Answers
T satisfies both the additive and scalar multiplication properties, it can be concluded that T is a linear transformation.
To prove that T is a linear transformation, we need to show that it satisfies two properties: additive property and scalar multiplication property.
Additive property:
Let z = (x1, x2) be an arbitrary vector in R2. We want to confirm that T(z1 + z2) = T(z1) + T(z2).
Let z1 = (x1, x2) and z2 = (y1, y2) be arbitrary vectors in R2.
T(z1 + z2) = T((x1 + y1, x2 + y2)) = (x1 + y1, x2 + y2)
T(z1) + T(z2) = T(x1, x2) + T(y1, y2) = (x1, x2) + (y1, y2) = (x1 + y1, x2 + y2)
We can see that T(z1 + z2) = T(z1) + T(z2), thus satisfying the additive property.
Scalar multiplication property:
Let z = (x1, x2) be an arbitrary vector in R2 and k be an arbitrary scalar. We want to confirm that T(kz) = kT(z).
T(kz) = T(kx1, kx2) = (kx1, kx2)
kT(z) = kT(x1, x2) = k(x1, x2) = (kx1, kx2)
We can see that T(kz) = kT(z), thus satisfying the scalar multiplication property.
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Related Questions
Select the correct answer. Given: is a rectangle with vertices , , , and , where . Prove: is a square. Statements Reasons 1. is a rectangle with vertices , , , and . 1. given 2. units 2. ? 3. units 3. distance formula 4. 4. ? 5. is a square. 5. ? What is the correct order of reasons that complete the proof?
Answers
The correct order of reasons that complete the proof is:
Given
AB = 6 units
BC = 4 units
AC = 4 units
Diagonals are congruent
AC = BD = 4 units
ABCD is a rhombus
ABCD is a square.
Based on the given statements and reasons, let's determine the correct order of reasons to complete the proof that ABCD is a square.
Given: ABCD is a rectangle with vertices A, B, C, and D.
Reason: Given.
AB = 6 units.
Reason: The length of AB is given as 6 units.
BC = 4 units.
Reason: The length of BC is given as 4 units.
AC = 4 units.
Reason: Since ABCD is a rectangle, opposite sides are equal. Therefore, AB = CD = 6 units and BC = AD = 4 units.
Diagonals are congruent.
Reason: In a rectangle, the diagonals are congruent. Therefore, AC = BD.
AC = BD = 4 units.
Reason: From reason 4, we know that AC = 4 units. From reason 5, we know that AC = BD.
ABCD is a rhombus.
Reason: In a rhombus, all sides are equal, and opposite angles are congruent. Since AC = BD = 4 units (reason 6), ABCD satisfies the properties of a rhombus.
ABCD is a square.
Reason: In a square, all sides are equal, and all angles are right angles. Since ABCD is a rectangle (reason 1) and a rhombus (reason 7), it must also be a square.
Therefore, the correct order of reasons that complete the proof is:
Given
AB = 6 units
BC = 4 units
AC = 4 units
Diagonals are congruent
AC = BD = 4 units
ABCD is a rhombus
ABCD is a square.
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Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The circle's radius is 2 units long and the terminal point is (−1.15,−1.64).
The terminal point is how many radius lenghts to the right of the circle's center?
h=
Then, cos−1(h)=
Does the number we get in part (b) give us the correct value of θ?
Therefore, θ=
Answers
Answer:
hello attached below is the sketch of the missing diagram
a) h = 2
b) cos^-1 ( 2 ) = ∞
c ) θ ≈ 215°
Step-by-step explanation:
a) The length ( h ) to the right of the circles center
= h^2 = ( -1.15)^2 + ( -1.64)^2
∴ h = 2
b) cos^-1 ( 2 ) = ∞
c) The value gotten from b does not give us the value of θ
AB = - 1.64
BC = -1.15
AC = 2
sin^-1 ( - 1.64 / -1.15 )
cos^1 ( -1.15 / 2 ) gives us the value of θ
tan^-1 ( -1.64 / -1.15 )
∴ θ ≈ 215°
two hikers walk on the trans-canada trail for 5.0 h and cover 42km what is there average speed for the trip
Answers
Answer:
about 8 km per hour
Step-by-step explanation:
8 kilometers every hour for 5 hours is 40 km wich is very close to 42km. hope this helps
please help i am stuck and trying not to fail lol. also if you can show work pls
Answers
Given:
The figure of rectangle.
To find:
a. The diagonal of the rectangle.
b. The area of the rectangle.
c. perimeter of the rectangle.
Solution:
(a)
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin 30=\dfrac{12}{Hypotenuse}[/tex]
[tex]\dfrac{1}{2}=\dfrac{12}{Hypotenuse}[/tex]
[tex]Hypotenuse=12\times 2[/tex]
[tex]Hypotenuse=24[/tex]
So, the diagonal of the of the rectangle is 24 units.
(b)
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\tan 30=\dfrac{12}{Base}[/tex]
[tex]\dfrac{1}{\sqrt{3}}=\dfrac{12}{Base}[/tex]
[tex]Base=12\sqrt{3}[/tex]
Length of the rectangle is 12 and width of the rectangle is [tex]12\sqrt{3}[/tex]. So, the area of the rectangle is:
[tex]Area=length \times width[/tex]
[tex]Area=12 \times 12\sqrt{3}[/tex]
[tex]Area=144\sqrt{3}[/tex]
So, the area of the rectangle is [tex]144\sqrt{3}[/tex] sq. units.
(c)
Perimeter of the rectangle is:
[tex]P=2(length+width)[/tex]
[tex]P=2(12+12\sqrt{3})[/tex]
[tex]P=24+24\sqrt{3}[/tex]
[tex]P\approx 65.57[/tex]
Therefore, the perimeter of the rectangle is about 65.57 units.
For which color is the difference between the theorectical probability and experimental probability greatest? A. Brown; The experimental probability is 19.52%, and the theoretical probability is 25%. B. Orange; The experimental probability is 18.9%, and the theoretical probability is 15%. C. Yellow; The experimental probability is 16.96%, and the theoretical probability is 20%. D. Green; The experimental probability is 22.7%, and the theoretical probability is 15%.
Answers
Answer: green
Step-by-step explanation:
Solve for x 103 (3x+4)
Answers
X=309 over 412
X=3 over 4
Select the correct answer.
What is the factored form of this expression?
X^2 - 12x + 36
OA. (x+6)^2
OB. (x - 12)(x - 3)
OC. (x-6)^2
OD. (x-6)(x+6)
Answers
Answer:
C
Step-by-step explanation:
since -6 and -6 are factors of 36 that add up to equal -12, the factored form of the expression is (x-6)^2.
Math 1 Sem 1 1 2.1.5 Quiz: Naming Functions Question 4 of 6 When you read S(h) aloud, you can shorten it to "S of h." O A. True O B. False
Answers
Answer: True!
Step-by-step explanation: When you pronounce the function you say it as is. :) Please rate and like thank you.
y = –3x + 7
y = 2x – 8
Answers
Answer:
Step-by-step explanation:
Using the comparison, substitution, and elimination method, the answer is:(x,y)=(3,-2)
When rewriting the equation the answer is:
3x+y=7
2x-y=8
find the value of x in the isosceles triangle shown below
Answers
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex]x=\sqrt{52-4^2}=6[/tex]
X=6
MARK ME BRAINLIEST PLEASE
Which of the fractions is equivalent to 2/5?
Answers
Answer:
4/10, 6/15, 8/20, 10/25
Step-by-step explanation:
what percentage of this shape is shaded?
Answers
Answer:
50%
Step-by-step explanation:
What is the solution set of x2 – 10 = 30x?
{–220, 250}
{–250, 220}
{15 – StartRoot 235 EndRoot, 15 + StartRoot 235 EndRoot}
{–15 – StartRoot 235 EndRoot, –15 + StartRoot 235 EndRoot}
Answers
9514 1404 393
Answer:
(c) {15 -√235, 15 +√235}
Step-by-step explanation:
For solutions p and q, the trinomial is ...
(x -p)(x -q) = x² -(p+q)x +pq
That is, the constant term (-10) must be the product of the roots, and the x-coefficient (-30) must be the opposite of their sum.
The sums of roots in the answer choices are ...
a) 30
b) -30
c) 30
d) -30
We know the sum of roots is 30, so we can eliminate choices 'b' and 'd'.
The product of the roots must be -10, eliminating choice 'a'. Thus, the only viable choice is C.
_____
The product of the roots of C is ...
(15 -√235)(15 +√235) = 15² -235 = -10 . . . . as required
Answer:
C
Step-by-step explanation:
ZABD and ZDBC are supplementary angles.
What is the measure of x?
X = [?]°
DR
X 148
B
>C
AT
Angles are not drawn to scale.
Answers
Answer:
Solution given:
x+148=180°[linear pair]
x=180°-148=32°
x=32° is your answer
Answer:
Solution:
Given,
X+48°=180°
X=180°-48°
X=32°
so,
X=32° answer
hope it is helpful to you
5. Find the surface area of a sphere with
the radius of 1.5 cm.
a. 28.26 cm
b. 7.065 cm
c. 18.84 cm
d. 14.13 cm
Answers
The scatter plot shows the heights ( in inches) and the shoe sizes of eight men. What is the height of the man whose shoe size is 12?
NO LINKS!!!
Answers
Answer: 72 inches
Step-by-step explanation:
Bart owns a neighborhood Kwik-E-Mart. At the end of the day on Wednesday, he counted total receipts in his store of $8,399.70. If the sales tax on food items is 2%, how much merchandise did Bart sell on Wednesday? How much sales tax did he collect?
Answers
Each side length is doubled. What is the AREA of the new figure?
Answers
Answer:
24 square units
Step-by-step explanation:
When the sides are doubled, new figure so obtained will have:
Base (b) = 2*3 = 6 units
Height (h) = 2*4 = 8 units
Area of the figure when each sides are doubled
[tex] = \frac{1}{2} \times b \times h \\ \\= \frac{1}{2} \times 6 \times 8 \\ \\ = 3 \times 8 \\ \\ = 24 \: square \: unite[/tex]
The length of the rectangle is 9 cm.
The perimeter of the rectangle is 31 cm.
(b) Work out the width of the rectangle.
Answers
Answer:
Perimeter = 2(L+W)
31 =2(9+w)
31 =18+2W
31-18=2W
13=2W
W=13/2
W=6.5cm
The list below shows the different choices of pizza at the local pizza shop: Pepperoni: 11 Supreme: 7 Cheese: 6 Hawaiian: 3 Based on these results, what is the theoretical probability of choosing a Hawaiian Pizza?
Answers
Step-by-step explanation:
11 + 7 + 6 + 3 = 27
total amount of pizza = 27
Hawaiian pizza = 3
3/27 = 1/9
Amy buys 22 envelopes for 13p each and pays with a £5 note.
How much change does she get?
Give your answer in pounds, £.
Answers
at his last baseball game, George missed 35% of the pitches thrown at him. based on this information, how many pitches will he miss if he has 40 pitches thrown at him?
Answers
Answer:
14
Step-by-step explanation:
35% of 40
= 35/100 × 40
= (35×4)/10
= 140/10
= 14
A car is traveling at a speed of y miles per hour. which situation would be described by the expression 1.2y?
Answers
nabiha wants to decorate her home for an upcoming party she bought a roll of ribbon from "dollarama" which is 3.2 m long
(a) how many 15 cm of ribbon can be cut from a 3.2m long ribbon
(b) how long is the remaining peice
Answers
Answer:
A = 21
B = 5
Step-by-step explanation:
1 meter = 100 centimeters
This means that she has 320cm of ribbon. Now you need to divide 320 by 15
320/15 = 21.3333333333
So to check your work you could multiply 15 by 21
15 x 21 = 315
This answer is less than 320 so you now know that Nabiha can cut 21 pieces of ribbon that are 15cm long. You also know that the remaining piece is 320 - 315 = 5.
Please award me brainiest! Hope this helps!
Which of the following is not an exterior angle of triangle BHE
Answers
Answer:
I dont know
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
Part 1: f(x)=0 has 0 solutions
Part 2: g(x)=0 has 2 solutions
Part 3: h(x)=0 has 1 solution
I graphed them
HOW LONG IS PQ?
special right triangles khan academy
Answers
Answer:
Step-by-step explanation:
The side opposite to the angle 30 degree in right triangle is half of hypothenuse.
what makes 1/3 x > 12 true
Answers
Answer:
I dont know I am sorry I really had to ask a question and i don't have enough points so sorry you can report me if you want but I really need some
Which numbers between 10 and 20 do not appear in the table at all?
Why don’t they appear?
Answers
Answer:
the answer is 11, 13, 17
Step-by-step explanation:
this is because they do not have any even number that multiplies into them.
Please help no links please help no links
Answers
14x10=140
140/2=70
So you have the area of the triangle
Now you just need to times it by 19 to get the depth
70x19=1330
Answer
1330 inches cubed
:)