Answer:
Step-by-step explanation:
The correct statement about the given equations is: "The equations are dependent because the lines are the same line."
In the equation y = 2x + 5, the slope is 2, which means the line has a positive slope and is upward sloping.
The y-intercept is 5, indicating that the line intersects the y-axis at the point (0, 5).
The equation y = -2x + 5 is equivalent to y = 2(-x) + 5, which has the same form as the first equation but with a negative slope.
However, the equations are still dependent because when you simplify the second equation, you obtain the first equation.
These two equations represent the same line with a different slope. Therefore, they are dependent, and any point that satisfies one equation will satisfy the other equation as well.
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A rectangular garden measures 28ft by 47ft. Surrounding (and bordering) the garden is a path 3ft wide. Find the area of this path. Be sure to include the correct unit in your answer.
Answer:
486 square feet
Step-by-step explanation:
To calculate the area of the path, first find the dimensions of the garden, including the path. Then find the area of this larger outer rectangle and subtract the area of the inner rectangle (the garden without the path).
The garden measures 28ft by 47ft.
The path is 3ft wide, so it adds a total of 6ft to the length (3ft on each side) and 6ft to the width.
The dimensions of the garden, including the path:
Length: 47ft + 6ft = 53ft
Width: 28ft + 6ft = 34ft
Find the area of the outer rectangle (including the path):
Area_outer = Length * Width = 53ft * 34ft = 1802 sq ft
Find the area of the inner rectangle (the garden without the path):
Area_inner = 28ft * 47ft = 1316 sq ft
Now subtract the area of the inner rectangle from the area of the outer rectangle to find the area of just the path:
Area_path = Area_outer - Area_inner = 1802 sq ft - 1316 sq ft = 486 sq ft
So, the area of the path is 486 square feet.
Answer: 486 square feet;
Step-by-step explanation:
Area of the garden = 28 x 47 = 1316ft.²
-
Length of the garden and path = Length of the garden + 3 ft. on both sides
Length of the garden and path = 28 + 3 + 3 = 34 ft.
-
Width of the garden and path = Width of the garden + 3 ft. on both sides
Width of the garden and path = 47 + 3 + 3 = 53ft.
-
Area of the garden and path = Length x Width
Area of the garden and path = 34 x 53 = 1802 ft²
-
Area of the path = Area of the garden and path - Area of the garden
Area of the path = 1802 - 1316 = 486ft²
-
Answer: 486ft²
a rectangular park is 70 meters wide and 105 meters long. Give the length and width of another rectangular park that has the same perimeter but a small area
The length and width of another rectangular park is 110 meters by 65 meters
From the question, we have the following parameters that can be used in our computation:
A rectangular park is 70 meters wide and 105 meters long
This means that
Width = 70
Length = 105
The area is calculated as
Area = 70 * 105
Area = 7350
For smaller area, we decrease the width and increse the length
So, we have
Width = 70 - 5
Length = 105 + 5
Evaluate
Width = 65
Length = 110
Hence, the length and width of another rectangular park is 110 by 65
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Integration by partial fraction but im unsure how to proceed
The solution is:
[tex]\int\limits^a_b {\frac{x^{3} }{x^{2} + x -2 } } \, dx[/tex] =[tex]ln|x| + \frac{2}{5} ln|x+2| + \frac{1}{3} ln|x-1| + C[/tex]
What is a partial fraction?The partial fraction expansion of a rational fraction is described as an operation that consists of expressing the fraction as a sum of a polynomial and one or several fractions with a simpler denominator.
To solve the above partial fraction decomposition,
[tex]x^3 + x^2 - 2x = x(x^2 + x - 2) = x(x+2)(x-1)[/tex]
we then write the fraction as a sum of partial fractions:
[tex]fx-2dx = \frac{A }{x } + \frac{B}{x + 2 } + \frac{C }{x - 1}[/tex]
We find the values of A, B, and C by multiplying both sides by the common denominator (x)(x+2)(x-1) and substituting
fx-2dx = A(x+2)(x-1) + B(x)(x-1) + C(x)(x+2)
We set x = 0
0 = -2A
A = 0.
We set x = -2
-2 = 20B/(-2)(-4)
-2 = -5B
B = 2/5.
we set x = 1
1 = 3C
C = 1/3.
fx-2dx = 0/x + 2/5/(x+2) + 1/3/(x-1)
We integrate each term separately and have the solution as :
[tex]\int\limits^a_b {\frac{x^{3} }{x^{2} + x -2 } } \, dx[/tex] =[tex]ln|x| + \frac{2}{5} ln|x+2| + \frac{1}{3} ln|x-1| + C[/tex].
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Given a mean of 34 and a standard deviation of 5. Find the following z-scores.
The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.
To find the z-scores, we need to use the formula:
z = (x - μ) / σ
where:
z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.
Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:
z = (39 - 34) / 5
z = 5 / 5
z = 1
So, the z-score for the raw score of 39 is 1.For a raw score of 30:
z = (30 - 34) / 5
z = -4 / 5
z = -0.8
The z-score for the raw score of 30 is -0.8.
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Find the amount that results from the given investment.
$500 invested at 4% compounded quarterly after a period of 3 1/2 years
Answer:
Therefore, the amount that results from the given investment is approximately $579.64.
Step-by-step explanation:
We can use the formula for compound interest to find the amount that results from the given investment:
A = P(1 + r/n)^(nt)
where:
A = the amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, P = $500, r = 0.04, n = 4 (since the interest is compounded quarterly), and t = 3.5 years.
Plugging in the values, we get:
A = 500(1 + 0.04/4)^(4*3.5)
A = 500(1.01)^14
A = 500(1.159274...)
A ≈ $579.64
Therefore, the amount that results from the given investment is approximately $579.64.
What is the total profit from purses?
15+ (-24)
Pls help me with this problem thanks!
Answer:
-9
Step-by-step explanation:
HELPP PLEASEE!
A) Step 3
B) Step 2
C) No flaws
D) Step 1
Symmetry means, hmmm usually a mirror image.
So when something is symmetry to another, is a way to say, one is the mirror image of the other, or namely they're just identical twins.
Now, if know that B is the midpoint, by definition is cutting AC into two equal halves, so AB is the mirror image of BC, so they're identical twins, there are no flaws, Q.E.D.
Check the picture below.
I don’t understand these questions can I please get some help on them?
The amounts of koalas are given as follows:
a. Initially: 47.
b. 13 weeks: 21.
c. 23 weeks: 19.
d. The virus will not kill all the koalas, as when t -> ∞, N(t) -> ∞.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is defined as follows:
N(t) = 15 + 96/(t + 3).
For the initial number of koalas, we have that t = 0, hence:
N(0) = 15 + 96/3 = 47.
After 13 weeks, the number is given as follows:
N(13) = 15 + 96/16 = 21.
After 23 weeks, the number is given as follows:
N(23) = 15 + 96/26 = 19.
As t -> ∞, we have that:
N(∞) = 15 + 96/∞ = 15 + 0 = 15.
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A beaker is shaped like a cylinder with a volume of 1,004.8 cubic centimeters. If the
radius of the beaker is 4 cm, find the height of the beaker.
The height of the beaker is 6.35 cm.
To find the height of the beaker, we can use the formula for the volume of a cylinder, which is given by:
Volume = π ×[tex]radius^2[/tex] × height
In this case, we have the volume of the beaker as 1,004.8 cubic centimeters and the radius as 4 cm.
1,004.8 = π × [tex]4^2[/tex] × height
Simplifying the equation:
1,004.8 = 16π × height
To solve for the height, divide both sides of the equation by 16π:
height = 1,004.8 / (16π)
Using a calculator for the approximation of π (pi) as 3.14159, we can calculate the height:
height ≈ 1,004.8 / (16 × 3.14159)
height ≈ 6.35 cm
The height of the beaker is approximately 6.35 cm.
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alvin is 11 years older than elga. the sum of their age is 59 whats elgas age?? please help
Answer:
24 years old.
Step-by-step explanation:
Let's say that Elga's age is x years old. Then Alvin's age would be 11 years older than Elga, or x + 11 years old.
We know that the sum of their ages is 59 years old, so we can write an equation:
x + (x + 11) = 59
Simplifying the left side of the equation:
2x + 11 = 59
Subtracting 11 from both sides:
2x = 48
Dividing both sides by 2:
x = 24
Therefore, Elga's age is 24 years old.
Answer: 24
Step-by-step explanation:
Set Elga's age to x and Alvin's age to x+11...
(x+11)+x=59
2x=48
x=24
For the given confidence level and values of x and n, find the following.
=x45, =n96, confidence level 95%
The point estimate is given as 0.4688
The standard error = 0.051
How to solve for the point estimateP = x / n
= 45 / 96
= 0.4688
The point estimate is given as 0.4688
How to solve for the standard error
SE = √[ p(1 - p) / n ]
Substituting the values we have:
SE = √[ 0.46875 * (1 - 0.46875) / 96 ]
= √[ 0.2482 / 96 ]
The standard error = 0.051
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Question
For the given confidence level and values of x and n, find the following.
=x45, =n96, confidence level 95% find the point estimate and the standard error
The base of a solid is a right triangle whose base side has length a and whose perpendicular side has length (1/2)a. Find the volume of the solid if cross sections perpendicular to the base of the triangle are semicircles.
Here's a box plot that summarizes the number of math questions on Ms. O'Brien's homework assignments.
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1, labeled Number of questions. A left whisker extends from 6 to 9. The box extends from 9 to 14 and is divided into 2 parts by a vertical line segment at 11. The right whisker extends from 14 to 18. All values estimated.
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1, labeled Number of questions. A left whisker extends from 6 to 9. The box extends from 9 to 14 and is divided into 2 parts by a vertical line segment at 11. The right whisker extends from 14 to 18. All values estimated.
Find the range of the data.
questions
Answer:
The range of the data is 12-------------------------
The range of the data is the difference of maximum and minimum values.
According to description of the box plot, the minimum value is 6 and maximum value is 18.
Hence the range is:
Range = 18 - 6 = 12NEED HELP ASAP PLEASE AND THANK YOU
[1st Picture] Answer: x = 3.98
Step-by-step explanation:
We are given the opposite side and adjacent side from our reference angle. This will use the tangent function. tanθ = [tex]\frac{opposite}{adjacent}[/tex].
tan(53°) = [tex]\frac{x}{3}[/tex]
3tan(53°) = x
x = 3.98
[2nd Picture] Answer: x = 3.13
Step-by-step explanation:
Here, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ = [tex]\frac{opposite}{hypotenuse}[/tex].
sin(23°) = [tex]\frac{x}{8}[/tex]
8sin(23°) = x
x = 3.13
[3rd Picture - #6] Answer: θ = 63.4°
Step-by-step explanation:
Again, we are given the opposite side from our reference angle and the hypotenuse. This will use the sine function. sinθ = [tex]\frac{opposite}{hypotenuse}[/tex]. To find the angle measurement of theta at the end, we will use the inverse of sine.
sin(θ) = [tex]\frac{6}{6.71}[/tex]
[tex]sin^{-1}[/tex](sin(θ)) = [tex]sin^{-1}[/tex]([tex]\frac{6}{6.71}[/tex])
θ = 63.4°
●
8
10 12 14 16 18 20
Minutes Traveled
O Bus 18, with a mean of 12
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. R
if necessary, and explain your answer.
O Bus 14, with a median of 14
O Bus 14, with a mean of 14
22
O Bus 18, with a median of 12
24 26 28
Based οn bοth the median and mean values, it appears that Bus 47 typically has the faster travel time cοmpared tο Bus 18.
We know that
Statistics is the discipline of mathematics concerned with data collection, analysis, interpretation, presentation, and organisation. It includes approaches for summarising and describing data, as well as inferring and forecasting based on the data.
Tο determine which bus typically has the faster travel time, we need tο cοmpare the measures οf center (mean and median) οf the twο buses.
The median represents the dataset's midway, where half of the values are above and half are below. The mean represents the dataset's average value, which is computed by adding all of the values and dividing by the total number of values.
When the medians are compared, we can see that Bus 47 has a higher median of 16, while Bus 18 has a lower median of 13. This shows that Bus 47 may have a faster average trip time.
However, we must also consider the methods. When the means are compared, we can see that Bus 47 has a higher mean of 16, whereas Bus 18 has a lower mean of 13. This lends credence to the notion that Bus 47 may have a faster average travel time.
Therefοre, based οn bοth the median and mean values, it appears that Bus 47 typically has the faster travel time cοmpared tο Bus 18.
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The complete question is:
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Match the given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
The slope (m) and y-intercept (b) with the equation of the line in slope-intercept form are given as: m = 2 and b = 5 is y = 2x + 5; m = 3 and b = 5 is y = 3x + 5; m = 5 and b = 4 is y = 5x + 4.
How to Write the Equation of a Line in Slope-intercept Form?If m represents the slope of a line and b represents its y-intercept, the equation of the line in slope-intercept form is written as: y = mx + b.
Where m = 2 and b = 5, the equation of the line would be expressed as: y = 2x + 5.
Where m = 3 and b = 5, the equation of the line would be expressed as: y = 3x + 5.
Where m = 5 and b = 4, the equation of the line would be expressed as: y = 5x + 4.
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The circumference of a circle is the distance around the outside of the circle. The formula for circumference is C = 2πRwhere ris the radius of the circle. Find the circumference of a circle with
a radius of 21 centimeters. Use π = 22/7
Show your work and state your answer in a sentence.
The circumference of a circle with a radius of 21 centimeters is 132 centimeters.
The circumference is the distance around the boundary of a closed curve or shape. In the case of a circle, the circumference is the total length of the circular boundary.
To find the circumference of a circle with a radius of 21 centimeters, we can use the formula C = 2πR, where R is the radius and π is the mathematical constant approximately equal to 22/7.
Substituting the given values:
C = 2 x (22/7) x 21
C = (44/7) x 21
C = 924/7
C ≈ 132 centimeters
Therefore, the circumference of a circle with a radius of 21 centimeters is 132 centimeters.
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Can someone help with this please?
Answer:
x = 65 degrees
Step-by-step explanation:
The sum of all 4 interior (inside) angles in a quadrilateral = 360.
So 82+118+95+x = 360.
295+x = 360
x = 360-295
x = 65
Check that all the angles add up to 360:
82+118+95+65 = 360
There are 245 mathematics books, 400 literature books and 100 children books in the local library. What
is the ratio of literature books to children books?
a) O 4 literature books: 1 children book
b) 1 literature book: 4 children books
c) O 2 literature books: 3 children books
d) O 3 literature books: 4 children books
The ratio of literature books to children books is: a) 4 literature books: 1 children book.
What is a Ratio?Ratio is simply the numerical quantity that relates two amounts of quantities, showing how much one contains of the other.
The ratio of literature books to children books can be found by dividing the number of literature books by the number of children books:
Ratio of literature books to children books = Number of literature books / Number of children books
Plugging in the given values, we get:
Ratio of literature books to children books = 400 / 100 = 4
So the ratio of literature books to children books is 4:1. Therefore, the answer is option a) 4 literature books: 1 children book.
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Three boxes are stacked one on top of the other. One box is 6 feet 7 inches tall, one is 5 feet 6 inches tall, and one is 5 feet 2 inches tall. How high is the stack?
Write your answer in feet and inches. Use a number less than 12 for inches.
Match the sine and cosine of an angle in radians or degrees to its correct value on the unit circle.
The value of sin (2π/3) is √3/2.
The value of sin (5π/4) is -√2/2.
The value of sin (180) is 0.
The value of cos (π/4) is √2/2.
The value of cos (300) is ¹/₂.
The value of cos (7π/6) is -√3/2.
What is the correct value of the sine and cosine of the angles?
The value of sin (2π/3) is calculated as follows;
sin (2π/3) = sin (2 x 180 / 3) = sin (120)
sin (120) = sin (60) = √3/2
The value of sin (5π/4) is calculated as follows;
sin (5π/4) = sin (5 x 180 / 4) = sin (225)
sin (225) = - sin (45) = -√2/2
The value of sin (180) is calculated as follows;
sin (180) = sin (0) = 0
The value of cos (π/4) is calculated as follows;
cos (π/4) = cos (180/4) = cos (45)
cos (45) = √2/2
The value of cos (300) is calculated as follows;
cos (300) = cos (60)
cos (60) = ¹/₂
The value of cos (7π/6) is calculated as follows;
cos (7π/6) = cos (7 x 180 / 6) = cos (210)
cos (210) = - cos(30) = -√3/2
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{ (-2, 4), (0, 2), (-1, 3), (4, -2)}
The set of ordered pairs above:
DONE
Domain
-3
4
-1
5
Range
3
7
-2
The mapping diagram above:
DONE
y=x²
DONE
x
-3
-1
y
5
2
-1
The table above:
DONE ✔
The set of ordered pairs above: is a function.
The mapping diagram above: is a function.
y = x²: is a function.
The table above: is not a function.
What is a function?In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).
In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).
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escribe la respuesta correcta:
Emilia dice: "Si a mi edad, lo duplico, luego le resto 5, finalmente lo divido
entre 3; obtengo el número 7". ¿Cuántos años tengo?
You give your friend $20 to invest in buyinh an authographed football for $50. You and your friend agree that you will receive 40% when he sells the football. How much profit did you make from your investment?
The profit did you make from your investment is $20
How to calculate how much profit did you make from your investmentTo determine how much profit you made from your investment, we need to find the value of P that makes your friend's profit equal to the initial investment of $20.
In other words, we need to solve the equation:
0.4P - 20 = 20
Adding 20 to both sides, we get:
0.4P = 40
Dividing both sides by 0.4, we get:
P = 100
if the football is sold for $100, your friend's profit will be $100 - $50 = $50, and your profit will be 40% of $50, or $20.
This means that you have made back your initial investment of $20, and have earned an additional profit of $20.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
A. (-4,2)
B. (4,-2)
C. (-2,4)
D. (-14,-20)
Answer:
C) (-2 , 4)
x = -2
y = 4
Step-by-step explanation:
Solving system of equations:We can use substitution method.
3x + 2y = 2 -------------(I)
-2x + y = 8 --------------(II)
Make y as the subject in equation (II)
y = 8 + 2x ----------------(III)
Substitute y = 8 + 2x in equation (I) and we can find the value of 'x',
3x + 2*(8 + 2x) = 2
3x + 2*8 + 2*2x = 2 {Distributive property}
3x + 16 + 4x = 2
3x + 4x + 16 = 2
Combine like terms,
7x + 16 = 2
Subtract 16 from both sides,
7x = 2 - 16
7x = -14
Divide both sides by 7,
x = - 14 ÷ 7
[tex]\boxed{\bf x = -2}[/tex]
Substitute x = -2 in equation (III)
y = 2*(-2) + 8
= -4 + 8
[tex]\boxed{\bf y = 4}[/tex]
raul wants to know if reading a book or watching a movie has a lower cost per minute the book Costs $15 and takes Raul 200 minutes to read the movie costs 14 and takes Raul 2 hours and 39 minutes to watch does the book or the movie have a lower cost per minute
The book has a lower cost per minute than the movie.
To find the cost per minute of the book, we divide the cost by the number of minutes:
cost per minute of book = $15 / 200 minutes = $0.075 per minute
To find the cost per minute of the movie, we need to convert the time to minutes.
2 hours and 39 minutes is equal to:
2 hours x 60 minutes/hour = 120 minutes
39 minutes = 39 minutes
Total minutes = 120 + 39 = 159 minutes
cost per minute of movie = $14 / 159 minutes = $0.088 per minute
Therefore, the book has a lower cost per minute than the movie.
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Which of these data set should be shown on a dot plot?
0.012, 0.078, 0.093, 0.147, 0.187
1.3, 1.9, 2.5, 2.7, 3.5, 4.8, 5.3, 7.9, 9.0
712, 722, 722, 723, 724, 724, 724, 725, 727, 728, 730
16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97
The all four data sets can be represented on a dot plot, as dot plots are both decimal and Integer values.
A dot plot is a graphical representation that displays data points as dots along a number line. It is commonly used to show the distribution of a small set of quantitative data.
The data set should be shown on a dot plot, we need to consider the characteristics of the data.
1. Data Set 1: {0.012, 0.078, 0.093, 0.147, 0.187}
This data set consists of decimal values. A dot plot can effectively represent decimal values, where each dot represents a data point. Therefore, Data Set 1 should be shown on a dot plot.
2. Data Set 2: {1.3, 1.9, 2.5, 2.7, 3.5, 4.8, 5.3, 7.9, 9.0}
Similar to Data Set 1, this data set consists of decimal values. Hence, it can also be effectively represented on a dot plot. Each value would be represented as a dot along the number line.
3. Data Set 3: {712, 722, 722, 723, 724, 724, 724, 725, 727, 728, 730}
This data set consists of integer values. Dot plots are commonly used for discrete data, including integers. Therefore, Data Set 3 can be appropriately represented on a dot plot.
4. Data Set 4: {16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97}
This data set also consists of integer values dot plots can effectively display discrete data. Hence, Data Set 4 can be shown on a dot plot.
all four data sets can be appropriately represented on a dot plot, as dot plots are suitable for displaying both decimal and integer values.
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Deposits are made at the end of the month into two savings accounts.
• Account W started with a balance of $0, and $100 is added each month.
• Account X started with a balance of $1, and 80% of the current balance is added each month.
If no withdrawals are made, when is the first time, excluding the initial deposits, that Account X will contain more money than Account W?
The first time that Account X will have more money than Account W, excluding the initial deposits, is in the fifth month.
To determine when Account X will contain more money than Account W, we need to compare the balances of the two accounts each month until Account X surpasses Account W.
Let's analyze the balances of the two accounts month by month:
Month 1:
Account W: $0 + $100 = $100
Account X: $1 + 80% × $1 = $1 + $0.80 = $1.80
Month 2:
Account W: $100 + $100 = $200
Account X: $1.80 + 80% × $1.80 = $1.80 + $1.44 = $3.24
Month 3:
Account W: $200 + $100 = $300
Account X: $3.24 + 80% × $3.24 = $3.24 + $2.592 = $5.832
Month 4:
Account W: $300 + $100 = $400
Account X: $5.832 + 80% × $5.832 = $5.832 + $4.6656 = $10.4976
Month 5:
Account W: $400 + $100 = $500
Account X: $10.4976 + 80% × $10.4976 = $10.4976 + $8.39808 = $18.89568
Please note that the values provided in this calculation assume no withdrawals and no interest earned on the balances.
As we can see, by the fifth month, Account X will contain more money than Account W. The first time that Account X will have more money than Account W, excluding the initial deposits, is in the fifth month.
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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than once.
By rewriting the 3 given systems, we will see that:
1) Independent and inconsistent.
2) Independent and consistent.
3) Independent and inconsistent..
Let's analyze each system.
Let's look at the first one, we can rewrite it as:
y = 3x - 1
And, 2y - 6x = 4
2y = 6x + 4
y = 3x + 2
Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.
Now let's look at the second system, we can rewrite it as:
2y = - x + 6
And, 4y + 2x = 12
y = - 1/2x + 3
So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.
For the final system we have:
y = 2x + 3
x + y = - 9
So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.
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Find dy/dx when y = ( 2x+1)^3
