The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
A. To find f(x) + g(x), we add the two functions together:
f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)
To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:
f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]
Simplifying the numerator:
f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]
Combining like terms:
f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]
B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:
(x^2 - 9) = 0 --> x = -3, 3
(x^2 + 3x) = 0 --> x = 0, -3
So, the excluded values are x = -3, 0, and 3.
C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.
At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.
At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.
Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
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What is the sign of -xy? A:Positive B:Negative or C:Zero
The sign of -xy cannot be determined without knowing the signs of x and y. It can be positive, negative, or zero.
The signs of x and y influence the sign of -xy. A positive result is produced when multiplying two numbers with the same sign (both positive or both negative), while a negative result is produced when multiplying two numbers with opposite signs (one positive and the other negative). Their product is 0 when either one or both of the values are zero.
Therefore, depending on the signs of x and y, the sign of -xy can be positive, negative, or zero.
-xy is negative if x and y are both positive.
-xy is positive if x and y are both negative.
Regardless of the sign of the other number, if either x or y is zero, then -xy is also zero.
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Rolling two sixes in a row on a number cube is independent or dependent
Rolling two sixes in a row on a number cube (a fair six-sided die) is an independent event. The outcome of one roll does not affect the outcome of the subsequent roll. Each roll of the number cube is an independent trial, and the probability of rolling a six on each trial is always 1/6, regardless of the previous outcome.
I need help with this homework It's 3 AM right now. I'm so tired
I will mark the first person to help me brainliest, they will also get 50 points
The missing parts of the hierarchy of the quadrilaterals is listed below
KiteRectangleSquareRhombusParallelogramQuadrilateralTrapezoidSquareWhat are the quadrilateralsA four-sided polygon is called a quadrilateral. A polygon having four sides is referred to as a four-sided polygon in general.
A geometric figure with two pairs of parallel sides. The quadrilateral shape known as a trapezoid (or trapezium in certain areas) can be restated in different words.
A quadrilateral having four angles measuring 90 degrees each and having opposite sides parallel is called a parallelogram.
Rhombus shape: This particular four-sided shape is distinguished by having every angle measuring 90 degrees.
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See text below
Hierarchy of a Quadrilateral Assignment
Fill in each of the missing parts of the hierarchy of the
quadrilaterals. Include the properties of each of the figures
Jim is participating in a 6-day cross-country biking challenge. He biked for 59, 52, 66, 45, and 68 miles on the first five days. How many
miles does he need to bike on the last day so that his average (mean) is 59 miles per day?
miles
I Don't Know
Submit
X
G
©2023 McGraw H LLC Al Rights Reserved. Terms of the 1 Privacy Center
DOU
Answer:295
Step-by-step explanati: 59 5 .
What is the percentage is the discount of$38 and $95
The percentage discount between $38 and $95 is 150%.
How to compute the percentage discount?We shall follow these steps to estimate the percentage discount between $38 and $95:
First, find the difference between the original price and the discounted price.
Next, divide the result by the original price.
Finally, multiply the result by 100 to present it as a percentage.
Given:
Original price = $95
Discounted price = $38
Difference = $95 - $38 = $57.
Next, Difference / Original price * 100:
($57 / $38) * 100 ≈ 150%
Therefore, the percentage discount between $38 and $95 is 150%.
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Convert the angle pi/3 radians to degrees.
Answer:
60 degrees
Step-by-step explanation:
To convert radians to degrees, multiply by 180/pi
pi/3 * 180/pi = 180/3 = 60 degrees
Step-by-step explanation:
3 radians =
171.887 degrees
AreaData Transfer RateDigital StorageEnergyFrequencyFuel EconomyLengthMassPlane AnglePressureSpeedTemperatureTimeVolume
ArcsecondDegreeGradianMilliradianMinute of arcRadian
ArcsecondDegreeGradianMilliradianMinute of arcRadian
Formula
3rad × 180/π = 171.887°
Tara looks up hotel room prices for a holiday.
A hotel has a 25% off sale on its prices.
A VAT charge of 20% must be added on at the end of the transaction after any discount.
If the regular price of a room is £80 per night, how much will Tara pay for 5 nights?
Tara will pay £360 for 5 nights if she chooses a hotel with a regular room price of £80 per night that has a 25% off sale on its prices, and the VAT charge of 20% must be added at the end of the transaction.
Tara looked up hotel room prices for her holiday. A hotel had a 25% off sale on its prices. A VAT charge of 20% must be added at the end of the transaction, after any discount. If the regular price of a room is £80 per night, then we have to determine how much Tara will pay for 5 nights.
A 25% discount on £80 is: 25/100 * 80 = £20. So the discounted price of a hotel room is: £80 - £20 = £60.Next, we add VAT of 20% to the discounted price: 20/100 * £60 = £12.
Hence, the final price for one night is: £60 + £12 = £72.Since Tara needs to stay in the hotel for 5 nights, she will pay: £72 * 5 = £360.
Therefore, Tara will pay £360 for 5 nights if she chooses a hotel with a regular room price of £80 per night that has a 25% off sale on its prices, and the VAT charge of 20% must be added at the end of the transaction.
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ery Test
What is the solution of this equation?
1
-3+
4
z = 1
Enter the correct answer.
The solution of this equation is z = 3.
We are given that;
1-3+4z = 1
Now,
To solve for z, we need to isolate it on one side of the equation. We can do this by following these steps:
Subtract −31
from both sides to eliminate it from the left side.
Multiply both sides by z to eliminate the fraction on the left side.
Divide both sides by 4 to isolate z on the left side.
Let’s see how this works:
−31+z4=1
−31+z4=1
z4=1+31
z4=34
4=4/3 z
z=3*4/4
z=4/4×3
z=3
Therefore, by the equation answer will be z = 3.
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The expression that is equivalent to 6/q is
The expression that is equivalent to 6/q is 6q/q²
How to determine what the expression is equivalent toFrom the question, we have the following parameters that can be used in our computation:
6/q = ?/q²
Multiply both sides of the equation by q²
So, we have
q² * 6/q = ?/q² * q²
Evaluate the products on both sides of the equation
? = 6q
Hence, the expression that is equivalent to 6/q is 6q/q²
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dos aviones de parte de una ciudad a las 8 AM el primer avión quiso regresar a la ciudad 5 horas y el segundo avión regresa casa 3 horas en cuanto tiempo volverán a dentrar a la ciudad
Both planes will reach the city at the same time again at 11 PM.
How to deal with periodic events?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods for this problem are given as follows:
5 hours.3 hours.As 5 and 3 are prime numbers, the least common factor is given as follows:
5 x 3 = 15.
15 hours after 8 AM is of 11 PM.
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Please and this question ASAP. Multiply 31.5 percent times 600
Answer:
189
Step-by-step explanation:
To multiply 31.5 percent by 600, you need to convert the percentage to a decimal by dividing it by 100 and then multiply it by 600.
31.5 percent = 31.5/100 = 0.315
Multiplying 0.315 by 600 gives us:
0.315 * 600 = 189
Therefore, 31.5 percent of 600 is equal to 189.
Natalya designed a patio for her backyard. The two brick
sections will be the same size and concrete fills the rest of
the patio. Her design and the scale she will use to build
the patio are both shown below.
The concrete portion of the patio will cost $3 per square
foot to construct and the brick portion of the patio will
cost $6 per square foot to construct.
How much will Natalya spend constructing the patio with
concrete and brick?
Scale
1 cm = 4 ft.
A
B
6 cm
$432
$648
Brick
Concrete
6 cm
3 cm
Brick
3 cm
OPTIONS
A
$432
B
$648
C
$2,160
D
$3,024
The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.
We are given that;
The concrete portion of the patio cost=$3 per square
To construct and the brick portion of the patio cost= $6 per square
Now,
The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:
6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft
Therefore, the area of the concrete portion is:
24 ft x 12 ft = 288 ft^2
The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:
3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft
Therefore, the area of one brick rectangle is:
12 ft x 24 ft = 288 ft^2
Since there are two brick rectangles, the total area of the brick portion is:
2 x 288 ft^2 = 576 ft^2
Now we can multiply the areas by their costs per square foot to get the costs of each portion:
Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456
The total cost of constructing the patio is the sum of the costs of each portion:
Total cost = $864 + $3456 = $4320
Therefore, by area the answer will be $4320.
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Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?
Deigo wrote 6^4*8^3=48^7. explain what his mistake was.
The index forms are of different bases and thus cannot be multiplied and their exponents added.
How to determine the valueTo determine Deigo's mistake, we need to know index forms and their rules.
Index forms are defined as mathematical forms that are used in representing numbers or variables that are too large or too small in more convenient forms.
They are also called scientific notation or standard forms.
The rules of index forms are;
Subtract the exponents when like bases are dividedAdd the exponents when like bases are multipliedFrom the information given, we have;
6⁴ × 8³ = 48⁴⁷
They are not of like bases and thus cannot be multiplied
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which two transformations are applied to pentagon ABCDE to create A''B''C''D''E''
The two transformations applied to pentagon ABCDE to create A''B''C''D''E'' are rotation and reflection.
To determine the two transformations applied to pentagon ABCDE to create A''B''C''D''E'', we need more specific information about the transformations or the corresponding points.
Transformations can include translations, rotations, reflections, dilations, or combinations of these.
Without knowing the specific transformations applied or having additional information, it is challenging to provide an accurate answer.
However, I can briefly explain some common transformations that could potentially be applied to a pentagon:
Translation: A translation involves moving the entire figure in a specific direction without changing its shape or orientation.
This transformation can be described by shifting the points of the pentagon horizontally or vertically.
Rotation: A rotation involves rotating the pentagon about a fixed point. The point of rotation could be inside or outside the pentagon, and the angle of rotation would determine the final position of the points.
Reflection: A reflection involves flipping the pentagon across a line, called the line of reflection.
Each point of the pentagon would be reflected across the line, resulting in a mirrored image.
Dilation: A dilation involves scaling the size of the pentagon by a certain factor.
This transformation can result in an enlarged or reduced version of the original pentagon.
Without specific details or information about the corresponding points in A''B''C''D''E'', it is not possible to determine the exact transformations applied.
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a tip of $10 is typically suitable for which kind of service?
a mover delivering furniture
a valet who parks your car
a waiter at a fast food restaurant
Students at Sunnyvale Middle School volunteered to work a 2-hour shift at a
car wash fundraiser. The table shows the number of people who worked each
shift and how many cars they washed.
Is the relationship between the number of
cars washed and the number of workers
proportional? Complete the statement.
The number of cars washed per person
?
of workers, so the relationship is
the same for each number
?
People Working
4
6
8
10
Cars Washed
8
12
20
25
The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The ratios between the output and the inputs are given as follows:
8/4 = 2.12/6 = 2.20/8 = 2.5.25/10 = 2.5.Different ratios, hence the relationship is not proportional.
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Simplify the rational expression
7x/14x^6
The simplified form of the rational expression [tex](7x)/(14x^6)[/tex] is [tex]1/(2x^6).[/tex]
To simplify the rational expression [tex](7x)/(14x^6)[/tex], we can begin by simplifying the numerator and denominator separately.
In the numerator, 7x, we can see that both 7 and x have a common factor of 7. So, we can rewrite the numerator as 7 × x = 7x.
In the denominator, [tex]14x^6[/tex], we can see that both 14 and x^6 have a common factor of [tex]2x^6[/tex].
So, we can rewrite the denominator as
[tex]14 \times x^6 = 2 \times 7 \times x^6 = 2 \times 7x^6.[/tex]
Now, we can simplify the rational expression by canceling out the common factors in the numerator and denominator:
[tex](7x)/(14x^6) = (7x)/(2 \times 7x^6) \\= (7x)/(2 \times 7 \times x^6) \\= (cross(7x))/(2 \times cross(7) \times x^6) \\= 1/(2x^6)[/tex]
Therefore, the simplified form of the rational expression[tex](7x)/(14x^6)[/tex] is [tex]1/(2x^6).[/tex]
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-) Aspirin has a half-life of 6 hours in the blood stream. If a person takes 625mg, how long will it take for there to be 150mg left in the bloodstream?
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
We have,
To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.
The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.
Let's calculate the number of half-lives required to reach 150mg:
Initial amount of aspirin = 625mg
Final amount of aspirin = 150mg
625mg / 150mg = 4.17
This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.
Since each half-life is 6 hours, we can calculate the total time it will take:
Total time = Number of half-lives * Half-life duration
Total time = 4.17 x 6 hours
Total time ≈ 25 hours and 1 minute
Therefore,
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
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How do I find the possible degree(s) of a function from the graph alone?
Answer:
To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:
Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.
Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.
Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.
Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.
7+(2x4)-8÷(12-6)x(6÷2)
Answer:
11
Step-by-step explanation:
Remember PEMDAS
7+(2x4)-8÷(12-6)x(6÷2)
7 + 8 - 8 : 6 × 3 =
7 + 8 - 8/6 × 3 =
7 + 8 - 4 =
11
In English classmates teacher gifts for horses each worth five points after three quizzes. She has the score for three and four. What does she need to get on the last quiz to have a mean score for
Answer:
5
She must therefore earn 5 points on the last test to achieve a mean score of 4.
Step-by-step explanation:
The sum of the data divided by the total number of data represents the mean, which is the average of a set of data.
Stephen is combining all juice shown to make fruit punch. Does the expression (64+28+76)/6 make sense’s
Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.
To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.
The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:
Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).
Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.
Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.
If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.
In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.
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Which data set could be represented by
the box plot shown below?
H
0 2 4 6 8
Choose 1 answer:
A
Creating box plots
B
C
D
10 12 14 16 18 20
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
The given box plot represented by the data sets in option A and B.
From the given box plot, we have
Minimum value = 3
Maximum value = 18
First quartile (Q1) = 7
Third quartile (Q3) = 13
Median = 10
Option A:
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
Median = 12
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option B:
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Option C:
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option D:
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Therefore, the correct options are B and D.
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you are dealt one card from a 52-card deck. find the probability that you are not dealt a two
Answer:
Step-by-step explanation:
48 out 52 cards are not a 2:
[tex]P(not 2)=\frac{48}{52} =\frac{12}{13}[/tex]
Line l has equation y= 5. find the distance between l and the point C (7, 0). Round your answer to the nearest tenth
The distance between the line y = 5 and point C (7, 0) is 5 units.
We have,
To find the distance between a line and a point, we can use the formula for the distance between a point (x1, y1) and a line ax + by + c = 0, which is given by:
Distance = |ax1 + by1 + c| / √(a² + b²)
In this case,
The equation of the line is y = 5, which can be rewritten as 0x + 1y - 5 = 0.
Comparing this to the general form ax + by + c = 0, we have a = 0, b = 1, and c = -5.
The coordinates of point C are (7, 0), so x1 = 7 and y1 = 0.
Let's calculate the distance using the formula:
Distance = |0(7) + 1(0) - 5| / sqrt(0² + 1²)
Distance = |-5| / √(1)
Distance = 5 / 1
Distance = 5
Therefore,
The distance between the line y = 5 and point C (7, 0) is 5 units.
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square root 3 radicand x squared 2 multiply square root 4 radicand x squared 3
The simplification of [tex]\sqrt{3x^2} * \sqrt{4x^2} is 2x^2\sqrt{3.[/tex]
The given expression is [tex]\sqrt{3x^2} * \sqrt{4x^2} .[/tex].
To simplify this expression, we can start by simplifying each square root individually and then multiply the simplified expressions.
[tex]\sqrt{3x^2[/tex] can be written as[tex]\sqrt{3} * \sqrt{x^2[/tex]. Since [tex]x^2[/tex] is a perfect square, its square root is x. Therefore, [tex]\sqrt{3x^2[/tex] simplifies to [tex]x\sqrt{3.[/tex]
Similarly,[tex]\sqrt{4x^2[/tex] can be written as[tex]\sqrt{4} * \sqrt{x^2.[/tex]The square root of 4 is 2, and the square root of[tex]x^2[/tex]is x. Thus, [tex]\sqrt{4x^2[/tex] simplifies to 2x.
Now, we can multiply the simplified expressions:
[tex]x\sqrt{3} * 2x.[/tex]
To multiply these terms, we multiply the coefficients (numbers in front) and the variables separately.
The coefficient of [tex]x\sqrt{3[/tex]is x, and the coefficient of 2x is 2.
Multiplying the coefficients gives us x * 2 = 2x.
The variables in x√3[tex]x\sqrt{3[/tex] are x and √3, and the variables in 2x are x and 1.
Multiplying the variables gives us x * x = x^2, and √3 * 1 = √3.
Therefore, the final simplified expression is [tex]2x^2\sqrt{3.[/tex].
In summary,[tex]\sqrt{3x^2 } * \sqrt{4x^2[/tex] simplifies to [tex]2x^2\sqrt{3.[/tex]
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Graph the line. y=3x-8
By connecting these points with a straight line, we can graph the line y = 3x - 8.
The line should have a positive slope, rising from left to right.
To graph the line y = 3x - 8, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope of the line, and b represents the y-intercept.
Comparing the given equation with the slope-intercept form, we can see that the slope, m, is 3, and the y-intercept, b, is -8.
To plot the graph, we'll start by plotting the y-intercept, which is the point (0, -8)T.
his point represents where the line intersects the y-axis.
Next, we can use the slope to find additional points on the line. The slope of 3 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.
Starting from the y-intercept (0, -8), we can move 1 unit to the right and 3 units up to reach the next point (1, -5).
We can continue this pattern to plot more points.
Using this information, we can plot multiple points and then connect them to form the line:
Point 1: (0, -8)
Point 2: (1, -5)
Point 3: (2, -2)
Point 4: (-1, -11)
Point 5: (-2, -14)
By connecting these points with a straight line, we can graph the line y = 3x - 8.
The line should have a positive slope, rising from left to right.
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What is the quantity of goods and services that sellers are willing and able to sell known as?
The quantity of goods and services that sellers are willing and able to sell is known as the quantity supplied.
What is quantity supplied of goods by a seller?Quantity supplied is defined as the amount of goods and services that a supplier is able to produce and sell at a given market price.
The quantity supplied differs from the actual amount of supply as price changes influence how much supply producers actually put on the market.
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Need help with those 3 questions
The general form of the solutions of the recurrence relation is
[tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]
We are given that;
Series=1, 1, 1, 1, -2, -2, -2, 3, 3, -4
Now,
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
If the characteristic equation has repeated roots, then the general solution is modified by multiplying each term by a polynomial in n whose degree is equal to the multiplicity of the root minus one. For example, if r is a root of multiplicity m, then the corresponding term in the general solution is
[tex]a_n = (A + B n + C n^2 + … + Z n^(m-1)) r^n,[/tex]
where A, B, C, …, Z are arbitrary constants.
In this question, the characteristic equation has roots 1, 1, 1, 1, -2, -2, -2, 3, 3, -4. The root 1 has multiplicity 4, the root -2 has multiplicity 3, and the roots 3 and -4 have multiplicity 2 each.
[tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]
where A, B, C, D, E, F, G, H, I, J and K are arbitrary constants.
Therefore, by the equation answer will be [tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]
To learn more about simultaneous equations :
brainly.com/question/16763389
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