Answers
Answer:
Step-by-step explanation:
-1 -1 3
1 -2 -2
The new coordinates of the vertices after a 90° clockwise rotation about the origin are:
[tex]\left[\begin{array}{ccc}-1&1&-3\\1&2&2\\\end{array}\right][/tex]
What occurred when you rotated 90 degrees clockwise?If we rotate a triangle 90° counter clockwise about the origin,
Then if one of its vertices be (x, y), it will be changed to (y, x).
The triangle is given as follows:
[tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\\\end{array}\right][/tex]
To rotate the given triangle 90° clockwise about the origin, we can use the rotation matrix:
[tex]\left[\begin{array}{ccc}cos90^{o}&-sin90^{o}\\sin90^{o}&cos90^{o}\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0&-1\\1&0\\\end{array}\right][/tex]
To apply this rotation matrix to each vertex of the triangle, we multiply it with the coordinate vector of each vertex.
Let's denote the vertices of the triangle as A, B, and C.
A = (-1, -1)
B = (2, -1)
C = (2, 3)
Applying the rotation matrix to each vertex, we have:
[tex]A' = \begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix} \begin{bmatrix} -1 \ -1 \end{bmatrix} = \begin{bmatrix} 1 \ -1 \end{bmatrix}[/tex]
[tex]B' = \begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix} \begin{bmatrix} 2 \ -1 \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}[/tex]
[tex]C' = \begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix} \begin{bmatrix} 2 \ 3 \end{bmatrix} = \begin{bmatrix} -3 \ 2 \end{bmatrix}[/tex]
Therefore, the new coordinates of the vertices after a 90° clockwise rotation about the origin are:
A' = (1, -1)
B' = (1, 2)
C' = (-3, 2)
This can be written as follows:
[tex]\left[\begin{array}{ccc}-1&1&-3\\1&2&2\\\end{array}\right][/tex]
Learn more about the rotating triangle here:
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Related Questions
Can anyone help with this problem??
Answers
Answer:
blue line : y = 3
black horizontal line : y = 0
black vertical line : x = 0
Step-by-step explanation:
it is really simple.
blue line : no matter what value we pick for x, the functional value for y is always 3. and that defines the equation y = 3 + 0*x or simply y = 3.
the same with the black horizontal line. the difference is that y is now always 0. so, y = 0.
plz help i have been asking this question way too much
Answers
Answer:
10/3 or 3 1/3
Step-by-step explanation:
You have 8 bags of groceries in your car. You can carry 5 bags each trip.
How many trips do you need to get all of the groceries from the car to the
house?
Answers
Answer:
2
Step-by-step explanation:
pls give branliest
What is the interquartile range of the data set 115, 98, 118, 102, 96, 90, 125, 94, 85, 100, 104
Answers
Answer:
21
Step-by-step explanation:
1. Re-order numbers from low to high
85, 90, 94, 96, 98, 100, 102, 104, 115, 118, 125
2. Find Q1 and Q3: they are the middle number of top and bottom half of the data
Q1 is 94, Q3 is 115
3. Find IQR
IQR = Q3 - Q1 = 115 - 94 = 21
Which is greater? 2/6 or 4/10?
Answers
4/10 = 1/5
2/6 is greater
Answer:
4/10
Step-by-step explanation:
4/10 = 0.4 = 0.40
2/6 = 0.33
so, 0.40 is greater than 0.33
What is the angle measure of the smaller angle ? (Geometry)
Answers
Answer:
85
Step-by-step explanation:
2x+192=180
2x= -12
x= -6
-6+91= 85
3. How many different ways can the letters in the word grade be arranged?
Answers
Answer:
Six letters---6
Step-by-step explanation:
You Welcome G!
The solution is, the letters in the word GRADE can be arranged in 120 ways.
What is combination?In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
here, we have,
Given that we are to evaluate the number of ways to arrange the letters in the word GRADE,
In the word GRADE, we have 5 distinct letters:
G(1), R(2), A(3), D(4), E(5).
There are 5 letters.
Thus, the number of ways of arranging the letters is evaluated as
5! = 1×2×3×4×5
=120
Hence, the letters in the word GRADE can be arranged in 120 ways.
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What do you call a fake noodle
Answers
Answer:
an impasta
Step-by-step explanation:
sus
Answer: an Impasta
Step-by-step explanation:
Give me brainliest please lol
aria and her two friends met up for dinner. They want to split the cost of dinner evenly between the friends but first had to get the total after adding the tax and tip. Their bill is shown below. The sales tax at this location of Sam’s World is 7.75%. They agreed to leave an 20% tip. The tip is added to the total after the sales tax is added.
The total is 38.96
Estimate the approximate total cost of the bill including tax and tip to the nearest dollar.
A
$50.38
B
$41.98
C
$38.96
D
$8.40
PLEASE HELp
Answers
Answer:
A. 50.38
Step-by-step explanation:
Bill is 38.96. Calculate sales tax: 38.96x.0775=3.02.
38.96 + 3.02=41.98 total before tip
41.98x.20=8.40 tip
41.98 + 8.40=50.38
what is photo synthesis?
Answers
Answer:
Photosynthesis is
Step-by-step explanation:
The process by which green plants and certain other organisms transform light energy into chemical energy. During photosynthesis in green plants, light energy is captured and used to convert water, carbon dioxide, and minerals into oxygen and energy-rich organic compounds.
Hope this answered your question :)
Answer:
the process by which green plants and some other organisms use sunlight to synthesize foods from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a byproduct.
And here is my email address vikrant:
(nobdy else needs this, just vikrant 'k.)
can someone help me im literally so confused
Answers
Answer: 65536a^4 b^2
Step-by-step explanation:
Find the perimeter of a field with the following dimensions:
Length: x^2+3x-1
Width: 2x+3
Answers
Answer:
yo the answer would be 2x^2 +10x +4. I think you are taking the same test I am
I need help lol ,forgot how to do this
Answers
Answer: i don get it
Step-by-step explanation:
Answer:
8.1
Step-by-step explanation:
Please I need help asapppp!
Answers
Answer:
-525 it is now 525 below sea level
Step-by-step explanation:
I'm kinda confused the question is weird to me so I don't know if this is right
You might need: Calculator A scale on a blue print drawing of a house shows that 10 centimeters represents 2 meters. What number of actual meters are represented by 18 centimeters on the blue print?
Answers
Answer:
3.6 meters
Step-by-step explanation:
18/10 x 2 = 3.6
so, 18 centimeters represents 3.6 meters
[tex]\huge\mathfrak\red{solve \: please..} \\ \\ \huge\mathcal\purple{ {2}^{2} + 3 {}^{2} = {?} } \\ \\ \huge\mathfrak\green{asap \: \: ..thanks.}[/tex]
Answers
Answer:
[tex]2^2+3^2[/tex]
[tex]2^2=4[/tex]
[tex]3^2=9[/tex]
[tex]=4+9[/tex]
[tex]=13[/tex]
----------------------
hope it helps..
have a great day!!
PLEASEEEE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
What is the surface area
Answers
Answer:
1190 mm²Step-by-step explanation:
The surface area of a prism is a sum of areas of all of its faces
2×(¹/₂×16×15) + 2×(17×19) + 16×19 =
= 240 + 646 + 304 = 1190 mm²
Help out
Sishsbnxbxbxxnxj
Answers
Answer:
y=-6/5x -8
Step-by-step explanation:
slope is the same as gradient(m) so find the c in the equation y=mx+c using the point (-5,-2) which gives u -8 then substitute values of m and c in that very equation
Answer:
[tex]y=-\frac{6}{5}x-8[/tex]
Step-by-step explanation:
Same process as the other two lol
y= -(6/5)x+b
solve for b by plugging in the required coordinates
-2= -(6/5)(-5)+b
-2= 6+b
-8=b
put it all together
Annika's class raised $800 by selling $5 and $10 movie gift cards. The class
sold a total of 115 gift cards. How many of each type of card did the class
sell?
Answers
Answer:
70 $5 movie gift cards and 45 $10 movie gift cards
Step-by-step explanation:
Betsy's high school is putting on a production of a play as a fundraiser for the school's music programs. A local bank has agreed to allow the school to use a line of credit from which they can withdraw money to pay for the play. Then, any deposits they make at the bank will be applied to the negative balance of the credit account.
The play cost $3,200.00 to produce, and they intend to sell tickets for $10 each. After the play, Betsy will take the ticket proceeds and deposit them with the bank. If 1,007 people attend the play's opening night, what will the balance of the bank account be?
A.
- $3,099
B.
$10,070
C.
$13,270
D.
$6,870
Answers
Answer:
10070//B
Step-by-step explanation:hope this helps <3
EASY MATH PLEASE HELP!! : ) : )
NO LINKS PLEASE
EXPLANATION REQUIRED
A new school is ordering math textbooks. They are 3/4 of an inch thick. How many of these books will fit into a bookshelf that is 2 feet long?
A) 2 books
B) 12 books
C) 26 books
D) 32 books
Answers
Answer:
32 Books
Step-by-step explanation:
You know that the bookshelf is 2 feet long, and you know the book is 3/4 inches thick. To start you have to get a common measurement in this case we will use inches. You already know that 1 foot is 12 inches so 2 feet will be 24 inches. Next all you do is divide the 24 inches by 3/4 inches. This will give you 32 which is the total amount of books that can fit on the bookshelf.
What is the mode for the following set of data?
5, 7, 9, 11, 13, 13
A. 8
B. 9.7
C. 10
D. 13
Answers
Answer:
Hello!
answer: 13
Step-by-step explanation:
The mode is simply just the number that is shown the most in the data set so as you can see 13 is shown the most so 13 is our mode Hope that helps!
A pole that is 12 feet tall casts a shadow that is 9 feet long. At the same time of day, how long is the shadow cast by a tree that is 45 feet tall?
A. 27 ft
B. 29.25 ft
C. 31.5 ft
D. 33.75 ft
Answers
Ten cards numbered 1 through 10 are mixed together and then one card is drawn. Find the probability of each event. Write each answer as a fraction, percent, and decimal. P(less than 5) P(greater than 3) P(odd) P(even) P(not a multiple of 4) P(not 5, 6, 7, or 8) P(divisible by 3)
Answers
Answer:
2/5, 0.4, 40%
7/10, 0.7, 70%
1/2, 0.5, 50%
1/2, 0.5, 50%
4/5, 0.8, 80%
3/5, 0.6, 60%
3/10, 0.3 ; 30%
Step-by-step explanation:
Sample space = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
P(less Than 5) :
Required = (1, 2, 3, 4) = 4 observations
P(less than 5) = 4 / 10 = 2 / 5 = 0.4 = 40%
Greater than 3) = (4, 5,6,7,8,9,10) = 7 observations
P greater Than 3) = 7/10 = 0.7 = 70%
Odd = (1,3,5,7,9) = 5
P(odd) = 5 / 10 = 1/2 = 0.5 = 50%
(even) = (2,4,6,8,10) = 5
P(even) = 5 / 10 = 1/2 = 0.5 = 50%
Not a multiple of 4 = (1,2, 3,5,6,7,9,10) = 8
P(not A multiple of 4) = 8/10 = 4/5 = 0.8 = 80%
not 5, 6, 7, or 8 = (1,2,2,4,9,10).= 6
P(not 5, 6, 7, or 8) = 6 / 10 = 3/5 = 0.6 = 60%
Divisible by 3 = (3, 6, 9) = 3
P(divisible by 3). = 3/10 = 0.3 = 30%
Paula has her own business making cakes for
special occasions. The total price (p) of one
of Paula’s cakes is represented by the equation
p=0.75s +10 , where s is the number of
people the cake serves. What does the .75
represent in this situation and what does the 10 represent in this equation?
Answers
Answer:
Since Paula has her own business of making cakes for special occasions, and the total price (P) of one of Paula's cakes is represented by the equation P = 0.75S +10, where S is the number of people the cake serves, for determine what does the 0.75 represent in this situation and what does the 10 represent in this equation, the following mathematical reasoning must be carried out:
P is the price of the cake
S is the number of servings
Therefore, 0.75 is the value of each serving, which can be variable (the number of servings can vary)
In turn, 10 is the fixed cost of each cake.
A building has three elevators. Each elevator is out of order 10% of the time.
The following set of random numbers represents 20 simulations of the
elevators, with 0 representing a broken elevator and 1,2,3,4,5,6,7,8, and 9
representing a working elevator. In how many of the simulations were all
three elevators working?
Answers
Answer:18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
Each bag of pears weighs 1 kg 160 gram. What is total weight of a sack which contains 5 bags of pears?
Answers
Answer:
5 kg 800 grams
5800g
Step-by-step explanation:
the first step is to convert 1kg to gram
100 kilogram = 1 gram
1kg x 1000 = 1000g
1kg 160 gram = 1000 + 160 = 1160 gram
If 1 sack weighs 1160 g
5 sacks = 1160g x 5 = 5800 gram
or 5800 / 1000 = 5 kg 800 grams
Landon earns 10% commission on his total sales. What must be his total sales in oder to earn a commission of $ 145?
Answers
Answer: [tex]\$1450[/tex]
Step-by-step explanation:
Given
Landon earns a 10% commission on his total sales
Suppose his total sales is x to get a commission of $145 i.e.
[tex]\Rightarrow x\times 10\%=145\\\Rightarrow 0.1x=145\\\Rightarrow x=\$1450[/tex]
Therefore, the amount of total sales must be $1450
Add t to 2 then add 4 to the result
Answers
Answer:
1. 2+t= 2t
2. 2t+4= 2t+4
Hope his right!