\(\\ \sf\longmapsto x^3+y^3+z^3=k\)
Use formula of (a+b+c)^3
\(\\ \sf\longmapsto (x+y+z)^3\)
\(\\ \sf\longmapsto x^3+y^3+z^3+2xy+2yz+2zx\)
Hence
\(\\ \sf\longmapsto x^3+y^3+z^3=-2xy-2yz-2zx\)
\(\\ \sf\longmapsto k=-2xy-2yz-2zx\)
Answer:
-2xy - 2yz - 2zx
Step-by-step explanation:
x³ + y³ + z³ = k
Use the Formula (x + y + z)³
\(\sf(x+y+z)^3\)
\( \sf = x^3+y^3+z^3+2xy+2yz+2zx\)
So ,
\( \sf x^3+y^3+z^3=-2xy-2yz-2zx\)
\( \sf k = -2xy-2yz-2zx\)
Conclusion:
If x³ + y³ + z³ then the value of k is -2xy - 2yz - 2zx.
What are the equations for the asymptotes of this hyperbola?
Y^2/36 - x^2/121=1
Answer:
\(\huge{\mathfrak{Solution}}\)
\(\huge{\bold{ \frac{ {y}^{2} }{36} - \frac{ {x}^{2} }{121} = 1 }}\)
\(\huge{\bold{ \frac{(y - k) {}^{2} }{ {a}^{2} } - \frac{(x - h) {}^{2} }{ {b}^{2} } = 1 \: is \: the \: standard \: equation \: with \: center \: (h ,k),semi-axis \: a \: and \: semi-conjugate \: -axis \: b.}}\)
\(\huge\boxed{\mathfrak{We \: get,}}\)
\((h,k) = (0,0),a = 6,b = 11\)
\(For \: hyperbola \: assymtoms \: are \: y = + \frac{a}{b} (x - h) + k\)
\(Therefore,y = \frac{6}{11} (x - 0) + 0,y = - \frac{6}{11} (x - 0) + 0\)
\(\large\boxed{\bold{y = \frac{6x}{11},y = - \frac{6x}{11} . }}\)
If y²/36 - x²/121 = 1, the asymptotes are y = (36/121) x and y = -(36/121) x.
To find the equations for the asymptotes of the hyperbola represented by the equation y²/36 - x²/121 = 1, we can compare it with the standard form of a hyperbola:
(y - k)² / a² - (x - h)² / b² = 1
where (h, k) represents the center of the hyperbola.
In the given equation, we have y²/36 - x²/121 = 1. To put it in standard form, we need to divide both sides by 1 (which is essentially dividing by 1 on the right side):
y²/36 - x²/121 = 1 / 1
Now, we can see that a² = 36 and b² = 121.
To find the equations of the asymptotes, we use the center (h, k) and the values of a and b. The asymptotes of a hyperbola have equations of the form:
y = k ± (a/b)(x - h)
In this case, the center (h, k) is (0, 0), a² = 36, and b² = 121:
The equations for the asymptotes are:
y = 0 ± (36/121) x
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By definition, (f \circ g)(x)=f(g(x)) \vee . So if g(5)=7 and f(7)=22 , then (f \circ g)(5)= Need Help?
By the definition of the composition of functions, we have (f ∘ g)(x) = f(g(x)).The value of (f ∘ g)(5) is 22.
Given that g(5) = 7 and f(7) = 22, we can substitute these values into the composition expression to find (f ∘ g)(5):
(f ∘ g)(5) = f(g(5))
Since g(5) = 7, we have:
(f ∘ g)(5) = f(7)
And since f(7) = 22, we can conclude:
(f ∘ g)(5) = 22
Therefore, the value of (f ∘ g)(5) is 22.
In other words, when we apply the function g to the input 5, it yields the value 7, and then when we apply the function f to the result 7, it yields the value 22. So, the composition of functions (f ∘ g) evaluated at 5 is equal to 22.
To summarize:
(f ∘ g)(5) = 22
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a. AAS
b. ASA
c. NOT CONGRUENT
d. SSS
e. SAS
(geometry)
A beetroot farmer owns two plots of land that are equal in area but with different soil conditions. The farmer wants to compare the average annual crop yields from the two plots The farmer selects a random sample of n1 = 6 years and gathers data for these years on the first plot's yield. He also selects a random sample of n2 = 7 years and gathers data for these years on the second plot's yield. Then he computes the mean yield for each sample Imagine that the annual crop yield from the first plot is normally distributed with ?| = 2,180 and ?? = 21,183, and that the annual crop yield from the second plot is normally distributed with 2-2,092 and ? -14,828 distribution with a mean of The difference between the two sample means follows a standard deviation equal to and Use the Distributions tool to help answer the question that follows. Standard Normal Mean-0.0 Standard Deviation 1.0 5000 5000 0.000 What is the probability that the sample mean yield for the first plot exceeds the sample mean yield for the second plot by at least 231 beetroots?
There will be a difference of at least 231 beetroots between the two sample means.
To calculate the probability that the sample mean yield for the first plot exceeds the sample mean yield for the second plot by at least 231 beetroots, we need to compare the difference in sample means to the given value.
The difference between the two sample means follows a normal distribution with a mean equal to the difference between the population means (2,180 - 2,092 = 88) and a standard deviation equal to the square root of the sum of the variances divided by the sum of the sample sizes [(21,183^2/6 + 14,828^2/7)/(6 + 7)].
Using the Distributions tool, we can calculate the probability of the difference being greater than or equal to 231 beetroots. We set the mean to 88, the standard deviation to the calculated value, and calculate the probability for values greater than or equal to 231.
The resulting probability will give us the likelihood of observing a difference of at least 231 beetroots between the two sample means.
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Least to greatest- 3/8 5/16 , -2/4. , 1/2
Answer:
-2/4 then 5/16 then 3/8 then 1/2 plz mark brainiest :)
Answer:
-2/4 , -3/8 , 5/16 , 1/2
Step-by-step explanation:
Using the given inputs:
-3/8 5/16 -2/4 1/2
The least common denominator (LCD) is: 16.
Rewriting as equivalent fractions with the LCD:
-3/8 5/16 -2/4 1/2
-6/16 5/16 -8/16 8/16
Sorting this table by the numerators of the equivalent fractions in order from least to greatest:
-2/4 -3/8 5/16 1/2
-8/16 < -6/16 < 5/16 < 8/16
Therefore, the sorted inputs in order from least to greatest is:
-2/4 < -3/8 < 5/16 < 1/2
PLS HELP
Evaluate the expressions:
h(x)=12/x
h(-2)
h(a)
Answer:
h(-2) = -6, h(a) = 12/a
Step-by-step explanation:
h(-2)
It says that you are supposed to do 12 divided by the number in the parentheses, so you have 12 / -2 = -6.
h(a)
Again, you have to do 12 divided by the number in the parentheses, so you have 12/a.
If the probability that the Islanders will beat the Rangers in a game is 5/9, what is the probability that the Islanders will win exactly three out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.
Answer:
0.235Step-by-step explanation:
Probability of win is:
p(w) = 5/9 = 0.555Probability of loss is:
p(l) = 1 - p(w) = 1 - 0.555 = 0.445Combinations of 3 wins out of 7 games is:
3C7 = 7!/3!4! = 7*6*5/2*3 = 35Required probability:
P = 35*(0.555)³(0.445)⁴ = 0.235 (rounded)|x+2), if x >- 1
Plz plz plz help
For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
stays the same
increases
decreases
Population standard deviation, level of significance are same.
Margin of error increased.
With increase in margin of error sample size decreases.
By dividing the population's standard deviation by the sample size and then multiplying the resulting number by the crucial factor, the margin of error—a statistical expression used to estimate how much a result will deviate from the value of the full population—can be determined.
The standard deviation of the sample statistics, if we could take several samples of the same size, is the standard error.
Population standard deviation, level of significance are same.
Margin of error increased.
Margin of error increases leads to decrease in the sample size
as the margin of error is in denominator position in sample size formula. Hence with increase in margin of error sample size decreases.
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Find vector and parametric equations of the line such that, the line contains the point (5,2) and is parallel to the vector (-1, 3) 2. Find the acute angle of intersection of these lines, to the nearest degree. * =(4,-2) + t(2,5), teR and F = (1, 1) + t(3, -1), teR. 3. Find a Cartesian equation of the line that passes through and is perpendicular to the line, F = (1,8) + (-4,0), t € R. 4. Let I be the line that passes through the points (4, 3, 1) and (-2, -4, 3). Find a vector equation of the line that passes through the origin and is parallel to 1. 5. Determine a vector equation for the plane containing the points P(-2,2,3), Q(-3,4,8) and R(1,1,10). 6. Determine a Cartesian equation of the plane that passes through (1, 2, -3) such that its normal is parallel to the normal of the plane x - y - 2z + 19 = 0. 7. Find the angle, to the nearest degree, between the given planes. x+2y-3z-4 = 0, x-3y + 5z + 7 = 0 8. Find parametric equations of the plane that contains the point P(5,-1,7) and the line * = (2, 1,9) + t(1, 0, 2), t € R. 9. Determine the intersection of the line and the plane. *==+2=and 3x + 4y-7z+7= 0 10. Where does the liner = (6,1,1) + t(3,4,-1) meet? a) the xy-plane? b) the xz-plane? c) the yz-axis? 11. Find the point of intersection of the plane 3x - 2y + 7z = 31 with the line that passes through the origin and is perpendicular to the plane. 12. The angle between any pair of lines in Cartesian form is also the angle between their normal vectors. For the lines x-3y +6=0 and x + 2y-7=0 determine the acute and obtuse angles between these two lines.
A vector equation can be used to represent a line or a plane by combining a direction vector and a position vector.
How to determine the vector and parameter equation1. The line has the vector condition r = (5, 2) + t(- 1, 3) where t is a real number.
2. Using the dot product equation, we can locate the acute angle point of intersection: The formula for cos is (u v) / (||u|| ||v||), where u and v are the direction vectors of the lines. By substituting the values, we arrive at cos = (-1 * 3 + 3 * 5) / ((-1)2 + 32) * (2 2 + 52)). 58 degrees are obtained when we solve for.
3. The dot product gives a Cartesian condition to the line opposite to F = (1,8) + (- 4,0)t: x - 1, y - 8) · (-4, 0) = 0. We can diminish this condition to - 4x + 32, which approaches 0.
4. The vector equation for the line parallel to I = (4, 3, 1) that runs through the origin is r = (0, 0, 0) + t(4, 3, 1). A real number is t.
5. r = (- 2,3) + s(- 1,2,5) + t(3,- 1,7) is the vector condition for the plane with P(- 2,2,3), Q(- 3,4,8), and R(1,1,10), where s and t are genuine numbers.
6. The dot product gives a plane Cartesian equation that is steady with the regular of x - y - 2z + 19 = 0 and going through (1, 2, - 3): ( x - 1, y - 2, z + 3) · (1, -1, -2) = 0.
7. The dot product formula can be utilized to decide the point between the planes x + 2y - 3z - 4 and x - 3y - 5z - 7 which equivalents zero: cos is equal to (n1 - n2)/(||n1|| ||n2||), where n1 and n2 are the normal plane vectors. By changing the values, we can substitute cos 59 degrees.
8. x = 5 + 2s + t, y = - 1 + s, and z = 7 + 9s + 2t are the parametric conditions for the plane containing P(5, - 1, 7) and the line * = (2, 1, 9) + t(1, 0), where s and t are genuine numbers.
9. The point of intersection between the lines * = 2 + 3t and 3x + 4y - 7z + 7 = 0 can be found by substituting the values of x, y, and z from the line equation into the plane equation and solving for t.
10. For the line * = (6, 1, 1) + t(3, 4, - 1), we can find the point of intersection by substituting the value of x, y, and z from the line equation into the different coordinate planes. We can also locate the intersection points between the x-plane and the yz-axis since the xy plane's z coordinate is zero (x, y, z) = t(3, 4, -1).
11. The point of intersection of the plane 3x - 2y + 7z = 31 and the line that passes through the origin can be determined by substituting x = 0, y = 0, and z = 0 into the plane equation and solving for the remaining variable.
12. The acute angle between the lines x - 3y + 6 = 0 and x + 2y - 7 = 0 can be found using the formula below: = arctan(|m1 - m2|/(1 + m1 * m2)), where m1 and m2 represent the lines' slants.
Finding out the characteristics, we view the acute angle as about 54 degrees, and the obtuse angle can be procured by removing the acute angle from 180 degrees.
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The output values for y = x² and y = 15 + x show patterns. Describe in words how the patterns differ. Use the words increase and decrease in your description.
The pattern in y = x² exhibits a nonlinear increase in y as x increases, forming a U-shaped curve, while the pattern in y = 15 + x shows a linear increase in y as x increases at a constant rate.
The patterns in the equations y = x² and y = 15 + x differ in terms of the direction of change. In the equation y = x², the pattern shows an increase in y as x increases.
As x increases from negative to positive values, the corresponding y values also increase, forming a symmetric U-shaped curve. The rate of increase for y becomes steeper as x moves further away from zero.
On the other hand, in the equation y = 15 + x, the pattern shows a linear increase in y as x increases. As x increases, the corresponding y values increase in a straight line.
The rate of increase for y remains constant at one unit per increase in x. This linear pattern reflects a constant upward shift of the graph as x increases.
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helppppppppppppppppppppppppppppppppp
Answer:
432
Step-by-step explanation:
Hope this helps!
For a 12-month period, the numbers of inches of snow per month in Chicago
were:
11, 10, 6, 1,0,0,0,0,0, 1, 2, 9
What is the range of the data values?
O A. 6.
B. 1
C. 11
D. 10
Answer:
C. 11
Step-by-step explanation:
Calculating range is subtracting the highest data value(11) from the lowest data value(0)
11 - 0 = 11
Samantha has found 3 points on the function f(x) = 4x - 1. They are (-3, -13), (0, -1), and (2, 7). Which answer choice shows three points on the inverse function?
Answer: (-13, -3), (-1, 0), and (7, 2).
Step-by-step explanation:
First, we have a function f(x) and we know that 3 points (x, y) of this function are:
(-3, -13), (0, -1), and (2, 7).
Now, if we have a function g(x) and we know that g(x) is the inverse of f(x), we have that:
g(f(x)) = x.
this means that if f(x) = y then g(y) = x.
then if (-3, -13) is a point in the f(x) graph, (-13, -3) must be a point in the g(x) graph.
Then 3 points in on the inverse of the function f(x) are:
(-13, -3), (-1, 0), and (7, 2).
subset the data set to include only x2, x3, and x4. how many missing values are there in these three variables?
The subset of the data set with x2, x3, and x4 would include 6 missing values.
The subset of the data set with x2, x3, and x4 would include 6 missing values.
1. Subset the data set to include only x2, x3, and x4.
2. Count the number of missing values in each variable.
3. Add the number of missing values for each variable together.
4. The total number of missing values in these three variables is 6.
The subset of the data set with x2, x3, and x4 would include 6 missing values.
Subset the data set to include only x2, x3, and x4.
The complete question is :
Subset the data set to include only x2, x3, and x4. How many missing values are there in these three variables?
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what is -4(x+3) - 12x + 5 distributed
The quadrilateral is a trapezoid. What is the value of x? if the top is 21 and the bottom is 27 and x is in the middleA) 4B) 5C) 48D) 25
The value of x for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.
Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.
From the given diagram, the expression below is true:
2(5x - 1) = 21 + 27
Expand
10x - 2 = 48
10x = 48 + 2
10x = 50
Divide both sides by 10
10x.10 = 50/10
x = 5
Hence the value of x is 5
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A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve f(x) = 1/30 for 0
We need to find the probability that John waits less than 20 minutes for the train.
To find this probability, we need to calculate the area under the density curve from 0 to 20:
P(X < 20) = ∫[0,20] (1/30) dx
P(X < 20) = [x/30] from 0 to 20
P(X < 20) = 20/30 - 0/30
P(X < 20) = 2/3
Therefore, the probability that John waits less than 20 minutes for the train is 2/3 or approximately 0.67.
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help pls i am comfused
alternate interior angles
PLEASE HELP HURRY PLEASE‼️‼️‼️‼️‼️‼️‼️‼️‼️
Question 25 of 25
Which of the following values are in the range of the function graphed below?
Check all that apply.
10
10
10
-10
Answer:
I think thé answer is C 0 contadict me if it is dring please
Option D is correct, 6 is the value of the range in the given graph.
What is a function?A relation is a function if it has only One y-value for each x-value.
We have to find the values are in the range of the function graphed below
The domain of the given graph is -2≤x≤4
What can go into a function is called the Domain.
What may possibly come out of a function is called the Codomain.
What actually comes out of a function is called the Range.
The range of the given graph is y values.
The y value is 6
Hence, 6 is the value of the range in the given graph.
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problem 5 (30 points, each 10 points). in a chemical plant, 24 holding tanks are used for final product storage. four tanks are selected at random and without replacement. suppose that four of the tanks contain material in which the viscosity exceeds the customer requirements. 1. what is the probability that exactly one tank in the sample contains high-viscosity material? 2. what is the probability that at least one tank in the sample contains high-viscosity material? 3. in addition to the four tanks with high-viscosity levels, four different tanks contain material with high impurities. what is the probability that exactly one tank in the sample contains high-viscosity material and exactly one tank in the sample contains material with high impurities?
1. The probability of selecting exactly one tank with high-viscosity material is 0.
2. The probability of selecting at least one tank with high-viscosity material is 1.
3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.
1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.
2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.
3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.
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!!PLEASE HELP!!
also if you could explain how you solved it. It would be awesome :)
f(x)=3x^3+4x^2-8x−2
g ( x ) = 3x −5
Find ( x ) (f−g)(x).
Answer:
3x^3+4x^2-11x+3
Step-by-step explanation:
(f-g)(x)=f(x)-g(x) = 3x^3+4x^2-8x-2-(3x-5)= 3x^3+4x^2-11x+3
You are looking at your power bill for the month, you pay 12 cents per kilowatt-hour. Your power bill came out to $76.49 how many KWH of energy were used in house this month?
-21.5%, 1/3, -4/5, 1.3, 4.5%, -0.04
Pls help I need order from greatest to least
Answer:
Sure, here are the numbers arranged from greatest to least
Step-by-step explanation:
Order from greatest to least
1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%
Answer:
From the greatest to least
Step-by-step explanation:
1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%
You can identify which number is greater than other by using a number line.
What is a number line?
A number line is what a math student can use to find the answer to addition and subtraction questions. A straight line, theoretically extending to infinity in both positive and negative directions from zero, that shows the relative order of the real numbers.
Hope this helps :)
Pls Brainliest...
Explain what bivariate data is and the purpose of the linear
regression model.
Bivariate data involves two variables analyzed together to determine their relationship, while the linear regression model is used to find a straight line that best fits the data points on a scatter plot and make predictions based on that relationship.
Bivariate data refers to a set of two variables that can be analyzed together to determine the relationship between them.
For example, if we are studying the relationship between a person's height and weight, we would collect data on both of these variables for each individual in our sample.
Linear regression modeling is a statistical technique used to analyze bivariate data and determine the relationship between the two variables. The purpose of the linear regression model is to find a straight line that best fits the data points on a scatter plot. This line can then be used to make predictions about the relationship between the variables, such as predicting a person's weight based on their height.
Overall, the linear regression model is an important tool in analyzing bivariate data because it allows us to understand the relationship between two variables and make predictions based on that relationship.
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Harry is at the store buying cheese. The cost of the cheese
is $0.25 per ounce. He buys 8 ounces of the cheese. How
much money does Harry spend on the cheese?
Answer: $2
Step-by-step explanation: for each 4 ounces. it is a dollar. and since Harry got 8 ounces, it would be $2
Integrate the given series expansion of term-by-term from zero to π to obtain the corresponding series expansion for the indefinite integral of . If Answer: a. -cos x + C b. sin x + C c. cos x + C d. -sin x + C
The corresponding series expansion for the indefinite integral of the given series expansion, integrated term-by-term from zero to π, is -cos x + C.
To obtain the corresponding series expansion for the indefinite integral of the given series expansion, we need to integrate term-by-term from zero to π. This means that we integrate each term of the series expansion individually, and then combine them to form the overall series expansion for the indefinite integral. The indefinite integral of sin x is -cos x + C, where C is the constant of integration.
The given series expansion is:
sin x - (sin x)^3/3! + (sin x)^5/5! - (sin x)^7/7! + ...
To obtain the corresponding series expansion for the indefinite integral of this series expansion, integrated term-by-term from zero to π, we need to integrate each term of the series expansion individually, and then combine them to form the overall series expansion for the indefinite integral.
The indefinite integral of sin x is -cos x + C, where C is the constant of integration. Therefore, integrating the first term of the series expansion, which is sin x, gives us -cos x + C. Integrating the second term of the series expansion, which is (sin x)^3/3!, gives us (-cos x^3)/3! + C. Continuing in this way, we can integrate each term of the series expansion and obtain the corresponding series expansion for the indefinite integral.
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Graph the function Plot any five points on the graph.
Given the equation,
\(y=-\frac{11}{8}x^3\)Let us pick 5 points starting from x = 0 to x = 4
Having picked from point x = 0, let us solve for the corresponding y-values.
When x = 0,
\(\begin{gathered} y=-\frac{11}{8}\times0^3=-\frac{11}{8}\times0=0 \\ \therefore y=0 \end{gathered}\)So when x = 0, y = 0
When x = 1
\(\begin{gathered} y=-\frac{11}{8}\times1^3=-\frac{11}{8}\times1=-\frac{11}{8}=-1.375 \\ \therefore y=-1.375 \end{gathered}\)So when x = 1, y = -1.375
When x = 2,
\(\begin{gathered} y=-\frac{11}{8}\times2^3=-\frac{11}{8}\times8=-11 \\ \therefore y=-11 \end{gathered}\)So when x = 2, y = -11
When x = 3
\(\begin{gathered} y=-\frac{11}{8}\times3^3=-\frac{11}{8}\times27=-37.125 \\ \therefore y=-37.125 \end{gathered}\)So when x = 3, y = -37.125
When x = 4
\(\begin{gathered} y=-\frac{11}{8}\times4^3=-\frac{11}{8}\times64=-11\times8=-88 \\ \therefore y=-88 \end{gathered}\)So when x = 4, y = -88.
Let us now plot the graph
A car travels at a constant speed. In 2 hours, it traveled 140 Kilometers. How many Kilometers would it travel in 14 hours?
Answer:980
Step-by-step explanation:If they traveled 140 kilometre in 2 hours, then you do 2 times 7 is 14 and that's how long you are driving, so you do 140 times 7 to see how many kilometres they traveled.