Answers
R₀, 270° is the rule that describes the transformation
How to determine the rule that describes the transformation?
Rotation simply means turning. In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through θ° about the origin, the position of the image P' is
a. (-y, x) for θ = 90°
b. (-x, -y) for θ = 180°
c. (y, -x) for θ = 270°
Given the: Triangle RST with vertices R(2, 0), S(4, 0), and T(1, -3). And the image of triangle RST after a rotation has vertices R'(0, -2). S'(0, -4), and T(-3, -1)
From the given vertices it is obvious that the relation between preimage and image is defined as
(x, y) => (y, -x)
Therefore, the rule that describes the transformation is (y, -x) for θ = 270° (i.e. when the figure rotates 270° counterclockwise). So the third option (R₀, 270° ) is the answer.
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Related Questions
Simplify 2.54 + 1.5 × 4
Answers
Evaluate the expression X - 2 + 2(4) - X when x =12
Answers
Answer: 6
Step-by-step explanation: You'll need to substitute x for 12 in the expression, which will be 12 - 2 + 2(4) - 12, and using BODMAS/BIDMAS/PEDMAS (or whatever you use), you should get 6 if you did it correctly.
Answer:
18
Step-by-step explanation:
using bodmas rule by working out brackets first
290 to 490 percent increase how much did it increase
Answers
answer the answer is 200
Step-by-step explanation:
490-290
This question number 7 and I need help
Answers
The product of two numbers exists done by multiplying a number with the other. The product of a number x and 7 exists 7x.
What is meant by product?The result of multiplying two or more numbers together is known as a product in mathematics. A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product.
The outcome of one or more multiplications is referred to as a "product." For instance, the mathematical statement "times equals" would be written with the multiplier, the multiplicand, and their product as the variables.
Let the variable be x
x be a number
So, the product of x and 7 exists calculated as:
Product = 7 × x
Product = 7x
Therefore, the product of a number (x) and 7 exists 7x.
The complete question is:
The product of a number and 7
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Peter and Parker work for a cleaning crew. Peter can clean a room in 15 minutes less time than it takes Parker to do the same job. Working together,
they can clean two rooms in 110 minutes. Approximately how long does it take Peter to clean a room by himself?
Answers
how long does it take Peter to clean a room by himself is[tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
What does "rate" mean mathematically?
A rate is a unique ratio where the two words are expressed in several units.
Let Peter take time to clean 1 room be = t
Let Parker take time to clean 1 room be = t+15
Total Time taken by both to clean to room T= 110
Equation for total time taken to clean 2 room by both
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{T}[/tex]
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{110}[/tex]
By taking LCM
[tex]\frac{2t+15}{t^{2}+15} =\frac{1}{55}[/tex]
By cross multiplication in above equation
[tex]110t+825=t^{2} +15t[/tex]
[tex]t^{2}-95t-825=0[/tex]
Hence the answer is [tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
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A new student, who has had very little experience solving equations algebraically, has just joined your study group. Show and explain all of the steps necessary to solve the equation 2(x + 1) = 6(x – 1) for x. Be sure to include a step for checking the solution.
Answers
The solution of the equation 2(x + 1) = 6(x – 1), is the value of x = 2.
How to Solve an Equation?To solve an equation means to find what the value of the variable of the equation would be that would make the equation true if the value of the variable is plugged into the equation.
The necessary steps taken to find the value of x in the equation, 2(x + 1) = 6(x – 1) are explained below:
2(x + 1) = 6(x – 1) [given]
Apply the distributive property
2x + 2 = 6x - 6
Combine like terms
2x - 6x = -2 - 6
-4x = -8
Divide both sides by -4
-4x/-4 = -8/-4
x = 2
The value of x is 2. To check the solution, plug in the value of x back into the equation:
2(2 + 1) = 6(2 – 1)
2(3) = 6(1)
6 = 6 [true]
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Richard made punch for a party. He used 1\2 cup of pineapple juice, 1\2 cup of ginger ale, and 1\4 cup of white grape juice. How much liquid did he use in the punch? cups
Answers
The liquid that Richard used in the punch is 1 1/4 cups.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Richard made punch for a party. He used 1/2 cup of pineapple juice, 1/2 cup of ginger ale, and 1/4 cup of white grape juice.
The total fraction will be:
= 1/2 + 1/2 + 1/4
= 1 1/4 cups.
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Which of the following is the correct factorization 64x^3+8?
Answers
The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
According to the question,
We have the following information:
[tex]64x^{3} +8[/tex]
The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.
So, we have the following expression:
[tex](4x)^{3} + 2^{3}[/tex]
Now, we can use the following identity to factor the given expression:
[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]
We have a = 8x and b = 2:
(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}
(8x+2) (16[tex]x^{2}[/tex]-16x+4)
Taking 4 as the common factor from the second bracket:
4(8x+2) (4[tex]x^{2}[/tex]-4x+1)
Now, finding the factors of second bracket:
4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)
4(8x+2) {2x(2x-1)-1(2x-1)}
4(8x+2) (2x-1) (2x-1)
4[tex](2x-1)^{2}[/tex] (8x+2)
Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).
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John can clean pools at a constant rate of \(\frac{3}{5}\)
pools per hour. How many pools can John clean in 10
hours?
Answers
Answer:
Step-by-step explanation:
3/5 pool/hr * 10hr = 6 pool
2(x+5)=20 what does x===???????????????????/
Answers
Answer:
x = 5
Step-by-step explanation:
2(x+5) =20 Distribute the 2
2(x) + 2(5) = 20
2x + 10 = 20 Subtract 10 from both sides of the equation
2x = 10 Divide both sides by 2
x = 5
Answer:
5
Step-by-step explanation:
2(x + 5) = 20 Divide both sides by 2
x + 5 = 10
x = 10 - 5
x = 5
What is the answer for -3 > -2x + 7
?
Answers
Swap sides so that all variable terms are on the left hand side. This changes the sign direction.
−2x+7<−3Subtract 7 from both sides.
−2x<−3−7Subtract -7 from −3 to get −10.
−2x<−10Divide both sides by −2. Since −2 is negative, the inequality direction is changed.
[tex]x > \frac{ - 10}{ - 2} [/tex]Divide −10 by −2 to get 5.
x>5( q2 − r2s) ( q4 + q2r2s + r4s2)
Answers
Hope it helps
Members of the student government are planning a movie night on campus. They have asked a random sample of students which of four movies the student would prefer. Here are the results Movie A- 31 students, Movie B- 27 students, Movie C- 34 students, Movie D- 28 students. There are 900 students total on campus. Based on the above information, how many students on campus would we expect to prefer Movie C? Round your answer to the nearest whole number. Do not round any intermediate calculations
Answers
There are 255 students who prefer Movie C.
In the given case, the total number of students in the campus = 900
Number of students in the random sample :
= 31 + 27 + 34 + 28
= 120
Number of students who prefer to watch movie C in the chosen sample:
= 34
To get number of students who would prefer to watch the movies C in the total population of 900, we can extrapolate the data from the chosen sample to the entire population.
Thus, number of students expected to prefer movie C in the campus =
34/120 × 900
= 255
Hence the expected number of students are 255.
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please if you can help me that would be very apricated :)
Answers
Answer: b
Step-by-step explanation:
Box A has a length of 5 feet, height of 1 foot, and width of 3 feet. Box B has a length of 4 feet, height of 3 feet, and width of 2 feet. Box C has a length of 7 feet, height of 2 feet, and width of 1 foot. Box D has a length of 3 feet, height of 3 feet, and width of 3 feet.
Lucas wants to use the box with the greatest volume. Which shipping box should he use?
Box
Answers
Lucas will be using the shipping box D as it is the box with the greatest volume of 27ft³
Volume of a rectangular boxThe volume of a rectangular box is calculated by multiplying its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.
volume of box A = 5ft × 3ft × 1ft
volume of box A = 15ft³
volume of box B = 4ft × 2ft × 3ft
volume of box B = 24ft³
volume of box C = 7ft × 1ft × 2ft
volume of box C = 14ft³
volume of box D = 3ft × 3ft × 3ft
volume of box D = 27ft³
Therefore, the shipping box with the largest volume is box D with 27ft³
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Answer:
Step-by-step explanation:
FEEL ME ITS D
ITS D
THE ONE WITH THE 333
Identify the values of the variables. Give your answers in simplest radical form. Help!
Answers
Considering the right angle triangle given the values of the variables are
n = 2√3k = 4√3How to determine the values of the variablesInformation from the question
right angle triangle
The values of the variables is worked using SOH CAH TOA
The right angle triangle of sides as described below
hypotenuse = k
opposite = n
adjacent = 6
The variable n is solved using tan, TOA, the angle is 30
tan 30 = Opposite / Adjacent
tan 30 = n / 6
tan 30 * 6 = n
n = 2√3
The variable k is solved using cos, CAH, the angle is 30
cos 30 = Adjacent / Hypotenuse
cos 30 = 6 / k
k = 6 / cos 30
k = 4√3
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Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.
line ED =45
line DF = 27
line EF = 36
sin D =
sin E =
cos D =
cos E =
Answers
The value of each term is
sin D = 4/5sin E = 3/5cos D = 3/5cos E = 4/5The length of the line ED = 45 units
The length of the line DF = 27 units
The length of the line EF = 36 units
Here we have to use the trigonometric function
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
Substitute the value in the equation
sin D = Opposite side / Hypotenuse
= 36/45
= 4/5
sin E = Opposite side / Hypotenuse
= 27/45
= 3/5
cos D = Adjacent side / Hypotenuse
= 27/45
= 3/5
cos E = Adjacent side / Hypotenuse
= 36/45
= 4/5
Hence, the value of each term is
sin D = 4/5sin E = 3/5cos D = 3/5cos E = 4/5Learn more about trigonometric function here
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Please help!! See screenshot attached below (100 pts)
Answers
Answer:
f(2) = 0
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
Therefore, applying the factor theorem, if (x - 2) is a factor of a polynomial f(x) then f(2) = 0.
Convert a person's weight of 122 pounds to kilograms. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
Ihs ✓
Answers
The conversion factor for lb to kg is:
1 lb = 0.453592 kg
=122 x 0.453592 = 55.338224 kg
Explanation of Solution:
Put very simply, a conversion factor is a number that can be used to change one set of units to another, by multiplying or dividing it. So when we need to convert 122 pounds into kilograms, we use a conversion factor to get the answer.
The conversion factor for lb to kg is:
1 lb = 0.453592 kg
Now that we know what the conversion factor is, we can easily calculate the conversion of 122 lb to kg by multiplying 0.453592 by the number of pounds we have, which is 122.
122 x 0.453592 = 55.338224 kg
So, the answer to the question "what is 122 pounds in kilograms?" is 55.338224 kg.
What is Pound?
A pound is smaller than a kilogram. I know that a lb is smaller than a kg because of something called conversion factors.
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Please help me I need help
Answers
Answer:
p = 20
Step-by-step explanation:
[tex]\rm \implies \dfrac{p}{2} - 9 = 1 \\ \\ \rm \implies \dfrac{p}{2} - 9 + 9 = 1 + 9 \\ \\ \rm \implies \dfrac{p}{2 } = 10 \\ \\ \rm \implies \dfrac{p}{ \cancel{2}} \times \cancel{2} = 10 \times 2 \\ \\ \rm \implies p = 20[/tex]
3
8
13
24
53
123
213
Answers
Answer:
321 is the next number that comes in the calculator.
plot 5/3 and its opposite on the number line
Answers
The numbers are plotted in the attached graph.
What is a number line?A number line is a representation of real numbers in the form of a graded straight line.
Note that 5/3 is approximately equal to 1.7.
Similarly, -5/3 is approximately equal to -1.7.
Now, use the number line to mark the points -1.7 and 1.7, the numbers lie near -2 and 2 respectively.
The numbers are plotted in the attached graph.
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Colton made a scale drawing of a city park. In real life, the soccer field is 90 meters long.
It is 18 millimeters long in the drawing. What scale did Colton use?
Answers
By using unitary method it is obtained that -
Scale used my Colton = 1 : 500
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here unitary method is used
18 mm long field in the drawing is equivalent to 9000 mm long field in real
1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real
1 mm long field in the drawing is equivalent to 500 mm long field in real
Scale used by Colton 1 : 500
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11/7 Thursday Math Math Hw. Fractions
Answers
Answer:
96, $ 144
Step-by-step explanation:
For the equation (x) = –3x2 + 2x – 1, explain if the graph will be pointing upward or downward. **20 POINTS**
Answers
Answer:
Step-by-step explanation:
the answer is "downward". If you say "why", it is because of the degree coefficient.
in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.
Parallel Lines relay race page C
Can someone lmk the answers
Answers
The value of the angle regarding the parallel lines are:
1. x = 14
2. x = 9
3. x = 17
4. x = 5
How to calculate the values?1. Lines 'l' and 'm' are the parallel lines and a transversal line is intersecting these lines.
(9x + 13)° = (12x - 29)° [Alternate interior angles]
9x - 12x = -29 - 13
-3x = -42
Divide
x = 14
2). By substituting x = 14 in the box.
(13x + 5)° + (8x - 14)° = 180° [Consecutive interior angles]
21x - 9 = 180
21x = 189
Divide
x = 189/21
x = 9
3). By placing x = 9 in the box,
(5x + 52)° = (9x - 16)° [Corresponding angles]
5x - 9x = -52 - 16
-4x = -68
x = 17
4). By placing x = 17 in the box,
(10x + 17)° = (12x + 7)° [Alternate exterior angles]
10x - 12x = -17 + 7
-2x = -10
x = 5
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12. Use the coordinate grid below to answer the question.
What are the coordinates of Point A?
Answers
Answer: (7, 12)
Step-by-step explanation:
The x-coordinate is 7.
The y-coordinate is 12.
Thus, the coordinates are (7, 12).
The photo added is the question.
Answers
By taking some products we will see that the total number of cupcakes ordered is 6 cupcakes.
How many cupcakes are ordered?Here we want to see how many cupcakes this person is ordering. We know that orders 9 halves of a cupcake for the family, plus a quarter of a cupcake for each of the 6 friends.
The total number of cupcakes is given by the order for the family plus the order for the friends.
The order for the familiy is given by the product:
9*(1/2) = 9/2 = 4.5
That is 9 times 1/2 of a cupcake, so for the family the person orders 4.5 cupcakes.
For the friends the person orders 6 times 1/4 of a cupcake, so now we have the product:
6*(1/4) = 6/4 = 3/2 = 1.5
If we add these two numbers we get the total number of cupcakes:
4.5 + 1.5 = 6
The person ordered 6 cupcakes.
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What is the quotient of 30 and 0.08
Answers
Answer:
30 divided by 0.08 will get you 375
Step-by-step explanation:
What are the corresponding angle pairs in the picture below?
Answers
The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.
From the given figure, we need to identify the corresponding angles.
What are corresponding angles?The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.
From the figure, ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7 are the corresponding angles.
The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.
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