Answers
T satisfies the homogeneity property.
To prove that T is a linear transformation, we need to show that it satisfies two properties: additivity and homogeneity.
Additivity:
Let's consider two arbitrary vectors z₁ = [x₁, y₁] and z₂ = [x₂, y₂] in R².
T(z₁ + z₂) = T([x₁ + x₂, y₁ + y₂])
= [-2(x₁ + x₂) - 1, -2(x₁ + x₂) + 2(y₁ + y₂)]
= [-2x₁ - 2x₂ - 1, -2x₁ - 2x₂ + 2y₁ + 2y₂]
= (-2x₁ - 1, -2x₁ + 2y₁) + (-2x₂ - 1, -2x₂ + 2y₂)
= T(z₁) + T(z₂)
Therefore, T satisfies the additivity property.
Homogeneity:
Let's consider an arbitrary vector z = [x, y] in R² and a scalar k.
T(kz) = T([kx, ky])
= [-2(kx) - 1, -2(kx) + 2(ky)]
= (-2kx - 1, -2kx + 2ky)
= k(-2x - 1, -2x + 2y)
= kT(z)
Since T satisfies both additivity and homogeneity, we can conclude that T is a linear transformation.
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Related Questions
Jessica is making a cake. The recipe calls for 2 3/4 cups of flour. She only has a measuring cup that holds 1/4 cup. Explain how she can use the measuring cup that holds 1/4 cup to measure 2 3/4 cups of flour.
Answers
Answer: Jessica can use her measuring cup 11 times.
(hope this helps!)
The box is a rectangular prism. He covered all the sides with the of the box with special wallpaper that cost a total of $504. How much wallpaper cost per square foot length is 6 feet width is 5 feet and height is 3 feet.
Answers
The cost of the wallpaper per square foot is $4.
To find the cost per square foot of the wallpaper, we first need to calculate the total surface area of the box. A rectangular prism has six faces, and each face is a rectangle.
The front and back faces have dimensions 6 feet by 3 feet, so their combined area is 6 ft * 3 ft * 2 = 36 square feet.
The top and bottom faces have dimensions 5 feet by 3 feet, so their combined area is 5 ft * 3 ft * 2 = 30 square feet.
The left and right faces have dimensions 6 feet by 5 feet, so their combined area is 6 ft * 5 ft * 2 = 60 square feet.
The total surface area of the box is 36 + 30 + 60 = 126 square feet.
Since the cost of the wallpaper is $504, we divide the total cost by the total surface area to find the cost per square foot: $504 / 126 sq ft = $4 per square foot.
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Tina wants to use rope to decorate a rectangular picture frame. The frame measures 13 inches wide and 35 inches tall. Tina has 7 feet of rope. Does she have enough rope to go around the perimeter of the frame? Explain. Remember, 1 foot = 12 inches.
Answers
explanation: 13 + 13 + 35 + 35 = 96
96in/12in= 8 ft of rope
Calculate the finance charge for a credit card that has an average daily balance of Php5,600 and a monthly interest rate of 1.35 %
Answers
Answer:The simplest way to calculate a finance charge is: balance X monthly rate
Step-by-step explanation:
i thinkk
500 X .015 = $7.50
The finance charge for a credit card that has an average daily balance of 5,600 and a monthly interest rate of 1.35 % is $75.6.
What is the finance charge?The finance charge is the product of an average daily balance to the monthly interest rate.
finance charge = balance x monthly rate
The simplest way to calculate a finance charge = balance x monthly rate
= 5,600 x 0.0135
= $75.6
Thus, the finance charge for a credit card that has an average daily balance of 5,600 and a monthly interest rate of 1.35 % is $75.6.
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The population of a city decreases by 2.5% per year. If this year's population is 237,000, what will next year's population be, to the nearest individual?
Answers
PLEASE HELP !!!! ILL GIVE BRAINLIEST !!!
Answers
Answer:
Hi it's down below! Hope it helps
Step-by-step explanation:
1) The angles are Supplementary
This is because both angles form 180°. The angle below angle "7x+9" is the same as 5x+3. The angle above angle"5x+3" is the same as 7x+9.
2) They are both supplementary
They form 180°
3)180° = 12x+12°
4) Solving that:
180° - 12° = 12x
168° = 12x
x = 168°/12
x = 14°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
the answer is 14°
Step-by-step explanation:
PLEASE MARK AS BRAINLIEST
what is maintenance culture
Answers
Answer:
ways of thinking,behaviour,perciption
Help please is for now
Answers
Answer:
In linear functions, rate of change is constant: as x goes up, y will go up a consistent amount. In exponential functions, the rate of change increases by a consistent multiplier
Step-by-step explanation:
Answer:
Linear functions change at a constant rate per unit interval. An exponential function changes by a common ratio over equal intervals.Step-by-step explanation:
ASAP PLEASE HELP!!! Given the cylinder with the given dimensions, match the measures of the radius, circumference, and area of the base.
Answers
Answer:
Radius of cylinder = 4.5 inch
Circumference of Base = 9π inch
Area of base = 20.25π
Step-by-step explanation:
Given:
Diameter of cylinder = 9 inch
Height of cylinder = 22 inch
Find:
Radius of cylinder
Circumference of Base
Area of base
Computation:
Radius of cylinder = Diameter of cylinder / 2
Radius of cylinder = 9 / 2
Radius of cylinder = 4.5 inch
Circumference of Base = 2πr
Circumference of Base = 2π(4.5)
Circumference of Base = 9π inch
Area of base = πr²
Area of base = π(4.5)²
Area of base = 20.25π
increase R700 in the Ratio 3:2
Answers
Step-by-step explanation:
³93521586335445555554555554488807799654
The overnight temperature in Tampa never
reached below 40°F during November.
Which inequality shows that?
A x < 40
B x> 40
© x= 40
DX > 40
Truman puts money into his savings
Answers
Answer:
Step-by-step explanation: C is the answer
Select the correct answer.
Which of these is a non-real complex number?
OA. 5/17 - 21/4
B.
9 + 375
2
OC. 2 - 0
OD. +
/
Dorot
Answers
Answer:
OD
Step-by-step explanation:
because it gives us error and there's no number
The correct option is (D) .
Which is a non-real complex number?Nonreal complex numbers include pure imaginary numbers and those with a and b values of zero, such as 7 + 2i.A non-real or imaginary number is the name given to the square root of a negative number. For instance, the numbers 1, 28, and 5 are all imaginary numbers.Complex numbers cannot be plotted on the actual number line because they contain imaginary numbers. On the complex number plane, which has a y axis (for the imaginary number) and an x axis (for the real number), they can, however, be measured starting from zero (for the imaginary number).In all these options , they are presenting real complex number .Real numbers can be positive or negative, and include the number zero. that is why we select option D .
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this is new information to me
Answers
I need the answer to
Answers
Answer:
I think its B
Hope this helps
Explain how you would graph the inequality: 3 ≤ x
Answers
Given : Explain how you would graph the inequality: 3 ≤ x .
Solution : Graph in attachment .
Answer:
When you are graphing the equation the line, theline on the graph is going to be vertical. Your line point will be ( 3, 0 ). Then there will be a shaded part of the graph on the right on of the line.
-1.32+x=1
-1 -1
Not sure about this??
Answers
Answer:
x=2.32
Step-by-step explanation:
-1.32+x=1
add 1.32 to both sides
1.32 cancels itself out
so you are left with x=2.32
The difference of two numbers is 3. Their sum is 13. Find the numbers.
Answers
Answer:
the correct numbers are 8 and 5
What is the sum of one sixth and thrice of n
Answers
Answer:
9
Step-by-step explanation:
6+3 is 9
Answer:
what do you mean by thrice of n?
Step-by-step explanation:
Wouldn't we need to know what n equals?
What is the length of a rectangle if its width is 7 feet and its area is 84 square feet?
Answers
Answer: The length is 12 feet.
Step-by-step explanation:
9. Solve 6/7 divided by 36/56 and put answer in simplest form.
A. 2/8
B. 8/6
C.4/3
D. 6/8
Answers
Answer: C
Step-by-step explanation:
Fraction division rule: 6 * 56 / 7 * 36
Then divide the numbers: 6 * 8 / 36
Cancel the numbers 6/36 = 1/6
That leaves us with 8/6
Then simplify by dividing by the common factor
8/2 = 4
6/2 = 3
Answer: 4/3
Zhen borrows $1,200. She borrows the money for 2 years and owes $180 in simple
interest. What is the yearly simple interest rate on Zhen's loan? Show your work
Answers
Answer: 7.5
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 7.5%/100 = 0.075 per year,
then, solving our equation
I = 1200 × 0.075 × 2 = 180
I = $ 180.00
The product of 1 1/2 and 2 is less than, equal to, or greater than 2
Answers
Answer:
The answer is 1 1/2 < 2
Step-by-step explanation:
If we convert 1/2 into a decimal, we would get .5. Add that to 1 and we get 1.5. Therfore, 2 > 1.5
Inequality question PLEASE HELP
Answers
Answer:
40x4x<60
x<5
Step-by-step explanation:
40x4x<60
4x<60-40
4x<20
x<20÷4
x<5
11. Find mZB.
С
B
(4x + 11)
(6x – 15°
D
A
Answers
Answer: 117
Step-by-step explanation:
first i found x which is 13
4x+11=6x-15
+15 +15
4x+26=6x
-4x -4x
2x=26
26÷2 2÷2
x=13
then i just put 13 nto the equation and got
m<B=117
if you know how to please mark brainlyest!
The district manager of four different restaurants wanted to investigate whether the four restaurants differed with respect to customers ordering dessert or not based on family classification (with children or without children). Independent random samples of 100 customers who ordered dessert were selected from each restaurant, and the customers were identified as either being with children or without children. After verifying the conditions for the appropriate hypothesis test, the manager calculated a chi-square test statistic of 6.45 with an associated p-value of 0.092. Based on the p-value and a = 0.05, what conclusion should the manager make regarding the proportion of customers who order dessert at each restaurant and the customers' family classification?
A. There is convincing statistical evidence to suggest that the proportion of customers who order dessert at each restaurant is the same based on family classification.
B. There is convincing statistical evidence to suggest that the proportion of customers who order dessert at each restaurant is not the same based on family classification.
C. There is not convincing statistical evidence to prove that the proportion of customers who order dessert at each restaurant is not the same based on family classification.
D. There is not convincing statistical evidence to suggest that the proportion of customers who order dessert at each restaurant is the same based on family classification.
E. There is not convincing statistical evidence to suggest that the proportion of customers who order dessert at each restaurant is not the same based on family classification.
Answers
Answer:
E
Step-by-step explanation:
Lyle uses a streaming service to watch movies. Last month he paid $26.91 and watched 9 movies. If he watches 11 movies this month, how much will he pay the streaming service?
Answers
Answer:
$32.89
Step-by-step explanation:
Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function ??
FE) = e²-
g(x) = ² - 4
O A.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function to the right.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a vertical compression of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the left.
Reset
Next
Answers
A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.
When the parent function [tex]f(x) = e^x -4[/tex] is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;
g(x) = kf(x)
g(x) = 1/2f(x)
[tex]g(x) = \frac{1}{2} e^x -4[/tex]
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Huh?! Its me DaBaby less gooo i need your help with this question. Yeah Yeah!
Answers
Answer:
Imaoo
Step-by-step explanation:
answer: C
Answer: Letsssss goooooo
the answer is 4y
dababy letssssssssssss gooooooooooooooooo
Step-by-step explanation:
The radius of a sector is 1 m
a. Find the area of a 1° sector of the circle.
b. What is the area of the circle containing the sector?
c. If 360 of the 1° sectors of the circle are placed side by side to approximate a parallelogram, what is the approximate area of the parallelogram?
d. What is the difference of the areas in parts (b) and (c) as a percentage of the entire circle?
Answers
How many digits are in 385,604 ?
Answers
Answer:
6
Step-by-step explanation:
because 385,604 there is 6 digits