The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N. To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N).
Reaction at Roller A:
2 m * 900 N = 1800 N
Reaction at Pin B:
3 m * 450 N + 600 N = 2450 N
To calculate the reaction at Roller A, you need to multiply the length of the roller (2 m) by the load (900 N). This gives you 1800 N.
To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N). This gives you 2450 N.
The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N.
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The scatter plot shows the number of hats and scarves each knitter sold at a knitting show. How many hats did the knitter who sold 9 scarves sell?answer choices2346
The scatter plot shows the number of hats and scarves each knitter sold at a knitting show. 02 hats did the knitter who sold 9 scarves sell.
Scatterplot:
A scatterplot is a graph or mathematical graph that displays the values of usually two variables of a data set using Cartesian coordinates. is a kind of Additional variables can be displayed if the points are coded (color/shape/size). The data is displayed as a set of points, where each point has the value of one variable that determines its position on the horizontal axis and the value of another variable that determines its position on the vertical axis.
According to the Question:
I need to find out how many hats were sold when the knitter sold his 09 scarves.
To find this out, in the scatterplot he needs to find the x-values corresponding to the y-values of the 9 scarves.
Corresponding to 9 on the y-axis, there is a point with a corresponding value of 02.
Therefore, when the weaver sold 09 scarves, he sold two(02) hats.
Option B) 02 is correct.
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In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown. The radius of the circle with center R is decreased so that the circle with center R remains tangent to BC, the circle with center R remains tangent to the other three circles, and the circle with center P becomes tangent to the other three circles. The radii and tangencies of the other three circles stay the same. This changes the size and shape of triangle ABC. r is the new radius of the circle with center R. r is of the form . Find .
On solving the provided question we can say that so the value of triangle - y + Z = 1+ r = > 1 -r +
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
in triangle
by construction = y0 = r - 1
Pythagoras =
Pythagoras =
so the value of triangle -
y + Z = 1+ r
1 -r +
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The correct question is
In the diagram, four circles of radius 1 with centers P, Q, R and S are tangent to one another and sides of △ABC△, as shown. Find the perimeter of △ABC△
.(A) 12+42√12+42
(B) 12+43√12+43
(C) 12+62√12+62
(D) 12+63√12+63
(E) 24
Find the circumcenter of the triangle ABC.
A(8,-8), B(-4, 4), C(8.4).
The circumcenter is
(Type an ordered pair.)
Answer:
Circumcenter (x) = 2
Circumcenter (y) = -2
Answer:
(2, -2)
Step-by-step explanation:
Midpoint of BC: ([-4 + 8]/2, (4 + 4)/2) = (2, 4)
Perpendicular bisector of BC has equation: x = 2
Midpoint of AC: ([8 + 8]/2, (-8 + 4)/2) = (8, -2)
Perpendicular bisector of AC has equation y = -2
Point of intersection of the two perpendicular bisectors:
(2, -2)
Answer: (2, -2)
Emmy took a math quiz lat week. There were 75 problem on the quiz and Emmy anwered 60% of them correctly. How many problem did Emmy get correct?
Emmy answered average of 60 out of 75 math problems correctly on the quiz she took last week, meaning she answered a total of 60 problems correctly.
60/75 = 0.8
0.8 x 75 = 60
Emmy took a math quiz last week and answered 60% of the 75 problems correctly. To calculate how many problems Emmy got correct, we need to divide 60 by 75, which gives us 0.8. Then, we multiply 0.8 by 75, which gives us 60. This means that Emmy correctly answered 60 out of 75 math problems on the quiz. This is equivalent to 60%, which is the percentage of problems she got correct. It is important to note that if Emmy had answered any more or any less problems correctly, the percentage of correct answers would have been different. Therefore, it is important to understand the relationship between percentages and total number of problems answered correctly in order to accurately calculate the number of correct answers.
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Which of the following is a polynomial with roots 4, 2i, and −2i?
a. f(x)= x^3-4x^2+8-4
b. f(x)=^3-8^2+16-4
c. f(x)= x^3-4x^2+4x-16
d. f(x)= x^3-4x^2+8x-16
The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.
c. f(x)= x^3-4x^2+4x-16
The polynomial with the given roots is a cubic polynomial. To get the coefficients of the polynomial, we can use the factor theorem. The factor theorem states that if a polynomial has a factor (x - a), then a is a root of the polynomial.
Therefore, the polynomial with roots 4, 2i, and -2i is f(x) = (x - 4)(x - 2i)(x +2i)
Expanding this polynomial, we get f(x) = x^3-4x^2+4x-16
The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.
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GIVING BRAINLIEST!!!
There are five horses in a race at Churchill Downs. For convenience’s sake, we’ll refer to them by the numbers 1-5. Three of the horses will finish in the top three – at the moment, we do not care what the order of finish is. List out all the possible arrangements of horses that could finish in the top 3.
Answer:123,234,345,132,432,543 and i think thats all
Step-by-step explanation:Hope it helps and have a good week:)
Calculate the double integral. ∫∫R 2x/1 + xy dA, R = [0, 2] × [0, 1]
The double integral. ∫∫R 2x/1 + xy dA, R = [0, 2] × [0, 1] is: 2*(1/2ln(3) - 1/2ln(1))
To calculate the double integral ∫∫R 2x/1 + xy dA, we need to integrate with respect to x and y over the region R = [0, 2] × [0, 1].
We can solve this by using the order of integration.
First we need to fix the limits of integration with respect to y and then integrate with respect to x.
∫∫R 2x/1 + xy dA = ∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy
∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy = ∫(0 to 1) ( 2*ln(1+xy)|x=0 to 2) dy
∫(0 to 1) ( 2ln(1+2y) - 2ln(1+0) ) dy
= 2*∫(0 to 1) ln(1+2y) dy
= 2*[y*ln(1+2y) - ∫(0 to 1) ln(1+2y) dy] |y = 0 to 1
= 2*[yln(1+2y) - (1/2 ln(3) - 1/2* ln(1))] |y = 0 to 1
= 2*(1ln(3) - 0ln(1) - 1/2* ln(3) + 1/2* ln(1))
= 2*(1/2ln(3) - 1/2ln(1))
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The length of a rectangle is 7 more than twice the width. Which equation could represent the area of the rectangle in terms of the width
Answer:
Step-by-step explanation:
A,B AND C form a triangle where BAC=90 AB=15MM and BC=18.1
find the length of AC giving your answer rounded to 1 decimal place
The measurement of side AC in the given right triangle is 10.12 units.
What is right triangle?A triangle having at least one angle measuring 90° is called a right triangle.
Given that, a triangle ABC, right-angled at A,
AB = 15 and BC = 18.1, we need to find AC,
Please refer to the figure attached,
Using Pythagoras theorem,
BC² = AB² + AC²
AC² = BC² - AB²
AC² = (18.1)² - 15²
AC² = 327.61 - 225
AC² = 102.61
AC = 10.12
Hence, the value of AC = 10.12
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If two sides of a triangle are 6cm and 10cm then the lenght of the third side can be
Answer:
6cm
Step-by-step explanation:
Given, the length of two sides of a triangle are 6 cm and 10 cm.
We have to find the length of the third side.
We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
Sum of two sides = 6 + 10
= 16 cm
We know that the third side must be greater than the difference between two sides and less than the sum of two sides.
Difference of two sides = 10 - 6
= 4 cm
So, the third side must be greater than 4 cm and less than 16 cm.
Therefore, the third side is 6 cm.
(02.04 HC)
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
f(x)
f(x) = -2(x-4)2 +2
X
-4-3-2
h(x)
For [tex]f(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. Matching with vertex form, we see the vertex of the graph of [tex]f(x)[/tex] has coordinates [tex](4,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=4[/tex].
Similarly, for [tex]h(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. The vertex of the graph of a quadratic function is either the minimum or maximum point (it depends on the leading coefficient of the function). Here, there is a maximum point, which has coordinates [tex](-2,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=-2[/tex].
Timothy purchased a computer for $1,000. the value of the computer depreciates by 20% every year.
this situation represents
the rate of growth or decay, r, is equal to
year.
so the value of the computer each year is
% of the value in the previous
it will take
years for the value of the computer to reach $512.
Answer: It takes 3 years
Step-by-step explanation:
20 percent of 1000 is 200 so 1000-200=800. Year 1
20 percent of 800 is 160 so 800-160=640. Year 2
20 percent of 640 is 128 so 640-128=512. Year 3
So in total in takes 3 years
Answer:
See photo
Step-by-step explanation:
Edmentum/Plato
The plot line shows the number of miles the individual members in a group of runners run each day How many runners run at most 2 miles per day?13963
13 number of runners run at most 2 miles per day .
calculation is explained below as
at 2 miles = 6 runners run
at 3 miles = 4 runners run
at 4 miles = 2 runners run
at 5 miles = 1runners run
on adding to calculate how many number of members run at most 2 miles per day is = 6 + 4 + 2 + 1 = 13 .
hence 13 number of members run at most 2 miles per day .
A number line plot is a simple way of visual representation of data patterns at the coordinate axis. on comparing the height of the specific columns, the least frequently of occurring number can be calculated. The number line of plot becomes a bar graph when the box is drawn around the Xs or dots in each and every column. A horizontal line, also called as x-axis, with equal intervals which are labelled with values which makes a number line plot. Xs or dots can be used to describe or evaluate the frequency in which a number, or a set a defined numbers, occurs on number line . Stacks of such producing Xs or dots that are used to represent data on the axis is known as plot number. .
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in 2008, the price of a gallon of unleaded gasoline was $4.02. in 1990, it was only $1.37 per gallon. what is the increase expressed as a percent change? round to the nearest percent.
a. 66%
b. 393%
c. 193%
d. 134%
please i need help'
...?
Answer: Answer is 193% or c
Step-by-step explanation: To solve this, we can use algebra. Suppose x represents the percent of increase. 1.37 * x = 4.02. Divide both sides by 1.37 to get x = 2.93. This represents 293% However, since it is asking for the increasing, we need to subtract 100% since we only want to increase, not the total value.
Answer:
b. 393%
Step-by-step explanation:
1.37 + 1.37x% = 4.02
your statistics class has 15 juniors out of 30 total students. you put the names of all the students in your statistics class on slips of paper into a hat. you mix up the names, and draw 4 of them without looking. what is the probability that you pick exactly 2 juniors?
The probability that you pick exactly 2 juniors is 15/30 x 14/29 x 13/28 x 12/27, or 0.081.
1. Probability of picking the first junior: 15/30
2. Probability of picking the second junior: 14/29 (14 remaining juniors out of 29 total students after the first pick)
3. Probability of picking the third non-junior: 13/28 (13 remaining non-juniors out of 28 total students after the second pick)
4. Probability of picking the fourth non-junior: 12/27 (12 remaining non-juniors out of 27 total students after the third pick)
Therefore, the probability of picking exactly 2 juniors is
15/30 x 14/29 x 13/28 x 12/27
= 0.081.
The probability of picking exactly 2 juniors out of 4 slips of paper from a hat with the names of all 30 students in your statistics class is 0.081. This is calculated by taking the probability of picking the first junior (15/30) and multiplying it by the probability of picking the second junior (14/29, since there are 14 remaining juniors out of 29 total students after the first pick), the probability of picking the third non-junior (13/28, since there are 13 remaining non-juniors out of 28 total students after the second pick), and the probability of picking the fourth non-junior (12/27, since there are 12 remaining non-juniors out of 27 total students after the third pick).
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Researchers are investigating the effectiveness of using a fungus to control the spread of an insect that destroys trees. the researchers will create four different concentrations of fungus mixtures: 0 milliliters
per liter (ml/l). 1.25 ml/l, 2.5 ml/l, and 3.75 ml/l. an equal number of the insects will be placed into 20 individual containers. the group of insects in each container will be sprayed with one of the four
mixtures, and the researchers will record the number of insects that are still alive in each container one week after spraying.
(a) identify the treatments, experimental units, and response variable of the experiment.
treatments
experimental units
response variable:
The treatments of this experiment are the four different concentrations of the fungus mixtures that are given. The four concentrations are 0 ml/l, 1.25 ml/l, 2.5 ml/l, and 3.75 ml/l.
The experimental units are the 20 individual containers, each containing an equal number of the insects.
The response variable of the experiment is the number of insects that are still alive in each container one week after spraying.
The researchers will measure the number of insects that are still alive in each container after one week and this will be used to determine the effectiveness of the fungus mixture.
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How does the Algebraic Expressions Calculator work?
The calculator helps to slove an expression. By putting all elements one by one of the expression to get result.
What is a calculator?
A calculator is a device that performs numerical arithmetic operations. Basic calculators can only perform addition, subtraction, multiplication, and division calculations.
To perform basic operations, use the basic operation symbols. Addition (+), subtraction (-), multiplication (), and division () are examples of these operations.
Don't be concerned about the order of operations. A scientific calculator will perform calculations in the correct order.
Using the parentheses keys, you can change the order of operations. The calculator's order of operations will be overridden.
Correct your errors. If you accidentally press the wrong key, press the DEL key. This will remove the last button you pressed, but it will not remove any calculations you've made.
Make a clean sweep of your work. To clear the line, press the CLEAR button. You can probably scroll up to see previous calculations. You can delete these by pressing delete after each line.
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how many different ways four kings can be next to each other and four queens can be next to each other
There are four ways for four kings can be next to each other and four queens can be next to each other.
The first way is by positioning the kings and queens diagonally opposite each other.
The second way is by arranging them in a cross shape, with two kings on the top, two queens on the bottom, two queens on the left, and two kings on the right.
This means that in total, there are four possible ways that four kings and four queens can be placed next to each other.
The kings and queens on a card set are four in number. Hence, the probability of their arrangement next to each other would be four.
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What is the greatest common factor of the terms in the polynomial 3x3 – 3x2 – 18x?
3
3x
3x2
3x3
Answer:
3
Step-by-step explanation:
every term is divisible by 3, therefore it is the greatest common factor
-2x+5y=14 3x-3y=-3 by elimination
Answer:
x = -5
y = -4
Step-by-step explanation:
-2x + 5y = 14
3x - 3y = -3 --divide by 3 --> x - y = -1 --multiply by 2 --> 2x - 2y = -2
-2x + 5y = 14
2x - 2y = -2
Add the two equations
-3y = 12
y = -4
PLUG INTO x - y = -1
x + 4 = -1
x = -5
Hope this helps :)
Have a great day!
Answer:x=3, y=4
sorry if im wrong
Step-by-step explanation:
The table of ordered pairs (x, y )gives an exponential function.
Write an equation for the function.
The exponential equation represented by the table is given as y = 12(2ˣ)
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The standard form of an exponential equation is:
y = abˣ
Where b is the rate of change and a is the y intercept.
From the table, at point (0, 12):
y = abˣ
Substituting the values gives:
12 = ab⁰
a = 12
At point (1, 24):
y = abˣ
Substituting the values gives:
24 = ab¹
24 = 12b
b = 2
The exponential equation is given as y = 12(2ˣ)
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An arborist sights the top of a tree using a clinometer and reads the angle of elevation to be 29º. Her clinometer is 28 meters from the base of the tree and is on a tripod making it 1.5 meters above ground level. How tall is the tree? Show all your work.
An arborist sights the top of a tree using a clinometer and reads the angle of elevation to be 29º, The height of the tree is 17.03 meters
What is the height?Generally, To find the height of the tree, we can use the tangent function and some basic trigonometry. The tangent of an angle is the ratio of the opposite side (the height of the tree) to the adjacent side (the distance from the base of the tree to the clinometer).
tan(29) = opposite / adjacent
We know that the distance from the clinometer to the base of the tree is 28 meters, and that the clinometer is 1.5 meters above ground level.
So we can use the Pythagorean theorem to find the adjacent side:
adjacent = √(28^2 + 1.5^2)
= 28.03 meters
Now we can use the tangent function to find the opposite side:
opposite = tan(29) * adjacent
Using a calculator we can get the opposite = 15.53 meters
The height of the tree is opposite + 1.5 (the clinometer height) '
= 15.53 + 1.5
= 17.03 meters
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how many places can you put the lens to form a well-focused image of the candle flame on the wall?
The number of places you put the lens to form a well-focused image of the candle flame on the wall is either we have to move the screen towards the lens or the lens towards the screen.
Here we have given that the lens to form a well-focused image of the candle flame on the wall.
As we all know that if the candle is further from the wall than the focal length of the lens, then there are two places which will result in an image. Here we have know that one of them is just beyond the focal length from the wall.
Here we have given the other is that same distance from the candle.
Then the position near the wall will yield a small image.
Here the position near the candle will produce a large image.
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Kin estimated the distance from his house to his grandmother’s house to be 4.5 miles. The actual distance is 4.32 miles. What is Kin’s percent error? Show your work and/or explain your reasoning.
A-18%
B-0.04%
C-4%
D-0.18%
Answer:
Step-by-step explanation:
To calculate the percent error, we use the formula:
(|(Actual distance - Estimated distance)| / Actual distance) * 100
So for this case:
(|(4.32 - 4.5)| / 4.32) * 100 = (0.18 / 4.32) * 100 = 0.041666666666666664 * 100 = 4.16666667%
Therefore, Kin's percent error is 4.16666667%.
It is important to note that the percent error can be positive or negative depending on whether the estimated value is higher or lower than the actual value.
So the answer is D-0.18%
Lucia is comparing monthly cell phone plans. Each plan will include a total of 6. 5% fees and taxes on the subtotal.
Features Plan A Plan B Plan C
Unlimited talk, text, regular data $52. 00 $50. 00 $48. 00
Unlimited high speed data Included in base price $10. 00 $12. 00
Hotspot $8. 00 Included in base price Not offered
Using the information provided, determine which plan is the least expensive
Answer:
Step-by-step explanation:
Plan C is the least expensive plan, as it has the lowest subtotal of $48.00 plus 6.5% fees and taxes.
The word "and" in probability implies that we use the ____ rule.
A. Subtraction
B. Division
C. Addition
D. Multiplication
The word "and" in probability implies that we use the Multiplication rule.
The correct option is Option D.
What is the Multiplication Rule of Probability?The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.
The relationship between two events is explained by the probability multiplication rule.
Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.
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the side-by-side dotplot below displays the arm spans, in centimeters, for two classes. a stemplot titled arm span (centimeters). for class a, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. for class b, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 182, 182, 189, 192, 202. which statement is not true? the mean arm span appears to be similar for the two classes. the arm spans for class a have less variability than the arm spans for class b. the arm spans for class b have more variability than the arm spans for class a. the arm spans for class a are roughly symmetric, while those for class b are skewed left.
The statement that correctly describes the proportion of arm spans that are longer than 170 cm in the stem plot is C.
The proportion of arm spans that are longer than 170 cm is about the same for Class A and Class B.
It should be noted that from the information given, the variability of the arm span shows that they have about the same variability.
Therefore, the statement that correctly describes the proportion of arm spans that are longer than 170 cm in the stem plot is C. The proportion of arm spans that are longer than 170 cm is about the same for Class A and Class B.
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-2(3n+6) = 3(-n+12)
Solve for n
Answer:
-16
Step-by-step explanation:
suzanne receives a t-score of -3.6 in her bone mineral density (bmd) test results. what does this score indicate to her doctor?
A T-score of -3.6 indicates that the individual has a severe case of osteoporosis
A T-score is a standard score used to compare an individual's bone mineral density (BMD) to that of a healthy young adult population. A T-score of -3.6 on a BMD test indicates that the individual's BMD is significantly lower than that of a healthy young adult. Specifically, it means that the individual's BMD is 3.6 standard deviations below the average BMD of a healthy young adult.
A T-score of -2.5 or lower is considered to indicate osteoporosis, which is a condition characterized by low bone density and an increased risk of fractures. Therefore, a T-score of -3.6 indicates that the individual has a severe case of osteoporosis, and the doctor will likely recommend treatment such as medication and lifestyle changes to help increase bone density and reduce the risk of fractures.
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100 POINTS: can someone convert these to vertex form? shown work is appreciated
The vertex form of the parabolae equations are, respectively:
y + 36 = (x - 3)² y - 3 = (x - 2)² y + 25 = (x + 5)² y - 1 = (x + 7)² y + 9 / 4 = (x - 3 / 2)² y - 7 / 4 = (x - 5 / 2)² y + 8 = 2 · (x + 2)² y - 7 = 3 · (x + 1)² y + 86 = 5 · (x + 4)² y + 49 = (x - 2)² y + 49 = (x + 3)² y + 16 = (x + 6)² y + 4 = (x + 4)² y + 9 / 4 = (x + 5 / 2)² y + 81 / 4 = (x - 1 / 2)² y + 2 = 2 · (x + 3)² y + 9 = (x + 3)² y + 108 = 3 · (x - 2)²How to find the vertex form of the parabola equation
Parabolae are described by quadratic equations, whose standard and factor form are shown below:
Standard form
y = a · x² + b · x + c
Factor form
y = a · (x - r₁) · (x - r₂)
Where:
a - Lead coefficientb, c - Other coefficientsr₁, r₂ - Roots of the quadratic equationThis equation can be modified into vertex form:
y - k = C · (x - h)²
Where:
C - Vertex constanth, k - Coordinates of the vertexThe complete procedure to find vertex form is described below:
Expand the polynomial to standard form.Complete the square.Factor the perfect square trinomial.Use algebra properties until vertex form is found.Now we proceed to find the vertex form of each expression:
Case 1
y = x² - 6 · x - 27
y = (x² - 6 · x + 9) - 36
y + 36 = (x - 3)²
Case 2
y = x² - 2 · x + 7
y = (x² - 2 · x + 4) + 3
y = (x - 2)² + 3
y - 3 = (x - 2)²
Case 3
y = x² + 10 · x
y + 25 = x² + 10 · x + 25
y + 25 = (x + 5)²
Case 4
y = x² + 14 · x + 50
y = (x² + 14 · x + 49) + 1
y = (x + 7)² + 1
y - 1 = (x + 7)²
Case 5
y = x² - 3 · x
y + 9 / 4 = x² - 3 · x + 9 / 4
y + 9 / 4 = (x - 3 / 2)²
Case 6
y = x² - 5 · x + 8
y = (x² - 5 · x + 25 / 4) + 7 / 4
y - 7 / 4 = (x - 5 / 2)²
Case 7
y = 2 · x² + 8 · x
y = 2 · (x² + 4 · x)
y + 2 · 4 = 2 · (x² + 4 · x + 4)
y + 8 = 2 · (x + 2)²
Case 8
y = 3 · x² + 6 · x + 10
y = 3 · (x² + 2 · x + 10 / 3)
y = 3 · (x² + 2 · x + 1) + 7
y - 7 = 3 · (x + 1)²
Case 9
y = 5 · x² + 40 · x - 6
y = 5 · (x² + 8 · x - 6 / 5)
y + 5 · 16 = 5 · (x² + 8 · x + 16) - 6
y + 86 = 5 · (x + 4)²
Case 10
y = (x + 5) · (x - 9)
y = x² - 4 · x - 45
y + 4 = (x² - 4 · x + 4) - 45
y + 49 = (x - 2)²
Case 11
y = (x - 4) · (x + 10)
y = x² + 6 · x - 40
y + 9 = (x² + 6 · x + 9) - 40
y + 49 = (x + 3)²
Case 12
y = (x + 2) · (x + 10)
y = x² + 12 · x + 20
y + 16 = x² + 12 · x + 36
y + 16 = (x + 6)²
Case 13
y = (x - 2) · (x - 6)
y = x² - 8 · x + 12
y + 4 = x² - 8 · x + 16
y + 4 = (x + 4)²
Case 14
y = (x + 1) · (x + 4)
y = x² + 5 · x + 4
y + 9 / 4 = x² + 5 · x + 25 / 4
y + 9 / 4 = (x + 5 / 2)²
Case 15
y = (x + 4) · (x - 5)
y = x² - x - 20
y + 1 / 4 = (x² - x + 1 / 4) - 20
y + 81 / 4 = (x - 1 / 2)²
Case 16
y = 2 · (x + 2) · (x + 4)
y = 2 · (x² + 6 · x + 8)
y + 2 · 1 = 2 · (x² + 6 · x + 9)
y + 2 = 2 · (x + 3)²
Case 17
y = x · (x + 6)
y = x² + 6 · x
y + 9 = x² + 6 · x + 9
y + 9 = (x + 3)²
Case 18
y = 3 · (x + 4) · (x - 8)
y = 3 · (x² - 4 · x - 32)
y + 3 · 4 = 3 · (x² - 4 · x + 4) - 3 · 32
y + 12 = 3 · (x - 2)² - 96
y + 108 = 3 · (x - 2)²
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