We know the following about the transformation A:
A ï1 0 ò=ï2 0 ò
and A ï0 1 ò=ï1 1 ò
73.1 Draw C2 and A(C2), the image of the unit square under A.
73.2 Compute the area of A(C2).
73.3 Compute det(A).
73.1 A(C2) is a quadrilateral with vertices (0, 0), (1, 0), (1, 2), and (0, 2).
73.2 The area of A(C2) is 2.
73.3 The determinant of A is 0
To draw C2 and A(C2), to understand the transformation A and to the unit square.
Given the information:
A:
| 1 0 |
| 2 0 |
A maps the vector [1, 0] to [2, 0], and it maps the vector [0, 1] to [1, 1]. This provides us with the information to draw C2 and A(C2).
73.1 Draw C2 and A(C2):
C2 represents the unit square with vertices (0, 0), (1, 0), (1, 1), and (0, 1).
To draw A(C2), the transformation A to each vertex of C2 and connect the transformed vertices to form the image of C2 under A.
Applying A to the vertices of C2:
A(0, 0) = (1 × 0, 2 × 0) = (0, 0)
A(1, 0) = (1 × 1, 2 × 0) = (1, 0)
A(1, 1) = (1 × 1, 2 × 1) = (1, 2)
A(0, 1) = (1 × 0, 2 × 1) = (0, 2)
Connecting the transformed vertices, we get the image of C2 under A:
73.2 Compute the area of A(C2):
To compute the area of A(C2), divide it into two triangles and calculate their areas separately.
Triangle 1: (0, 0), (1, 0), (1, 2)
Base of Triangle 1 = 1 - 0 = 1
Height of Triangle 1 = 2 - 0 = 2
Area of Triangle 1 = (1/2) × Base × Height = (1/2) × 1× 2 = 1
Triangle 2: (0, 0), (0, 2), (1, 2)
Base of Triangle 2 = 1 - 0 = 1
Height of Triangle 2 = 2 - 0 = 2
Area of Triangle 2 = (1/2) × Base × Height = (1/2) × 1 × 2 = 1
Total Area of A(C2) = Area of Triangle 1 + Area of Triangle 2 = 1 + 1 = 2
73.3 Compute det(A):
To compute the determinant of A (denoted as det(A)), use the formula for a 2x2 matrix.
A:
| 1 0 |
| 2 0 |
det(A) = (1 ×0) - (0 × 2) = 0 - 0 = 0
To know more about area here
https://brainly.com/question/1631786
#SPJ4
¿Cuáles son los números primos entre 2 y 20?
Answer:
2 3 5 7
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest. Need answer and explanation/work. Thank you.
Answer:
Parallel: y = -2x + 2 (Or any value that isn't 4), Perpendicular: 1/2x + (Anything),
Neither: y = 4x - 7 (Or any random equation that does not have the same, or opposite reciprocal slope)
Step-by-step explanation:
Methods to rid a model of multicollinearity include:
Methods to rid a model of multicollinearity include: Include determination,Collection of data,Variable change,Regression ridge
Multicollinearity in a model can be addressed in a number of ways, including:
Include determination: Eliminating at least one connected factors can assist with mitigating multicollinearity. Stepwise regression or LASSO regression can be used to select the most important features by analyzing the correlation matrix.
Collection of data: By introducing variation in the predictors, more diverse and independent data can help reduce multicollinearity. Expanding test size can likewise help in relieving multicollinearity impacts.
Variable change: Multicollinearity can be reduced by transforming variables using centering, standardization, or power or logarithmic transformations. These changes change the scale or type of the factors, making them less associated.
Regression ridge: By adding a penalty term to the least squares estimation, ridge regression reduces the impact of multicollinearity and reduces the coefficients. This regularization method balances out the appraisals and works on model execution.
PCA, or Principal Component Analysis,: PCA can be used to generate uncorrelated linear combinations of the starting variables. These new factors, known as head parts, can be utilized as indicators in the model, successfully lessening multicollinearity.
To know more about Multicollinearity refer to
https://brainly.com/question/30691253
#SPJ11
3/5 + 7/8 + 3/10
please help
Answer:
soln,
3/5+7/8+3/10
3×8/5×8+7×5/8×5+3×4/10×4
24/40+35/40+12/40
24+35+12/40
71/40
find the value of x for both problems.
Answer:
Step-by-step explanation:
In Problem 6, 3/x = tan 30 degrees, or x/3 = 1 / (tan 30 degrees), or
x = 3 / (tan 30 degrees). Using a calculator: x = 3 / (0.449) = 6.68 units
In Problem 9, we begin by finding the length of the hypotenuse of the upper triangle: sin 60 degrees = 9√3 / hypotenuse, or
hypotenuse = 9√3/ (√3 / 2) = 9/2. Then the hypotenuse of the 45-45-90 triangle is 9/2. Thus, cos 45 degrees = x / (9/2), or
2x √3
---- = -------
9 2
9√3
Cross-multiplying, we get 4x = 9√3, so that x = -------------
4
encontre as raízes quadradas dos números:
a)²√625
25
porque al multiplicar 25×25 nos da 625
Answer:
25
Step-by-step explanation:
25x25=625
A password is required to log into a system that only recognizes numbers and letters of the alphabet (not case sensitive). You want to create a password using 5 numbers or letters, but cannot reuse any of them. How many different passwords are possible?
There are 60,466,176 possible passwords for a system that acknowledges both digits and letters of the alphabet (and does not differentiate between uppercase and lowercase letters) and requires a 5-character password with no repeated characters.
For the purpose of computing the total number of possible passwords, it is necessary to take into account the number of options available for each character position. Within the constraints of the system, there are 10 different options for each number (0-9) and 26 different options for each letter (A-Z).
There are a total of 36 options available to us when it comes to the first character position (26 letters and 10 numerals). We are left with 35 options for the second place because we are unable to recycle any of the characters (36 options, minus the one that has already been used). In a similar fashion, we have 34 options for the third position, 33 options for the fourth position, and 32 options for the fifth position.
To calculate the total number of possible passwords, we multiply the number of choices for each position together: 36 * 35 * 34 * 33 * 32 = 60,466,176. Given the parameters of this system, there are consequently sixty-four million, four hundred sixty-six thousand, one hundred seventy-seven different passwords that might be used.
Learn more about number here:
https://brainly.com/question/3589540
#SPJ11
How many real solutions exist for this system of equations? Y = -x + 1 y = -x2 + 4x − 2 A. Zero B. One C. Two D. Infinite
Answer:
Two solutions
Step-by-step explanation:
Given the functions Y = -x + 1 y = -x² + 4x − 2
Since they are both y values, we will equate them to have:
-x+1 = -x² + 4x − 2
Equate to zero
x²-x-4x+1+2=0
x²-5x+3 = 0
Since the resulting equation is quadratic (highest degree being 2), hence there will be two solutions to the equation
Find the basis for the kernel and imagine of this transformation. Let T : P₂ → R where T(p(x)) = p(1). Find a or the kernel and image of this transformation.
The basis for Ker(T) is {}, and the basis for Im(T) is {1}.
Since, The kernel of T, denoted Ker(T), is the set of all elements in P₂ that are mapped to zero in R by T.
In other words, Ker(T) is the set of all polynomials in P₂ such that
T(p(x)) = p(1) = 0.
Hence, To find the kernel, we need to solve the equation p(1) = 0.
Since, The only polynomial that satisfies this condition is p(x) = 0.
Therefore, Ker(T) = {0}.
Now, the image of T.
The image of T is the set of all elements in R that are mapped to by some element in P₂ under T.
In other words, Im(T) is the set of all possible values of p(1) for all polynomials p(x) in P₂.
Some example: - If p(x) = 1 + 2x + x², then p(1) = 1 + 2 + 1 = 4.
So, we can see that Im(T) is the set of all real numbers.
Hence, the basis for the kernel and image of T.
Since Ker(T) = {0}, the basis for the kernel is the empty set, denoted by {}.
Since Im(T) is the set of all real numbers, any non-zero real number can be expressed as a scalar multiple of any other non-zero real number.
Therefore, the basis for Ker(T) is {}, and the basis for Im(T) is {1}.
Learn more about the standard deviation visit:
https://brainly.com/question/475676
#SPJ4
Mario tiene 4 pantalones de diferente color (azul, café, negro y blanco) y 6 camisas también de diferente color (blanca, negra, azul, café, gris y verde). Si Mario escoge una combinación al azar, ¿cuál es la probabilidad de que se vista con pantalón azul y camisa blanca?
Kai's mom gave him $25 to spend at the book fair. Kai wants to buy as many books as he can. The
cost of each book is $3. He also wants to buy one poster for $2. Write an inequality to show how
many books he can buy. Highlight your inequality in green. Then,solve the inequality
Answer:
7 books
Step-by-step explanation:
i cant write it in an equaction but basically 25 - 2 = 23
then 3 x 7 = 21 so he can only buy 7 books and he'll have 2 dollars left
Find the cross product a x b where a = (3, -3, -2) and b = (3,-1,-2). ахь Find the cross product cx d where c = (1, -2,-2) and d=(-5,3,-1).
The cross product of vector c and d is equal to (-4,9,13).
The cross product of two vectors a and b in three-dimensional space is a vector that is perpendicular to both a and b and thus normal to the plane containing them. Here, we have to find the cross product of two given vectors. The given vectors are:a = (3, -3, -2) and b = (3, -1, -2) So, a x b = (4,0,6).The second one is given as: c = (1, -2,-2) and d=(-5,3,-1).
A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.
In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.
Know more about vector here:
https://brainly.com/question/29740341
#SPJ11
PLSSSS HELPPPP PLSSSS PLS HELPPPPP!!!!!!
Answer:
B -- (5 smoothings)(price of 1 smoothie) + tip = $23
Step-by-step explanation:
5 smoothies(price of 1 smoothie)+tip=23
Please hurryyyyy !!!! What's the slope and y intercept of 4y = 2x - 12
Answer:
slop is 0.5 and intercept of y is -3
Answer:
½ is the slope,-3 is the intercept
Step-by-step explanation:
now to find the slope and intercept
we use the equation,
y=mx + c
where m is the slope
and c is the y intercept
so we compare 4y=2x-12 to the equation
but we first have to make y the subject of the equation in the question – 4y is already the subject –
y=2x-12/4
y=2x/4 -3
comparing...
we see that m is 2/4=½ c= -3
How many days in April
Answer:
There are 30 days according to the Georgian calender of the month of april.
Step-by-step explanation:
What is the median of the data set? {5, 3, 4, 2, 6} Enter your answer in the box. Round to the nearest tenth.
The best answer will receive brainiest.
Answer:
4
Step-by-step explanation:
To find median, arrange the data set in ascending order. Then the middle term is the median
2 , 3 , 4 , 5 , 6
Median = 3rd term = 4
Answer:
4 is the median
Step-by-step explanation:
From least to greatest:
2,3,4,5,6
Since the total values is odd, the middle number is the median
4 is the median
Can someone please help me with math
Answer:
A. 20.2 ft
Step-by-step explanation:
use the pythagorean theorem to get your answer.
a^2+b^2=c^2
17^2+11^2=c^2
289+121=410
***IMPORTANT, remember to square root the answer. 410 isn't your final answer, it's still in c^2 form. 20.2 is the correct answer after square rooting it. don't forget that for future problems
Answer:
A. 20.2 ft
Step-by-step explanation:
Hope it helps..
Simplify this expression
find the area of this polygon
Answer:
answer is 65 in²
hope this helps
In desperate need of help. If anyone could help it would be greatly appreciate. Will rate brainliest!
Answer:
7 people
Step-by-step explanation:
Chocolate: 350 / 100 = 3.5 x 2 = 7
Butter: 45 / 10 = 4.5 x 2 = 9
Eggs: 8 / 2 = 4 x 2 = 8
The amount of chocolate is the limiting factor as you have enough eggs for 8 people and enough butter for 9 people, but only enough chocolate for 7 people
A rectangular prism has a base perimeter of 28 inches and a height of 6 inches. What is the lateral surface area of the prism?
Answer:
uhuhuhuhuhuhuhuhuhuhuh oh yeah
Step-by-step explanation:
Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be . Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.
The question is incomplete. The compete question is :
Saul decides to use the IQR to measure the spread of data. Saul calculates the IQR of the data set to be 27. Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine. 25, 30, 50, 50, 50, 50, 56, n, 250. What is the value of n that will make the IQR of the data set equal to 27?
Solution :
The inter quartile range is being measured as : 3rd quartile - 1st quartile
The 1st quartile = 25% mark
The 3rd quartile = 75% mark
The data set as given in the question is :
25, 30, 50, 50, 50, 50, 56, n, 250
Therefore, the total number of the sample = 9
And the median is = 50
The median separates the given data sets into two equal halves-- that is the upper half and the lower half.
Let the middle of a lower half is the 1st quartile be [tex]$Q_1$[/tex]
And the middle of a 2nd half is the 3rd quartile be [tex]$Q_3$[/tex]
∴ [tex]$Q_1=\frac{30+50}{2}$[/tex]
[tex]$=40$[/tex]
[tex]$Q_3=\frac{56+n}{2}$[/tex]
Now for the IQR of the data set to be equal to [tex]$27$[/tex],
[tex]$\frac{56+n}{2}-40=27$[/tex]
[tex]$\frac{56+n}{2}=27+40$[/tex]
[tex]$\frac{56+n}{2}=67$[/tex]
[tex]$56 +n=134$[/tex]
[tex]$n=134-56$[/tex]
[tex]$n=78$[/tex]
CORRECT ANSWER GETS BRAINLIEST
Explain how you would apply exponent rules to evaluate for the value of (x³/x)² if x =1/2?
Answer:
1/16
Step-by-step explanation:
Picture is attached. The quickest way is to simplify BEFORE plugging in x = 1/2
Use the box method to distribute and simplify (2 + 1)(2x - 3). Drag and drop the
terms to the correct locations of the table.
Answer:
2x^2-x-3
(2x)(-3)
(x)
(1)
Step-by-step explanation:
Distribute
(2x^2) (-3x)
(2x) (-3)
Tina drew a triangle with side lengths 6, 8, and 14. She claims it is a right triangle. Is she correct?
Answer:
No such a triangle can not exist.
Help pls I’m on a time limit. Please and thank you <33
Answer: the answer is 3/10
Step-by-step explanation: because its 3/10
Answer:
es
3/ 10
Step-by-st
Use the following diagram to answer question 4 and 5
Exterior Angle Theorem
8.6 points
The measure of ZA is
Given the following diagram, find the measures of
LA and ZB
Type your answer...
B (2x + 4)
5
8.6 points
The measure of ZB is
Type your answer...
(3x - 13)
116°
А
Answer:
3x-13+2x+4=116( the sum of two interior angle is epual to the sum of exterior angle )
5x =116-9
5x=107
x=21.4 degree
then
angle a= 3*21.4-13
a=51.2degree
angle b=2*21.4+2
b =44.8degree
Step-by-step explanation:
plz make me brainliest
Im giving brainliest
Answer:
√17 - 3 > -2 + √5Can i pass 7th grade with 3 Fs?
Answer:
Depends on the state you’re from
Step-by-step explanation:
Answer:
Yes you can! Grades from middle school don't matter when you get to high school. But try to get those grades up!