Which transformation is shown by the coordinates below? L (-1, 9) M (-8, 8) N (-3, 5) L '(- 9, -1) M' (- 8, -8) N '(- 5, -3) A. Reflection over the x-axis / B. Translation 8 units left and 8 units down / C. Rotation 90 degrees clockwise / D. Rotation 270 degrees clockwise
Answer:
D. Rotation 270 degrees clockwise.
Step-by-step explanation:
The transformation used in the coordinates below was a rotation 270 degrees clockwise, whose definition is:
[tex](x', y') = (r\cdot \cos (\theta - 270^{\circ}), r\cdot \sin (\theta -270^{\circ}))[/tex]
Please note that clockwise rotation is represented by the minus sign.
Where [tex]r[/tex] is the norm of original point, defined as:
[tex]r =\sqrt{x^{2}+y^{2}}[/tex], [tex]\forall \,x,y\in \mathbb{R}[/tex]
And [tex]\theta[/tex] is the direction of the point centered at origin and with respect to +x semiaxis, measured in sexagesimal degrees:
[tex]\theta = \tan^{-1} \frac{y}{x}[/tex]
Now we proceed to prove the statement:
[tex]L (x, y) = (-1, 9) \longrightarrow L'(x,y)[/tex]
Norm
[tex]r = \sqrt{(-1)^{2}+9^{2}}[/tex]
[tex]r = \sqrt{82}[/tex]
Direction
The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:
[tex]\theta = \tan^{-1}\left(\frac{9}{-1} \right)[/tex]
[tex]\theta = 96.340^{\circ}[/tex]
Rotation
[tex]L'(x,y) = (\sqrt{82}\cdot \cos (96.340^{\circ}-270^{\circ}),\sqrt{82}\cdot \sin (96.340^{\circ}-270^{\circ}))[/tex]
[tex]L'(x,y) = (-9, -1)[/tex]
[tex]M(x,y) = (-8,8) \longrightarrow M'(x,y)[/tex]
Norm
[tex]r = \sqrt{(-8)^{2}+8^{2}}[/tex]
[tex]r = \sqrt{128}[/tex]
Direction
The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:
[tex]\theta = \tan^{-1}\left(\frac{8}{-8} \right)[/tex]
[tex]\theta = 135^{\circ}[/tex]
Rotation
[tex]M'(x,y) = (\sqrt{128}\cdot \cos (135^{\circ}-270^{\circ}),\sqrt{128}\cdot \sin (135^{\circ}-270^{\circ}))[/tex]
[tex]M'(x,y) = (-8, -8)[/tex]
[tex]N(x,y) = (-3,5)\longrightarrow N'(x,y)[/tex]
Norm
[tex]r = \sqrt{(-3)^{2}+5^{2}}[/tex]
[tex]r =\sqrt{34}[/tex]
Direction
The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:
[tex]\theta = \tan^{-1}\left(\frac{5}{-3} \right)[/tex]
[tex]\theta = 120.964^{\circ}[/tex]
Rotation
[tex]N'(x,y) = (\sqrt{34}\cdot \cos (120.964^{\circ}-270^{\circ}), \sqrt{34}\cdot \cos (120.964^{\circ}-270^{\circ}))[/tex]
[tex]N'(x,y) = (-5, -3)[/tex]
Hence, the correct answer is D.
Hewp me pwease :( *insert puppy dog eyes*
11 + (−7)^2−9
Answer:
51
Step-by-step explanation:
11+(-7)^2-9 would be
11+49-9 (49 because 7^-2 = 49)
60-9 = 11
Answer:
51
Step-by-step explanation:
According to PEMDAS, the first step would be to take care of the exponents. -7 times -7 is positive 49, so the equation would look like this:
11+49-9 From there, just add and subtract as normal!
60-9
51
Hope this helps!
Select all values that make the equation true.
2(x - 8) = x + 5x
X = -4
X = -16
X = -2
X = 0
Answer:
the only Answer is -4
Step-by-step explanation:
hope this helps
Three friends entered a race around a track. Edward takes 6 minutes to run one lap. Bernie takes 3 minutes to run one lap and it takes Freddie 5 minutes to run one lap. If all three friends begin the race at the same time, how many minutes will it take for all three friends to be at the starting point again?
Answer:
It will take 30 minutes
Step-by-step explanation:
Here, we want to calculate the time it will take for the three friends to be at the starting point again
What we do here is to note the time it will take for each of the three friends to run a lap
That will be 6 , 3 and 5
What we now need to know the time is to find the lowest common multiple of the three amount of time
The lowest common multiple of 6,3 and 5 is 30
So the amount of time it will take the friends to be at the starting point again is 30 minutes
DUE SOON
evaluate -3 1/5 + 7 3/5 =
-5 +2 - 8 -(-14)= show work pls
(2x-27)
(x+2)
What is x?
Answer:
7
Step-by-step explanation:
do the math
The formula F=95C+32 changes a temperature reading from the Celsius scale C to the Fahrenheit scale F. What is the temperature measured in degrees Fahrenheit when the Celsius temperature is 50°C?
A. 42°F
B. 90°F
C. 58°F
D. 122°F
Answer:
D, 122°F
Step-by-step explanation:
°F = 9/5°C + 32
°F = 9/5(50) +32
°F = 90 + 32
°F = 122
How many hours will you have to work each weekend day to have a 33 hour work week? Assume you don't work during the weekdays.
Which graph best represents the function y = - 1/2 (x +4)?
Answer:
y=-1/2x-2
Step-by-step explanation:
simplify the expression to get the equation in slope intercept form, and find the graph that fits it
The regular price of a baseball hat is $16.85. If Emesto buys the baseball hat on sale for 20% off the regular price, how much change will be
receive after paying with $20?
Answer:
$ 6.52
Step-by-step explanation:
marked price =16.85
discount 20%=3.37
net payable .=.13.48
Amount paid==$ 20
payable .=====13.48
balance to receive=$ 6.52
I need help with 15.
Answer:
x = 7
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)
a projectile is thrown upwards from an initial height of 1584 feet so that it's distance above the ground after t seconds is modeled by the given function.
h(t)=-16t^2+480t+1584.
what is the maximum height it will reach?
Answer:
5184 ftStep-by-step explanation:
Given
A quadratic function
h(t)= -16t^2+480t+1584.Its maximum is its vertex
Vertex formula for ax^2 + bx + c is
x = -b/2aApplying this to our function
t = -480/2(-16) = 15Maximum height is reached after 15 seconds and is
h(15) = -16*15^2 + 480*15 + 1584 = 5184 ft1 + 216 = (a + b)(a2 + ka +36), what does k equal?
PLEASE ANSWER NOW NOW NOW
Answer:k=−a3−a2b−36a−36b+217/a2+ab
Step-by-step explanation:Step 1: Flip the equation.
a3+a2b+a2k+abk+36a+36b=217
Step 2: Add -a^3 to both sides.
a3+a2b+a2k+abk+36a+36b+−a3=217+−a3
a2b+a2k+abk+36a+36b=−a3+217
Step 3: Add -a^2b to both sides.
a2b+a2k+abk+36a+36b+−a2b=−a3+217+−a2b
a2k+abk+36a+36b=−a3−a2b+217
Step 4: Add -36a to both sides.
a2k+abk+36a+36b+−36a=−a3−a2b+217+−36a
a2k+abk+36b=−a3−a2b−36a+217
Step 5: Add -36b to both sides.
a2k+abk+36b+−36b=−a3−a2b−36a+217+−36b
a2k+abk=−a3−a2b−36a−36b+217
Step 6: Factor out variable k.
k(a2+ab)=−a3−a2b−36a−36b+217
Step 7: Divide both sides by a^2+ab.
k(a2+ab)
a2+ab
=
−a3−a2b−36a−36b+217
a2+ab
k=
−a3−a2b−36a−36b+217
a2+ab
lan has $6,000. He wants to buy a car within $1,500 of this
amount. What is the price range of the car he wants to
purchase?
f. x2 $4,500 or x 2 $7,500 g. $4,500 2 x 2 $7,500
h. x < $4,500 or x = $7,500 j. $4,500 < x < $7,500
Answer: $7,500
Step-by-step explanation:
Use the graph to answer the question.
Which rational function is shown on the graph?
y
O Rx) = x+1
fa
x²+1
f(x) =
x + 1
Ax) = x + 1
10
10
O fx) =*+1
Answer:
C. f(x)=x-1/x+1
Step-by-step explanation:
edge2020
Functions can be represented by tables and equations
The function represented by the table is f(x) = x + 1
From the table, we have the following ordered pairs
(x,y) = (-1,0) (0,1) (1,2) and (2,3)
Notice that the difference between the x and y values is 1.
So, we have:
y - x = 1
Add 1 to both sides
y = x + 1
Express as a function
f(x) = x + 1
Hence, the function represented by the table is f(x) = x + 1
Read more about linear functions at:
https://brainly.com/question/15602982
13+7²÷7/9-20÷4-16 equals
Answer:
45
Step-by-step explanation:
12r-5=
what is the anser to this problem
solve 2x−3y=−1 , 3x+4y=24
Which could be the result of compressing the graph of y = -8x – 12 and reflecting it across the horizontal line
containing the y-intercept of the function?
A)y = -2x - 12
B)y = -4x - 12
C)y = 2x - 12
D)y = 3x - 12
E)y = 16x -12
Answer:
C or D
Step-by-step explanation:
Plzz help me!!!!!!!!!!
Answer:
50
Step-by-step explanation:
HELP PLEASE
Which expression would be easier to simplify if you used the associative
property to change the grouping?
A. 4+ (1.2+(-0.2))
B. (2+ $) + 4
C. 85+ (120 + 80)
O D. (-40+ (60)] + 52
Answer:
c
Step-by-step explanation:
im not for sure but i think its c
Answer:b
Step-by-step explanation:
i need some help ill give brainly
Answer:
Step-by-step explanation:
El valor de una casa es de $655 000 al contado, pero al venderla a plazos se le carga 25.5% de su precio. ¿Cuál es el costo final de la casa si se vende a plazos?
Answer:
la respuesta seria,487,975
Step-by-step explanation:
Si resta 655,000 - 25.5% entonces la respuesta es 487,975 dólares con el plazo se le carga.
Espero que esto haya ayudado :)
The price when selling on installments be $822025.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is that the value of a house is $655,000 in cash, but when selling it on installments, you are charged 25.5% of its price.
Assume the price when selling on installments be $x. Then, we can write new price as -
[x] = 655000 + {25.5% of 655000}
[x] = 655000 + {25.5/100 x 655000}
[x] = 655000 + {25.5 x 6550}
[x] = 655000 + 167025
[x] = $822025
Therefore, the price when selling on installments be $822025.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
{Question in english would be
The value of a house is $655,000 in cash, but when selling it on installments, you are charged 25.5% of its price. What is the final cost of the house if it is sold in installments?}
A pool gained 10 gallons of water on Friday due to rain. How could the owner of the pool bring the water level back to its previous level? Select three that apply. A Let 10 gallons of water evaporate. B Add 10 gallons of water with a hose. C Drain 10 gallons of water from the pool. D Increase the amount of water by 10 gallons due to rain. E Let her kids play in the pool and splash out 10 gallons of water. F Fill 10 old milk gallons with water and dump them into the pool.
Answer:
A, C, and E
Step-by-step explanation:
we want to eliminate 10 gallons of water, not add 10 gallons
What necessary information is missing from this formula page?
W-work F-force x-distance
Work = force(distance) W = Fx
a. Formula numbers
C.
Formula origin
b. Formula title
d. All of these
Please select the best answer from the choices provided
A
B
OOOO
С
D
Answer:
B. formula title
Step-by-step explanation:
i got it right
PLEASE HELP MEEE!!!!!
Answer:
use photmath or sum
Step-by-step explanation:
Answer:
a. given
b. addition property of equality
c. multiplication property of equality
Solve c = ab? for b.
Answer:
b = c/a
Step-by-step explanation:
Line perpendicular to y = -2x - 7 when it passes the points (-2,-3)
Answer:
The line is y = 1/2x - 2
Step-by-step explanation:
The required line will have a slope of -1/-2 = 1/2.
Using the point slope form of a line:
y - (-3) = 1/2(x - (-2))
y + 3 = 1/2x + 1
y = 1/2x - 2.
Brad jarred 12 liters
of jam after 2 days.
How much jam did
Brad jar if he spent 3
days making jam?
Answer:
18 liters
Step-by-step explanation:
We can use ratios to solve
12 liters x liters
----------- = -----------
2 days 3 days
Using cross products
12 *3 = 2x
36 =2x
Divide by 2
36/2 = 2x/2
18 =x
18 liters
Find the y-intercept of the line which passes through (-2,-2) and (2,-4).
Answer:-4,2
Step-by-step explanation: