now, let's first simplify each term.
We have:
[tex]\begin{gathered} 3^{\frac{1}{3}}=\sqrt[3]{3} \\ \\ 4^{\frac{1}{2}}=\sqrt{4}=2 \\ \\ \sqrt[3]{9} \\ \\ 1^8=1 \\ \\ -(\frac{1}{2})^{-2}=(-2)^2=4 \end{gathered}[/tex]Therefore, arranging the numbers from the least to the greatest, we have:
[tex]\begin{gathered} 1 \\ \\ \\ 3^{\frac{1}{3}} \\ \\ \\ 4^{\frac{1}{2}} \\ \\ \sqrt[3]{9} \\ \\ \\ (-\frac{1}{2})^{-2} \end{gathered}[/tex]2d a researcher wanted to know if there was a significant difference in cyber security breaches between cities on two different continents. what test should he conduct to determine if there is a significant difference in cyber security breaches between the continents? write up the results and determine what do the results mean? here is the data set: asia europe 40 25 52 35 63 20 70 18 25 19 19 14 11 9
There is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
We use two sample t-test to check for the significance.
We take the sample of Asia as treatment 1 and that of Europe as treatment 2
Treatment 1
[tex]N_{1}[/tex]: 5
[tex]df_{1}[/tex] = N - 1 = 5 - 1 = 4
[tex]M_{1}[/tex]: 24.6
[tex]SS_{1}[/tex]: 77.2
[tex]S^{2} _{1}[/tex] = [tex]SS_{1}[/tex]/(N - 1) = 77.2/(5-1) = 19.3
Treatment 2
[tex]N_{2}[/tex]: 6
[tex]df_{2}[/tex] = N - 1 = 6 - 1 = 5
[tex]M_{2}[/tex]: 23.5
[tex]SS_{2}[/tex]: 1051.5
[tex]S^{2} _{2}[/tex] = [tex]SS_{2}[/tex]/(N - 1) = 1051.5/(6-1) = 210.3
T-value Calculation
[tex]S^{2} p_{}[/tex] = (( df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((4/9) * 19.3) + ((5/9) * 210.3) = 125.41
s2M1 = s2p/N1 = 125.41/5 = 25.08
s2M2 = s2p/N2 = 125.41/6 = 20.9
t = (M1 - M2)/√(s2M1 + s2M2) = 1.1/√45.98 = 0.16
The t-value is 0.16221. The p-value is .874721. The result is not significant at p < .05
Hence the answer is there is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
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PLEASE HELP AND HURRY!!!!!! Simplify: 7/8+3/4
Answer: 1.625
Step-by-step explanation:
13/8 = 1 5/8 = 1.625
fluorescent powder comes in 20 G vials with 12 vials in a set, each vilal a different color. so if I order 3 sets I will have 3 viles of each colorI have 496 cups of paint to fillratio of powder to paint is one part powder to five part paint I know that 3 vials of powder which is 60g= 0.2536 cups. & .2536 cups ×5 parts paint= 1.268 cups of mixture. I got this from theBecks on hereknowing this how many sets of powder do I need to buy in order to us all my paint?
First you need to know how many cups of powder you are going to need for the 496 cups of paint you already have
[tex]\begin{gathered} 1\text{ CUP POWDER}\Rightarrow5\text{ CUP PAINT} \\ x\text{ CUP POWDER}\Rightarrow496\text{ CUP PAINT} \end{gathered}[/tex]We write this as a ratio
[tex]\begin{gathered} \frac{x}{496}=\frac{1}{5} \\ x=\frac{496}{5} \\ x=99.2 \end{gathered}[/tex]for the 496 cups of paint you will need 99.2 cups of powder.
Continue by seeing how may grams there are in 99.2 cups
[tex]\begin{gathered} 60g\Rightarrow0.2536\text{ CUPS POWDER} \\ x\Rightarrow99.2\text{ CUPS POWDER} \end{gathered}[/tex]write it as a ratio and solve for x again.
[tex]\begin{gathered} \frac{x}{99.2}=\frac{60}{0.2536} \\ x=23470.03155 \end{gathered}[/tex]now find how many vials you will need
[tex]\begin{gathered} 1\text{vial}\Rightarrow20g \\ x\Rightarrow23470.03155g \end{gathered}[/tex]write the ratio and solve
[tex]\begin{gathered} \frac{x}{23470.03155}=\frac{1}{20} \\ x=\frac{23470.03155}{20} \\ x=1173.5\approx1174 \end{gathered}[/tex]If each sets comes with 12 sets, write the ratio and find the number of sets you will need
[tex]\begin{gathered} 1\text{set}\Rightarrow12vials \\ \text{xsets}\Rightarrow1174vials \end{gathered}[/tex][tex]\begin{gathered} \frac{x}{1174}=\frac{1}{12} \\ x=\frac{1174}{12} \\ x=97.83\approx98 \end{gathered}[/tex]you will need 98 sets for this amount of paint.
Which of the following are equivalent to the function y = 3cOS X + 2? Check all that apply. A. y = 3cos(-x) + 2 B. y = -3cOS X-2 C. y = 3sin(x + 1) +2 + D. y = 3sin(x-7)+2
We need to plot the graphs of these functions on the same axis:
[tex]\begin{gathered} \text{From the graph, we s}e\text{ the function} \\ y\text{ = 3cosx + 2 has the same grap as } \\ y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2} \\ \\ \text{Please note from angles in trigonometry:} \\ \sin \text{ (90 + }\theta)\text{ = cos }\theta \\ \cos x\text{ = sin (90 + x)} \end{gathered}[/tex]Hence, the correct option
[tex]y\text{ = 3sin(x + }\frac{\pi}{2})\text{ + 2 (option }C)[/tex]A stationary store sells large and small packages of greeting cards. Each large package contains h greeting cards. Each small package contains kgreeting cards, which is 4 less than the larger package. Express h in termsof k. *
In this case the answer is very simple. .
Step 01:
Data
large package = h cards
small package = k cards
Step 02:
large package - 4 = small package
h - 4 = k
h = k + 4
The answer is:
h = k + 4
Please help as soon as you can
The coordinates of the triangle S'T'U' is (2, -1), (5,3), (1, -4) and the triangle S"T"U" is (1,3), (4,5),(0,-2)
Coordinates:
Basically, the pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes is known as coordinates.
Given,
The triangle STU is graphed at S(2,-1) T(5,-3) U(1,4). Triangle STU is reflected over the x-axis to create triangle S'T'U' and then translated by the rule (x,y) ->(x-1,y+2) to create S"T"U".
Here we need to find the coordinates for triangle S'T'U' and S"T"U".
In order to find the correct transformation for this triangle, we have to do the following,
The formula that is used to reflect a coordinate point about the x-axis.
(X2,Y2) = (X1,Y1) * (1,-1)
So, based on this rule, the coordinates of S'T'U' is,
S(2,-1) => S'((2 x 1), (-1 x -1)) = > S'(2,-1)
T(5,-3) => T'((5 x 1), (-3 x -1)) => T'(5, 3)
U(1,4) => U'((1 x 1), (4 x -1)) => U'(1, -4)
Now we have to apply the next rule,
=> (x, y) -> (x-1, y+2)
S'(2,1) => S'((2 - 1), (1 + 2)) = > S'(1, 3)
T'(5,3) => T'((5 - 1), (3 + 2)) => T'(4, 5)
U'(1,-4) => U'((1 - 1), (-4 + 2)) => U'(0, -2)
Therefore, the coordinates of S'T'U' is (2, -1), (5,3), (1, -4) and the coordinates of S"T"U" is (1,3), (4,5),(0,-2)
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lin is mixing orange paint for a play. the color takes 3 parts red to 2 parts yellow. if lin has 18 cups of yellow paint how many cups of red does he need?
the number of cups of red Lin needs is 27 cups
Explanation:number of parts of red = 3
number of parts of yellow = 2
the ratio of red to yellow = 3:2
when lin's number of cups of yellow = 18
let the number of cups of red = x
3 red = 2 yellow
x red = 18 yellow
cross multiply:
3(18) = 2(x)
54 = 2x
divide both sides by 2:
54/2 = 2x/2
x = 27
Hence, the number of cups of red Lin needs is 27 cups
Romano pays 312.50 for a television set. The markup price of the television set is 25%. What equation could you use to find the amount of money that the ...
The equation used to find the amount of money the store bought the television sets is 1.25a = 312.50
How to find the equation that depict the amount of money paid for the television sets?Romano pays 312.50 dollars for a television set. The mark up price of the television set is 25%.
The equation that can be used to find the amount of money the store paid for the television sets can be calculated as follows;
Therefore,
25% of a + a = 312.50
where
a = cost of the television0.25a + a = 312.50
Therefore, the equation is 1.25a = 312.50
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Complete the table below to find solutions to the linear equation y = 5x + 35
y = 5x + 35
When x = 0, we substitute x = 0 into the equation above and then solve for y
y = 5(0) + 35
y = 0+ 35
y = 35
when x =3, substitute into the equation and then solve for y
y = 5(3) + 35
y = 15 + 35
y = 50
when x=-7, substitute x=-7 into the equation above and then solve for y
y = 5(-7) + 35
y = -35+ 35
y=0
x y (x,y)
0 35 (0, 35)
3 50 (3, 50)
-7 0 (-7, 0)
I need help with this problem. please if you can?
Answer:
1. Sometimes True.
2. Sometimes True.
3. Always True.
Explanation:
Given the statements;
1.
A percent of a number is smaller than the original number.
Sometimes True.
When the percentage is less than 100% it will be less than the number which makes the statement true, while when the percentage is greater than or equal 100% then the number will be greater than or equal to the original number which makes the statement false.
2.
It saves you more money to have a coupon for an amount of money off instead of a percent off.
Sometimes True.
It depends on the amount of money off and the percent off. Either of them could save more money.
3.
An improper fraction written as a percent will be greater than 100%.
Always True.
when an improper fraction is written as a percentage it will always be greater than 100%
If an object is dropped, the distance it fails during t seconds is given by d(t)=1/2gt^2, where g is about 32ft/sec^2. Find the distance an object would fall in 8 seconds.
Since the distanc function is given by
[tex]d(t)=\frac{1}{2}gt^2[/tex]in order to find the distance at 8 seconds, we need to substitute t=8 into this function, that is,
[tex]d(8)=\frac{1}{2}g(8)^2[/tex]By taking into account that g=32 ft/sec^2, we have
[tex]d(8)=\frac{1}{2}(32)(64)[/tex]which gives
[tex]\begin{gathered} d(8)=16\times64 \\ d(8)=1024 \end{gathered}[/tex]Therefore, the answer is 1024 ft, which corresponds to the last option.
help meeeeeeeeee pleasee
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
x 31 36 41 46y 10 8 6 4I need to find the slope with these points
x 31 36 41 46
y 10 8 6 4
I need to find the slope with these points
we know that
To find out the slope, we need two points
take the points (31,10) and (36,8)
so
m=(8-10)/(36-31)
m=-2/5
m=-2/5
m=-0.40
therefore
the answer is -0.40Part 2)
we have
x -7 -4 -1 2
y -7 14 35 56
take the points (7,-7) and (-4,14)
m=(14+7)/(-4-7)
m=21/-11
m=-21/11
the answer is -21/11A dozen muffins is 12 muffins. A recipe calls for 3/4 cup of almonds to make half a dozen muffins. Use a complex fraction to find how many cups of almonds are needed to make a dozen muffins.
1) Firstly, let's set a proportion to find out how mny cups of almonds are needed.
muffins cups of almonds
6 3/4
12 x
2)
Cross multiplying it:
6x = 12 * 3/4
6x = 9
x= 9/6
3
The volume of a cube is 614.125 cubic inches. What is the length of each side of the cube?
The length of the side of cube is 8.5 inches.
What is volume of a cube?
A cube is a solid object that is three dimensional and has six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, and the only regular hexahedron, is the cube. It consists of 8 vertices, 12 edges, and 6 faces.
The volume of a cube is a^3 cubic inches where a is the length of side of cube.
Give volume of a cube is 614.125 cubic inches.
Let the length of a side of cube is x inches.
Then volume of cube = x^3 cubic inches.
Now,
x^3 = 614.125
Finding cube root and we get
=> x^3 = 8.5 * 8.5 * 8.5
=> x = 8.5 inches
Therefore, the length of the side of cube is 8.5 inches.
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In a right triangle, the length of one leg is 20 units. The length of the other leg is 12 units. What is the length of the hypotenuse?
The of the hypotenuse of the right triangle having a length of 20 units for one leg and 12 units for the other is √( 544 ) units.
What is the length of the hypotenuse?Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
This is expressed as;
(Hypotenuse)² = (Leg 1 )² + (Leg 2)²
Given the data in the question;
Length of leg 1 = 20 unitsLength of leg 2 = 12 unitsLength of hypotenuse = ?Plug the given values into the formula above and solve for hypotenuse.
(Hypotenuse)² = (Leg 1 )² + (Leg 2)²
Hypotenuse = √( (Leg 1 )² + (Leg 2)² )
Hypotenuse = √( (20 )² + (12)² )
Hypotenuse = √( 400 + 144 )
Hypotenuse = √( 544 ) units
Therefore, √( 544 ) units is the length of the hypotenuse.
Option D) is the correct answer.
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2 gallons = 9 litres
16
to convert 17 gallons into liters
Answer:
Step-by-step explanation:
17/2=8.5
8.5 x 9=76.5
which of the following present for their transformation is equivalent to reflection across the x axis .Arotation 90 degrees about the origin of reflection across the x-axis B rotation 90 degrees about the origin reflection across the y-axisC rotation across degrees about the origin and reflection across the x axis D rotation 180 degrees about the origin reflection across the y axis
for transformation equivalent to reflection across the x axis
rotate 180 degree about the origin and reflection about the x axis.
option C is correct.
0.6 times 2.2 with 2 diffrent models
Answer:
0.6 x 2.2 = 1.32
2.2 x 0.6 = 1.32
Step-by-step explanation:
You just have to do 0.6 x 2.2 and flip it to get your second model.
Answer:
0.6 x 2.2 = 1.32
2.2 x 0.6 = 1.32
Step-by-step explanation:
the commutative property allows this to happen; flip the order in which the numbers fall
yw have a great day
Tim measured a house and made a scale drawing. In real life, the hall closet is 6 feet long. It is 10 inches long in the drawing. What is the scale of the drawing?
Answer:
60
Step-by-step explanation:
he graph of a function is shown.
5
4
3
2
-
y
--5-3-2-1₁ 1 2 3 4 5 x
-2-
-3+
7 9
Which function is represented by the graph?
O f(x) =
O
f(x) = {3
O f(x):
x-3, x<0
3,
x20
11
x + 3, x < 0
x 20
-x+ 3, x ≤ 0
3,
x>0
○ f(x) = { 3*
O
-x-3, x ≤0
x > 0
The function f(x) = {x + 3, x < 0, 3 x ≥ 0} represents the graph.
What is graph?
In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function f. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
As show in the graph we can see that the function has a graph of x + 3 on left side of the y - axis for x < 0.
And the function has the constant graph y = 3 for x ≥ 0.
Therefore, the given graph is the graph of the function,
f(x) = {x + 3, x < 0, 3 x ≥ 0}.
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Find the scale factor.
Answer:
scale factor k = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
the scale factor of Δ QRS to Δ LMN is the ratio of corresponding sides , image to original.
scale factor = [tex]\frac{QS}{LN}[/tex] = [tex]\frac{4}{3}[/tex]
(It would be great if there were an explanation, I'm struggling to understand how this works.) Triangle FGH has vertices F(−4, 0), G(0, 4), and H(4, 0). A dilation, centered at the origin, is applied to this triangle. The image has vertices F′(−12, 0), G′(0, 12), and H′(12, 0).
What is the scale factor of this dilation?
Enter your answer in the box.
Nevermind, solved. The answer is 3 because if you multiply each of the original points by 3 you get the new points. Since I already put this question up, you can answer just for points.
A scale factor is defined as the ratio between the scale of a given original object and a new object.
The scale factor of this dilation is 3.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
We have,
Triangle FGH has vertices:
F = (−4, 0)
G = (0, 4)
H = (4, 0).
The image of the triangle has vertices:
F′ = (−12, 0)
G′ = (0, 12)
H′ = (12, 0)
We see that,
Multiplying 3 on all the vertices of
F = (−4, 0)
G = (0, 4)
H = (4, 0)
we get,
F′ = (−12, 0)
G′ = (0, 12)
H′ = (12, 0)
This means,
A dilation with a scale factor of 3 is applied to the triangle.
Thus,
The scale factor of this dilation is 3.
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BRAINLIST PLEASE HELP!
(a) Angle B = Angle C = 65 degree.
(b) Angle x and Angle y is 70 degree .
Given,
In the question:
9. Write a sequence of rigid motion to take figure ABC to figure DEF.
Now According to the question:
Take a figure ABC to figure DEF
So, CB = FE
BA = ED
Angle B = Angle E
10.(a) To find the unknown measure:
In triangle ABC
Angle A = 90 degree
To find the Angle B and C
Let the angle B and C be x
We know that :
Sum of angle triangle is 180 degree
50 + x + x = 180
50 + 2x = 180
2x = 180 - 50
2x = 130
x = 65°
Hence, Angle B = Angle C = 65 degree.
10. (b) Given,
Angle ABC = Angle BAC
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Substitute Angle ABC = y and Angle BAC = x into Angle ABC = Angle BAC .
Angle (ABC + ACB + BAC) = 180 degree (Angle sum theorem)
=> y + 40 + x = 180
=> x + 40 + x = 180
=> 2x = 180 - 40
=> 2x = 140
x = 70°
Hence, Angle x and Angle y is 70 degree .
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Hi this is the question that I have. I don’t know if the one that I have chose is right or not. Please help me
To answer this question we must carefully understand the scope of the numbers of the table.
* It represents the number of adults that listen to audiobooks or not. But not all adults, just the surveyed adults.
* Nothing is said about books, only about audiobooks.
Some of the choices are tricky. For example, second and fourth choices talk about books, so they must be discarded.
The third choice refers to all adults, but the table refers only to the 640 adults that were asked.
The first choice is the best question that can be answered using the table.
Can please help me here
Answer:B your correct
Step-by-step explanation:the x axis is the domain so if the point is directly on the y axis the x whould be zero so the answer is -1.5
Which is the graph of f (x ) = x^3 + 2x^2 – 4x– 1?-(Notice the increments on the graph are by 2.)
We must identify which graph corresponds to the function:
[tex]f(x)=x^3+2x^2-4x-1.[/tex]1) The function f(x) is a polynomial of degree 3, so it has 3 roots, i.e. it must cross the x-axis in 3 places. Taking into account this fact, we know that the 1st and 3rd graphs cannot represent the function f(x).
2) Now, when x takes a very big value, the cubic term of the polynomial dominates, and f(x) > 0 for x → ∞. From the remaining options, we see that the 2nd takes f(x) < 0 for x → ∞, so we can discard that option. The remaining option is the 4th graph, so we conclude that that is the correct option.
Answer: 4th graph.