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.
Please help
Dion bought tickets for Fun Park so that he and his friends would each have the same number of tickets. There are enough tickets so that each person can
ride the go-carts once, play video games three times, and play laser tag twice.
When Dion purchased the tickets for himself and his eight friends, he realized
that he could purchase ticket books, individual tickets, or a combination of
books and individual tickets. Dion figured out the cheapest way to buy tickets for his
group. What was the cheapest way and what was the total cost?
Answer:
25
Step-by-step explanation:
What is an equation of the line that is parallel to y = 9- 4x and passes through (0, 7)
Answer:
y = -4x + 7
Step-by-step explanation:
Since they are parallel they must have the same gradient which is -4
[tex]y = mx + c[/tex]
m = -4
x = 0
y = 7
7 = -4 × 0 + c
c = 7
[tex]y = - 4x + 7[/tex]
A boat has a speed of 9 mph in Coldwater. It takes about four hours to travel upstream but only two hours to travel the same distance down stream. Which equation can be used to find C, the speed of the current in miles per hour?
what is a point that must lie on the line representing a proportional relationship with a proportionality constant of 8.
Answer:
linear equation?
Step-by-step explanation:
FIRST CORRECT ANSWER GETS BRAINLIEST, 43 ISNT THE ANSWER THANKS
Step-by-step explanation:
10+2+2+7+5+3+8+8= 21+24= 45units
Write an equation for the parabola with the vertex (0,0) and focus (5,0)
Answer:
Step-by-step explanation:put ha times 4 then divide it by ha 23Paul spent 1/4 of his money on food and another 3/10 of his money on soda. If he had 5 dollars to begin , how much money does he have left?
What is the midpoint of a segment with endpoints at (3,5) and (7,7)
Answer:
5,6
Step-by-step explanation:
its a guesssssssssssssssssssssss
1/5 X– 5 = 15
I have no clue how to do this please help
I don't know where you got 15 from.
Answer: -1
Step-by-step explanation:
Multiply
1/5 × ( −5 ) = -5/5
Simplify
-5/5− = -1
Answer:
x=100
Step-by-step explanation:
1/5x -5 =15
-5
+5
___
0
then u do
1/5 divided by 20 =100
and the 1/5 cancel out and makes it only x so u drop it and it the answer will be
x=100
Quadrilateral JKLM is dilated by a scale factor of 2 with a center of dilation at the origin to form quadrilateral J' K’ L’ M’
What are the coordinates of point J ?
A.(2,2)
B.(4,6)
C.(6,2)
D.(6.4)
Help FASTTT‼️‼️‼️‼️
The answer is
A.(2,2)
The new coordinates of point J' of the quadrilateral J' K’ L’ M’ is option (D) (6,4) is the correct answer.
What is transformation of dilation?Dilation is a kind of transformation in which an object is resized based on a scale factor. Dilation is the process of enlarging or reducing the size of a geometrical object without changing its shape.
For the given situation,
Quadrilateral JKLM is dilated by a scale factor of 2 with a center of dilation at the origin to form quadrilateral J' K’ L’ M’.
To dilate the figure by a factor of 2, we need to multiply the x and y-value of each point by 2.
Here the coordinates of J is (3,2).
The dilation factor is 2, so multiply both the x and y value by 2.
Thus x value is
[tex]3(2)=6[/tex]
and y value is
[tex]2(2)=4[/tex]
Hence we can conclude that the new coordinates of point J' of the quadrilateral J' K’ L’ M’ is option (D) (6,4) is the correct answer.
Learn more about transformation of dilation here
https://brainly.com/question/17102666
#SPJ2
Determine the domain of the function (f of g)(x) where f(x)=1/ x+3, g(x) =2/x.
Answer:
(-infinity, -2/3)u(-2/3,0)u(0, infinity)
Step-by-step explanation:
since it is asking for f(g(x)) we plug g into x which looks like:
f(2/x)
now we plug that into the f(x) equation for all of the x's because that is what replaced the x so:
1/(2/x)+3
we look at the denominator so we can pull the 2/x+3 out and set it equal to zero, therefore solving for x
this gives us -2/3
and we get the 0 from g(x) 's denominator
that should be correct and hope this helps!
Write the equation in standard form.
5−3(x−2y)=1−5x
Answer:
2x+6y=-4
Step-by-step explanation:
The length of the side of a regular nonagon is 7.86cm. Evaluate the perimeter of the nonagon.
Answer: 70.74
Step-by-step explanation:
A Nonagon has 9 equal sides, and each side of the given is 7.86
So 7.86 multiplied by 9 is 70.74
Given g(x) = 3x + 8 , what is the value of g(− 4) ?
Answer:
- 4
Step-by-step explanation:
Step 1:
g ( x ) = 3x + 8 Function
Step 2:
g ( x ) = 3 ( - 4 ) + 8 Input x
Step 3:
g ( x ) = - 12 + 8 Multiply
Answer:
g ( x ) = - 4 Add
Hope This Helps :)
Answer:
g(-4) = -4
Step-by-step explanation:
So we are given the function g(x) = 3x + 8 and we are asked to find g(-4). To find g(-4), we would have to plug in -4 for x in the equation for g(x).
g(-4) = 3(-4) + 8 = -12 + 8 = -4
So g(-4) = -4.
I hope you find my answer and explanation to be helpful. Happy studying.
Ok so the mass of a proton is 0.000000000000000000000000001672622 how do I make this in scientific notation
Answer:
1.7 x 10^-27
Step-by-step explanation
Move the decimal to the right until it's a single digit number, because you are moving it to the right, it would be a negative number. If you are able to round up then please do. Remember to check your significant figures if you're in chemistry.
What is the remainder of 832 divided by 77?
Answer:
[tex]10\frac{62}{77}[/tex]
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Answer:
62
Step-by-step explanation:
find it out then you see what is left after the question is through
(8 x __) x 7 = 8 x (9 x 7)
Answer:
the answer in the blank is 9
Step-by-step explanation:
an average student spend 4½ minutes to read one page of a book. how much time will he need to read 5½ pages?
Answer:
About 24.75 minutes or 24 3/4 minutes
Step-by-step explanation:
Kali had a total of 21 balloons at her birthday party. The ratio of blue balloons to green balloons is shown in the tape diagram.
Answer:
there were 12 blue balloons at Kali’s party
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
1. Here is a polygon. Draw a scaled copy of the polygon using a scale factor of 1/2.
The scale of a map says that 8 cm represents 5 km.
What distance on the map (in centimeters) represents an actual distance of 8 kilometers?
Must show your math thinking on the sketchpad.You may use a calculator, but must show the calculations you used.
Answer: For the first question it is basically half of the polygon.
Step-by-step explanation:
If you count the units, for example one of the side is 4 units. What is half of 4. It is 2
Is the square root of 16.45 a rational number or irrational number?
Answer:
Irrational
Step-by-step explanation:
The square root of 16.45 would be a number that will never end, making it irrational.
Answer:
irrational
Step-by-step explanation:
4.05585995813
does not terminate or repeat
not an integer
The cheerleading squad received 1/4 of the total sales of foam fingers and pom-poms at a pep rally. The squad received $258 in sales for the foam fingers and a total overall in sales of $136.75. What was the value of pom-pom sales?
Answer:102.56
Step-by-step explanation:136.75 - 25% = 102.56
25% of 136.75 = 34.19
9. Let p be "an animal is a dog" and let q be "an animal is a golden retriever." Write the conditional statement.
Then decide whether it is true or false.
a. If an animal is a golden retriever, then it is a dog; true
b. If an animal is not a golden retriever, then it is not a dog; false
C. If an animal is a dog, then it is a golden retriever; false
If an animal is not a dog, then it is not a golden retriever; true
Answer:
C. If an animal is a dog, then it is a golden retriever; false
Step-by-step explanation:
Logical reasoning is an important aspect of mathematics.
The conditional statements in the question are represented by the letters p and q. The if-then statement in which the statement p will lead to a conclusion in q is a glaring characteristic of conditional statements. A conditional will be held to be true unless a statement that is true has a false conclusion derived from it.
In the question above, the conditional statement is; If an animal is a dog, then it is a golden retriever. We can clearly see that this conclusion is false.
6 is greater than or equal to 9, is that the same thing as ALL REAL NUMBERS?
Answer:
No it is not the same
Step-by-step explanation:
A real number is any number, positive or negative, whole number or decimal.
(EX) 1, 1.00567, -2, -2.659365
Any number!
A candy store owner has chocolate candies worth $2.50 per pound and sour candies worth $0.90 per pound. How much of each kind of candies should she combine to get 60 lb of mixed candies worth $1.70 per pound? (Include units with your numerical answers.)
Answer:
Weight of chocolate candies = 30lbs
Weight of sour candies = 30lbs
Step-by-step explanation:
We are told in the question that :
Chocolate candies worth $2.50 per pound
Sour candies worth $0.90 per pound. How much of each kind of candies should she combine to get 60 lb of mixed candies worth $1.70 per pound?
Let x represent the number of pounds of chocolate candies
Let 60 - x represent the number of pounds of sour candies
Hence, we have the equation
x × $2.50 + (60 - x) × $0.90 = 60 × $1.70
= 2.5x + 54 - 0.9x = 102
Collect like terms
2.5x - 0.9x = 102 - 54
= 1.6x = 48
x = 48/1.6
x = 30 lbs
x represent the number of pounds of chocolate candies,
60 - x represent the number of pounds of sour candies
= 60 - 30
= 30lbs
Weight of chocolate candies = 30lbs
Weight of sour candies = 30lbs
Therefore, she should combine 30lbs of chocolate candies and 30lbs of sour candies to get 60 lb of mixed candies worth $1.70 per pound.
A hospital stores one type of medicine in 2-decagram
containers. Based on the information given in the
box above, how many l-milligram doses are there in
one 2-decagram container?
A) 0.002
B) 200
C) 2,000
D) 20,000
Answer:
There are 20,000 milligrams in one 2-decagram container . Thus option D is correct.
Step-by-step explanation:
The given information is one type of medicine in 2 decagram container.
Here, we know ,
1 decagram = 10 grams
and, 1000 milligrams =1 gram
now -: 2 decagram = 2 × 10grams {since 1decagarm = 10 grams }
= 20 grams .
then , = 20× 1000milligrams {since 1 gram = 1000 milligrams}
=20,000 milligrams .
Hence, the correct option is D that is 20,000 milligrams .
My age is 9 years, My sister is half of my age. Now I'm 49 years, How old is my sister?
Answer:
i think it is 24
the sum of two consecutive integers is -35. Name the integers
if u pour all the liquid in a cone into a cylinder with the same height and radius then you will fill half of the cylinder with liquid
Answer:
No, the liquid will not fill half of the cylinderStep-by-step explanation:
The volume of a cylinder is 3 times bigger than a cone with equal radius and height
To know this we have to compare the volumes of both solids first.
Let us assume the height and radius of the cone and radius are
6 and 2 mm respectively
so that the volume of a cone is given as
Volume of cone= 1/3 πr^2h
and the volume of cylinder is given as
Volume of cylinder= πr^2h
1. Volume of cone= 1/3 πr^2h
Volume of cone= 1/3 *3.142*(2)^2(6)
Volume of cone= 75.408/3
2. Volume of cylinder= πr^2h
Volume of cone= 3.142*(2)^2(6)
Volume of cone= 75.408
From the analysis the volume of a cylinder is three times bigger the volume of a cone with similar radius and height
Large and small cans of peanuts were sold at a school fundraiser. One student sold
three small cans and nine large cans of peanuts for a total of $75. Another student
sold five small cans and seven large cans of peanuts for a total of $69. What is the
cost of the small and large cans of peanuts?
A Small can for $6.29 and large can for $7.00
B Small can for $4.86 and large can for $6.00
C Small can for $4.00 and large can for $7.00
D Small can for $7.00 and large can for $9.00
Answer:
the answer is c.
Step-by-step explanation:
4 x 5 + 7 x 7 = 69
4 x 3 + 7 x 9 = 75
Cost is small can for $4.00 and large can for $7.00.
What is the system of equation?One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Let S be the number of small cans and L be the number of large cans.
According to the question,
One student sold three small cans and nine large cans of peanuts for a total of $75.
That means the equation is ;
3S + 9L = 75 {equation 1}
And similarly for another student;
5S + 7L = 69 {equation 2}
Now we have two system of the equation.
3S + 9L = 75 {equation 1}
5S + 7L = 69 {equation 2}
Using elimination process,
we multiply 5/3 to equation 1,
5S + 15L = 125
And subtract equation 1 to the equation 2,
we get L = 7 and S = 4
Therefore, small can for $4.00 and large can for $7.00
To learn more about the system of equation;
brainly.com/question/13729904
#SPJ2