the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.
What is Diagonalizable matrix?
If there is an invertible matrix P and a diagonal matrix D such that
P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.
If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.
The given statement is false.
If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.
Hence, the given statement is false.
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For the following, find the length of AB:
(Use \large \pi=3.14 when necessary and round your final answer to the hundredths.)
Arc AB =
In the given diagram, the length of arc AB is 10.05.
Calculating the length of an arc ABFrom the question, we are to determine the length of arc AB.
From the formula for calculating the length of an arc, we have that
Length of an arc = θ/360° × 2πr
Where θ is the angle subtended by arc at the center of the circle
and r is the radius of the circle
In the given diagram,
Angle subtended by the arc = 48°
Radius, r = 12
Therefore,
The length of the arc = 48/360 × 2×3.14×12
Length of the arc = 2/15 × 1884/25
Length of the arc = 10.05
Hence, the length of AB is 10.05
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one plus one is equal to what?
Answer:
One plus one is equal to two
Step-by-step explanation:
1. Identify the numbers being added: In this case, the numbers being added are "one" and "one."
2. Write the equation using the proper mathematical notation: The equation would be written as "1 + 1."
3. Perform the addition: To solve the equation, you would add the numbers together. In this case, 1 + 1 = 2.
4. Write the final answer: The final answer to the equation "one plus one" is "two."
I hope this helps! Let me know if you have any other questions.
Silicone implant augmentation rhinoplasty is used to correct congenital nose
deformities. The success of the procedure depends on various biomechanical
properties of the human nasal periosteum and fascia. The article "Biomechnics in
Augmentation Rhinoplasty" reported that for a sample of 15 (newly deceased)
adults, the mean failure strain (%) was 25.0, and the standard deviation was 3.5.
(p. 277 #35)
a. Assuming a normal distribution for failure strain, estimate true average strain in
a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about
precision and reliability. How does the prediction compare to the estimate
calculated in part (a)?
A true average strain in a way that converys information about precision and reliability (23.0616, 26.9384)
In this question we have been given:
sample size n = 15
the mean failure strain x(bar) = 25.0
the standard deviation s = 3.5
Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.
A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.
c = 0.95 or 95%
In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.
Here, the degree of freedom :
df = n - 1
df = 15 - 1
df = 14
and the column with α =(1-c)/2
=0.025
To find the t-value:
t_(α/2) = 2.145
Therefore, the error margin is:
E = t_(α/2) × s/√n
E = 2.145× 3.5/√15
E ≈1.9384
The confidence interval's outer limits are thus:
x{bar} - E = 25.0 - 1.9384
= 23.0616
x{bar} + E = 25.0 + 1.9384
= 26.9384
Therefore, the confidence interval is: (23.0616, 26.9384)
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Determine the polynomial y(x) that has roots at x=-0.7, x=0.5, x=3.4 and x=5.8
Make a plot of the polynomial in the domain -1<=x<=6
The polynomial with given roots is,
y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.
What is factor of polynomial?
In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
Given:
The polynomial y(x) that has roots at x = -0.7, x = 0.5, x = 3.4 and x = 5.8.
Since if 'a' is a root of the polynomial then (x - a) is the factor of the polynomial.
So, the factors of the polynomial are, (x + 0.7), (x - 0.5), (x - 3.4), (x - 5.8).
⇒ y(x) = (x + 0.7)(x - 0.5)(x - 3.4)(x - 5.8)
= (x^2 - 0.5x + 0.7x - 0.35)(x^2 - 5.8x - 3.4x + 19.72)
= (x^2 + 0.2x - 0.35)(x^2 - 9.2x + 19.72)
y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902
The graph of the polynomial on the domain -1 ≤ x ≤ 6 is attached below.
Hence, the polynomial with given roots is,
y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.
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Question 3 (1 point) Use the table below to determine 1) which is the correct graph and 2) answer whether the relationship is proportional or not. Time (mins) 2 3 4 Height of Balloon (meters) Hot Air Balloon Height over Time 123456 Time (minutes) Height (meters) 22 33
Answer:
See below for the graph
It is proportional. The graph is a straight line going through the origin.
Step-by-step explanation:
The equation of the line is
y = 11x
Determine lim F(t) for F(t) if Fis a solution to the logistic differential equation dF dt 100 0.2(5F with an initial value of F(0) = 47. a. 2.5 b. 5
c. 10 d. 15.3
The value of lim F(t) for F(t) if F is a solution to the logistic differential equation dF/dt is 10 in option (c).
Finding through differential equation
[tex]\small \text{Consider the differential equation}\\ \frac{\mathrm{d} F}{\mathrm{d} t}=0.2\left ( 5F-\frac{F^2}{2} \right ),\quad F(0)=47\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{0.2}{2}\left ( 10F-F^2 \right )\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{F}{10}\left ( 10-F \right )\\[/tex]
[tex]\text{Separable the variables of F and t on both sides}\\ \int \frac{1}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{10}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{(10-F)+F}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{10F}dF-\int \frac{1}{10\left(F-10\right)}dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{F}dF-\int \frac{1}{\left(F-10\right)}dF= \int \: dt\\[/tex]
[tex]\small \ln \left|F\right|- \ln \left|F-10\right|=t+\ln C\\ \ln \left|\frac{F}{F-10}\right| =\ln \left |Ce^{t} \right |\\ \frac{F}{F-10}=Ce^{t}\\ F(0)=47\Rightarrow \frac{47}{47-10}=C\Rightarrow C=\frac{47}{37}\\ \text{Therefore,}\\ \frac{F}{F-10}=\frac{47}{37}e^{t}\\ F=\frac{47}{37}e^{t}(F-10)\\ F=\frac{47}{37}e^{t} F-\frac{470}{37}e^{t}\\ F\left ( \frac{47}{37}e^{t}-1 \right ) =\frac{470}{37}e^{t}\\ =\frac{\frac{470}{37}e^{t}}{\left ( \frac{47}{37}e^{t}-1 \right )}\\[/tex]
[tex]\small F(t) =\frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ \lim_{t\rightarrow \infty }F(t)=\lim_{t\rightarrow \infty } \frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ = \frac{\frac{470}{37}}{\left ( \frac{47}{37}-0 \right )}\\ = \frac{\frac{470}{37}}{\frac{47}{37}}\\ =\frac{470}{47}\\ =10\\[/tex]
If F is a solution to the logistic differential equation then dF/dt is 10 in option (c).
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Subtract expression 2 from expression 1
Expression 1: -9x + 8y
Expression 2: -8x - 2y
please help!!!!!!!!!!!!!!
Answer:
-6/7p + 1/7
Step-by-step explanation:
If f(x) = sinx, then (f^-1)’(sqrt3/2)=
The function has a maximum point at (-pi/2, 5) and a minimum point at (pi/4, -4)
The sinusoidal function is y = -4.5cos(8(x + π/2)) + 1/2
How to determine the cosine function for the functionFrom the question, we have the following parameters that can be used in our computation:
Maximum = (-π/2, 5)
Minimum = (π/4, -4)
A cosine function is represented as
y = A cos(B(x+C)) + D
Where
A = amplitude, 2π/B = Period, C = phase shift leftD = vertical shift up.The cosine function has a max and min of 1 and -1.
So, we have
Difference = |-4 - 5|
Difference = 9
This means that
Amplitude, A = 9/2
A = 4.5
Also, we have
Vertically shift = (5 - 4)/2
Vertically shift = 1/2 up
So, the function becomes
y = 4.5cos(θ) + 1/2
Next, we calculate the value of θ
The period is calculated as
Period = π/4 + π/2
Period = -π/4
This means that
2π/B = -π/4
So, we have
B = -8
This gives
y = 4.5cos(-8(x + c)) + 1/2
cos(0) = 1,
So we want -8(-π/2) - 8C = 0
Solving for c, we have
8C = 8(π/2)
Divide
C = π/2
Substitute C = π/2 in y = 4.5cos(-8(x + c)) + 1/2
y = 4.5cos(-8(x + π/2)) + 1/2
y = -4.5cos(8(x + π/2)) + 1/2
Hence, the function is y = -4.5cos(8(x + π/2)) + 1/2
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Complete question
The function has a maximum point at (-pi/2, 5) and a minimum point at (pi/4, -4)
Determine a cosine equation for this function.
12 dozen pieces of gum to a box 12 full boxes 1 ooen bix with 32 how many pieces of gum n all
The number of gums available, with the 12 boxes, each containing 12 dozens of gums and one open box containing 32 gums, found using the values of the non verbal units of measure, indicates that the number of gums are 1760 gums.
What is a non verbal unit of measure?Non verbal units of measure are used to describe the quantity of an item using verbal terms such as pairs (2 units), dozens (12 units), scores (20 units), gross (12 dozens or 144 units), bushels (8 gallons or 4 pecks), ream (500 units).
The number of dozens of pieces of gum are in a box = 12 dozens
The number of boxes of gum available = 12 boxes
The remaining number of gums = 1 open box with 32 gums
1 dozen of an items = 12 units of the specified item
12 dozens of an item = 1 gross of the item
The number of pieces of gums in a box, therefore is 1 gross of gums.
Therefore, the number of pieces of gum in all = 12 × 12 × 12 + 32 = 1760
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True or False: An asymptote is a line that a curve gets infinitely close to
True
False
when adding an entry to a binary search tree, the search ends at a leaf if the entry is not already in the tree.
The statement " when adding an entry to a binary search tree, the search ends at a leaf if the entry is not already in the tree" is true.
A tree is a type of data structure made up of nodes and contains the following features:
1- Every tree has a root node (also known as a parent node) at the top that contains some value (can be any datatype).
2- There are 0 or more child nodes of the root node.
3- There are zero or more child nodes for each child node, and so forth. As a result, the tree gains a subtree. Each node has a separate subtree that consists of its offspring and their offspring, etc. This implies that any node can function as a tree on its own.
In addition, a binary search tree (BST) has the following two features:
1- Each node has a maximum of up to two children.
2-For each node, the values of its left descendent nodes are less than that of the current node, which in turn is less than the right descendent nodes (if any).
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shan sees his friends for 90 minutes each day. In 7 days, how many minutes does he spend with his friends? use place value to find out
Answer:
90 x 7= 630 minutes
Step-by-step explanation:
what is the solution to the system of equations y23x3 x 2
The Solution for the given system of equations is (-2) and [tex](\frac{5}{3})[/tex].
The given are linear equations as follow:
y = [tex]\frac{2}{3}x[/tex] + 3 .. ... ...(1)
and x = -2. .. .... ...(2)
We already know the first part of the solution (x) which is -2. We can find the other part (y) by putting the value of equation (2) in equation (1).
By putting the values of x in equation (1), we get
y = [tex](\frac{2}{3})(-2)[/tex] + 3
y = [tex]\frac{-4}{3}[/tex] + 3
Taking the L. C. M of denominators which will be '3', we get:
y = [tex]\frac{-4 + 9}{3}[/tex]
y = [tex]\frac{5}{3}[/tex]
So the second part (y) of the solution of the given equation is [tex]\frac{5}{3}[/tex].
Hence, the overall solution to the given system of equation is [tex](-2, \frac{5}{3})[/tex].
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When used inside a function with a parameter, an asterisk groups a variable number of positional arguments into a single A of parameter values
When used inside a function with a parameter, an asterisk groups a variable number of positional arguments into a single tuple of parameter values
Tuples are utilized to store different things in a solitary variable. A tuple is one of 4 implicit information types in Python used to store assortments of information, the other 3 are Rundown, Set, and Word reference, all with various characteristics and use. A tuple is an assortment that is requested and unchangeable. At the point when we say that tuples are requested, it implies that the things have a characterized request, and that request won't change. Python likewise incorporates the * administrator, which permits you to make another rundown with the components rehashed the predetermined number of times. *args permits us to pass a variable number of non-catchphrase contentions to a Python capability. In the capability, we ought to utilize a bullet ( * ) before the boundary name to pass a variable number of contentions.
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Find the measure of the arc or central angle indicated.
The central angle of the given arc LKJ is; 211°
How to find the length of an arc of a circle?
We want to find the length of the arc LKJ. The central angle for this arc length is; 115° + 96° = 211°
The formula for length of arc is;
L = θ/360 * 2πr
where;
θ is central angle
r is radius
We are not given the radius and as such, we can only find the central angle which is 211°
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John started his employment with a salary of Sh. 120,000 per annum which was increased
by Sh. 10,000 every year up to the top of the scale of Sh. 1,500,000 per annum.
REQUIRED
i. In how many years’ time does he reach to the top scale? (3 marks)
ii. What is the total amount he would earn during this period
In 138 years time, john will reach to the top scale and the total amount he would earn during this period will be $1380000.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have John who started his employment with a salary of $120,000 per annum which was increased by $10,000 every year up to the top of the scale of $1,500,000 per annum.
We can write the equation governing the increase as -
y = 120000 + 10000x
For -
y = 1500000, we can write -
1500000 = 120000 + 10000x
10000(12 + x) = 1500000
x + 12 = 150
x = 138 years
The total amount he would earn during this period will be -
A = 10000 x 138 = $1380000
Therefore, in 138 years time, john will reach to the top scale and the total amount he would earn during this period will be $1380000.
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A quadrilateral with one pair of parallel side is a
A) Parallelogram
B) Square
C) Rectangle
D) Trapezium
A quadrilateral with one pair of parallel side is a D) Trapezium
Given :
A quadrilateral with one pair of parallel side is.
we know that ,
Trapezium :
A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.
The trapezium is a two - dimensional shape that appears as a table when drawn on a sheet of paper.
In Euclidean Geometry, a quadrilateral is defined as a polygon with four sides and four vertices.
so a trapezium also has four sides, four angles and four vertices.
Area of trapezium = 1/2 * ( a+ b ) h
where a and b are bases
and h is height of altitude.
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Ten families were randomly selected and their daily water usage (in gallons) before and after viewing a conservation video was recorded. The sample mean difference was found to be 4.8 and the corresponding standard deviation 5.25, where differences were found (Before - After). Assume the data is normally distributed. Find a 90% confidence interval for this data. State the lower bound [x] and the upper bound [y].
lower bound = 1.76
Upper bounds = 7.84
The 90% confidence interval for the given data is 4.8 ± 2.73.
What is Confidence interval?A confidence interval is a type of interval computation used in statistics that determines the true value of an unknown parameter based on the observed data. The interval estimates the deterministic parameter with a level of confidence that is quantified by the confidence level.
Given, sample mean (x) = 4.8
z at 90% confidence level = 1.645
sample standard deviation (s) = 5.25
sample size (n) = 10
We know that, Confidence interval = x ± (z × s) ÷ √n
= 4.8 ± (1.645×5.25)/√10
= 4.8 ± 8.63625/3.1622
= 4.8 ± 2.73
∴ Lower bound = 4.8 - 2.73 = 2.07
and, Upper bound = 4.8 + 2.73 = 7.53
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3. (1 point) there are 8 people participating in a focus group for a new software product related to the health system, 3 of them are software engineers, 2 of them are nurses, 1 of them is a doctor, and the remanining 2 people are technicians. in how many ways they can be seated in a row so that no two software engineers are together? show all your work step by step to get credit. final answers must be provided in decimal form
In 480 ways these 8 people can be seated in a row so that no two software engineers are together
In this question, we need to find the number of ways 8 people can be seated in a row so that no two software engineers are together.
3 software engineers can sit in 3! ways
2 nurses can sit in 2! ways
2 technicians can sit in 2! ways
and a doctor need only one seat
Given that no 2 software engieers are to be seated together.
we first place the 5 people in a row and software engineers has to sit between them so no 2 software engieers are to be seated together.
In 6 place they can sit in 6c3 ways and 3 can be combine themself in 3! ways.
Using the formula of combination,
6c3 = 20
so total will be 2 * 2* 1*20*6=480 ways.
Therefore, the number of possible ways = 480
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Premature Birth and Education Does the length of term of pregnancy play role in the level of education of the baby? Researchers Norway followed over million births between 1967 and 1988 and looked at the educational attainment of the children: The following data are dased the results of their research: Note that full-term pregnancy 38 weeks. gestational period independent of completing high school diploma? Use the 0.05 level of significance. Show five steps unnmen Perud (neeks) 21-27 272 W4J6 J7-2 4 04 Than Hih Ved Sbor [get 30n)
The length of pregnancy does play a role in the education level of the baby. A significant relationship can be established using the chi square test.
What is a chi square test?A chi square ( χ2) test is performed in order to find a co relation between two unrelated variables. The main objective of the test is to prove whether the relationship holds true or is just a product of mere chance. For example, if we are conducting a survey of two different parameters, first being the population of people who are married and the other about their educational qualification, we will get two distinct table of values without any significant co relation. But now if we want to establish a relationship, lets say that married people have less educational qualifications, we need to prove our statement by performing a chi square test. The final value can either be a null hypothesis which states that their is no convincing relationship between the two parameters or can be a alternate hypothesis with significant co relation.
Using chi square for the problem:Following data can be represented on tabular form and calculated:
Gestation Period (Observed)
22-27 28-32 33-36 37-42 43+ Tot
Less than high YES 14 34 140 1010 81 1279
school degree NO 26 65 343 3032 208 3674
40 99 483 4042 289 4953
Gestation Period (Expected)
YES 10.32 25.56 124.72 1043.75 74.62
NO 29.67 73.43 358.27 2998.24 214.37
χ2 = ∑ [tex]\frac{(Observed-Expected)^2}{Expected}[/tex]
= [tex]\frac{13.54}{10.32} +\frac{71.23}{25.56} +\frac{233.47}{124.72} +\frac{1139.06}{1043.75} +\frac{40.70}{74.62} +\frac{13.46}{29.67} +\frac{233.17}{358.27} +\frac{1139.73}{2998.24}+\frac{40.57}{214.37}[/tex]
= 1.31+2.78+1.87+1.09+0.54+0.45+0.96+0.65+0.38+0.18 = 10.21
Now, calculating the degree of freedom= (coulmn-1)(row-1)= (5-1)(2-1) = 4
Looking at the reference table at 0.05 significance level, the value is 9.488
As the calculated value is more than the table value/critical value, null hypothesis can be rejected proving the alternate hypothesis that there might be a relationship between gestation period of a mother and the education level of her kid.
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TRUE/FALSE. matrix organizations have a flexible structure that brings together specialists from different areas of the company to work on individual projects on a temporary basis.
True Matrix organizations have a flexible structure that brings together specialists from different Areas.
Teams in a matrix organization report to several leaders inside the business. The matrix structure promotes open communication between teams and can assist businesses in producing more creative goods and services. By using this framework, teams are spared the hassle of constantly realigning themselves for new projects.
How can teams be empowered to work fast on challenging projects without being slowed down by reviews and approvals from stakeholders? The solution might lie in organizational structure. Most workplaces have established hierarchies of command so that everyone is aware of who has the final say.
There are two or more management reporting structures in matrix organizations. Team members often have a principal manager for their department, despite the fact that this may at first seem unclear.
Comparable to a traditional organizational structure is reporting to a department manager. For instance, team members in the IT department answer to the head of the department. The vice president of their division is responsible for overseeing the IT department. All reporting lines ultimately lead to the CEO.
In contrast, team members in a matrix organization also report to project managers. It is appropriate to choose a separate manager for each project because tasks associated with them frequently require assistance from employees from different areas, such as IT, marketing, and finance.
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which of the following best describes the result of running the code segment?the number 0 is displayed.the number 4 is displayed.the number 10 is displayed.nothing is displayed; the program results in an infinite loop.
A statement that describes the result of running the code segment is: the number 10 is displayed
The correct answer is an option (B)
In this question, we have been given the program code.
We need to select a correct statement that describes the result of running the code segment.
Consider the given code.
Start by setting n and sum to 0.
Add the value of n to sum. The first time, the value of n is 0, so sum remains 0.
Increment n by 1, so now the value of n is 1.
The Boolean condition (n = 5) is still false, so the loop will run again. Add 1 to sum (which is now 1), and then increment n (so n is now 2).
Repeat this three more times (while the value of n = 2, 3, and 4)
Increment n, so the value of n is now 5. Now the Boolean condition is true, so the loop stops.
Display sum is 10
Therefore, the result of running the code segment : the number 10 is displayed
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The complete question is:
Consider the following program code.
Which of the following best describes the result of running the program code?
A. The number 0 is displayed.
B. The number 10 is displayed.
C. The number 15 is displayed.
D. Nothing is displayed; the program results in an infinite loop
A 39-inch board is cut into two pieces. One piece is two times the length of the other. Find the length of the shorter piece.
The shorter piece is
inches long.
Answer:
The shorter piece is 13 inches long.
Step-by-step explanation:
39=2x+x
39=3x
/3 /3
13=x
1) 9x² + 4y² - 36x + 8y + 4 = 0
Write the standard form equation of each ellipse
Please help me solve this?
The value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]
What is Combination of Function ?
The domain of an arithmetic combination of functions f and g consists of all real numbers that are common to the domains of f and g.
Given expression,
f(x) = 4x + 1
g(x) = √x
Now, find (f · g)(x)
(f · g)(x) = f( g(x) )
Next, insert the value of g(x) in f(x) value by replacing x value in f(x)
(f · g)(x) = 4 ( √x ) + 1
= 4√x + 1
Next, find (g · f)(x)
(g · f)(x) = g( f(x) )
Now, insert the value of f(x) in g(x) value by replacing x value in g(x)
(g · f)(x) = √4x + 1
= [tex]\sqrt{4x+1}[/tex]
Hence, the value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]
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Greenpoint had 224,710 residents at the time of its founding. Currently it is 20% smaller. What is the current population?-
Answer:
179,768
Step-by-step explanation:
Greenpoint had 224,710 residents at the time of its founding. Currently it is 20% smaller. What is the current population?
100% - 20% = current population is now 80%
80% = 0.8
0.8 * 224,710 = 179,768
Find the x-intercept(s) and the coordinates of the vertex for the parabola y=-x-8x-16. If there is more than one x-intercept, separate them with commas.
x-intercept(s):
vertex
Answer:
x-intercept(s): (- 4, 0)Vertex: (- 4, 0)----------------------------------------
Given parabola:
y = - x² - 8x - 16Convert the equation into vertex form y = a(x - h)² + k, where (h, k) is the vertex.
y = - x² - 8x - 16y = - (x² + 8x + 16)y = - (x + 4)²The vertex is ( - 4, 0).
The x-intercepts are the points with the y = 0, which as we see is same as the vertex:
- (x + 4)² = 0x + 4 = 0x = - 4What does the statement below mean?
Range: {-7 < y < 12}
The statement -7 < y < 12 meant y is greater than -7 and less than 12.
How to interpret inequality?{-7 < y < 12}
This is a compound inequality.
A compound inequality is a type of inequality which combones two or more simple inequality.
-7 < y < 12
This can be broken down into two parts;
-7 < y (minus 7 less than y)y < 12 (y is less than 12This can also be written together as y is greater than -7 and less than 12.
This means y is between the values that are greater than -7 but less than 12
So,
y could be -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Therefore, y can be said to be within the range of values between -6 and 11
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