What are the coordinates of the point (-9, 4) after a 90 degree rotation followed by a translation 3 units right?
Answers
The coordinates of the point (-9, 4) after a 90 degree rotation followed by a translation 3 units right are (8,9) (for clockwise rotation) and (0,-9) (for counterclockwise rotation)
How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?Let the point be having coordinates (x,y).
Case 1: If the point is in first quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 2: If the point is in second quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 3: If the point is in third quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 4: If the point is in fourth quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 5: For points on axesYou can take that point in any of the two surrounding quadrants. Example, if the point is on positive x axis, then it can taken as of first quadrant or fourth quadrant.
Case 6: On originNo effect as we assumed rotation is being with respect to origin.
For this case, the point (-9,4) (present in second quadrant) is rotated by 90 degrees.
This rotation can be either clockwise, or counterclockwise.
Thus, for each case, we have:
case 1: Clockwise rotation:Then (x,y) → (y, -x), therefore, (-9,4) → (4, 9)
case 2: Counterclockwise rotation:Then (x,y) → (-y, x), therefore, (-9,4) → (-4, -9)
Now, when shifting to right by 4, that means, we're making no changes vertically, but old x-coordinates are increased by 4 to make them shift to right side as value of x increases as we go more and more to the right side with respect to the origin and in defaultly oriented cartesian space.
Thus, we have:
case 1: Clockwise rotation:
After translation of 4 units right:
(4, 9) → (4+4, 9) = (8,9)
case 2: Counterclockwise rotation:After translation of 4 units right:
(-4, -9) → (-4+4, -9) = (0,-9)
Thus, the coordinates of the point (-9, 4) after a 90 degree rotation followed by a translation 3 units right are (8,9) (for clockwise rotation) and (0,-9) (for counterclockwise rotation)
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Which relation is a function
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Answer:
Look at image posted.
Step-by-step explanation:
The one I circle would be the answer because there should not be 2 points for every x-axis value. The 1st one has 2 points with x=0, the other 2 also have 2 points on the asme x axis value
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Find the slope of the line in the graph.
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Answer: m = -2
Step-by-step explanation: To get from one point to the next along this line,
we must first go down 2 units so we say that our rise is -2.
From there we move 1 unit to the left so our run is 1.
So our slope or rise over run is -2/1 or -2.
What is the relationship between the ratios? 10:14 and 30:36 Drag and drop to complete the statement. The ratios are (porportional, not porportional)
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Answer:
Not Proportional
Step-by-step explanation:
30/10 = 3
36/14 = 2.57142857143
Answer:
The ratios are not proportional
Step-by-step explanation:
The number of tourists at the beach per weekend in July was 55,000. In November, the number of tourists per weekend was 18,000. Find the percent of change from July to November. (Round to the nearest Thousands place)
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problem in the picture
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Answer:
B)
Step-by-step explanation:
65 x 2.5 = 162.5
70 x 1.5 = 105
162.5+105=267.5
65 x 2.5=162.5
70x 1.5=105
105+162.5=267.5
Please help id appreciate it and please give me full answers. I will report.
Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet Jane at the end of her run.
How much farther does Jane travel than her trainer? Answer the questions to find out.
1. What is the total distance Jane travels biking and running? Include units with your answer.
2. Use the Pythagorean theorem to write an equation for the distance Jane's trainer bikes.
3. Solve your equation to find the distance Jane's trainer bikes. Show your work.
4. How much farther does Jane travel than her trainer?
Answers
Answer:
Part 1. 28 miles
Part 2. 16^2 + 12^2 = c^2
Part 3. 8 miles. All work is in step by step explanation.
Part 4. 8 miles
Step-by-step explanation:
Part 1. The total distance that Jane travels biking and running is 28 miles. This is because we add 16 and 12 which is her total route.
Part 2. The Pythagorean theorem is a^2 + b^2 = c ^2. In this case, the variable a is Jane's bike route(16 miles), the variable b is Jane's running route(12 miles), and the variable c is the Trainer's biking route as given. If we replace all variables with the values in miles, the equation would be 16^2 + 12^2 = c^2.
Part 3. WORK USED FROM EQUATION
16^2 = 16*16 = 256
12^2 = 12*12 = 144
Now we replace the numbers with the exponents with the solved numbers.
256 + 144 = c^2
256 + 144 = 400
400 = c^2
c = sqrt400
c = 20
Finally, we take the value of c and subtract it from the total distance of Jane's route which is 28 miles(as explained above).
28 - 20 = 8.
Hence, the answer is 8 miles
I NEED YOUR HELP!!
The table shows input and output values of a function given a rule. Which function represents the rule?
Input: x, a number; Output: y, 3 less than 2 times x
Input,x -2 -1 0 1 2
Output,y -7 -5 -3 -1 1
A. Y= 2x - 3
B. Y= -2x + 3
C. Y= -3x - 2
D. Y= 3x + 2
Answers
Because 2 times x is 2x, and 3 less than that is -3. So we can write them into 2x - 3 = Y
The correct function for the given rule will be;
⇒ Y = 2x - 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Input: x, a number
Output: y, 3 less than 2 times x
And,
Input, x -2 -1 0 1 2
Output, y -7 -5 -3 -1 1
Now,
Since, For the function we have;
Input: x, a number
Output: y, 3 less than 2 times x
So, We get;
The function is,
⇒ Y = 2x - 3
And, Here given that;
Input, x -2 -1 0 1 2
Output, y -7 -5 -3 -1 1
Substitute all the values and check it as;
⇒ Y = 2x - 3
Put Y = - 7 , x = - 2
⇒ - 7 = 2 × - 2 - 3
⇒ - 7 = - 4 - 3
⇒ - 7 = - 7
Thus, The value of function is,
⇒ Y = 2x - 3
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You pick a card at random.
6789
What is P(9)?
Answers
- i am assuming P(9) means probability of 9.
what we know:
there is only one 9 in the number.
there are 4 digits in total.
answer:
1/4
-- let me know if you have questions regarding this.
Michael deposits $2650 into an account. The interest rate on the account is 6% compounded annually. What is the balance in Michael's account after 2 years? After 3 years?
Answers
Answer:
1 year would be 2809
Step-by-step explanation:
Answer:im late but 1 year would be 2809
Step-by-step explanation:
At a school health fair, individual pieces are places in paper bags and distributed to students randomly. There are 20 apples, 15 apricots, 25 bananas, 25 pears and 30 peaches. What is the probability of getting an apple?***Hint: Reduce
A. 19/23
B. 4/23
C. 20/100
D. 1/2
Answers
Answer:
B
Step-by-step explanation:
B)90/115 so the probability is 18/23
C)95/115 so the probability is 19/23
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Answers
Answer:
2:50
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
equation: y= -3x+3
Step-by-step explanation:
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Answer:
I picked C because it depends on the temperature that is being presented in the area. In a hotter area, a larger scale wind will be place. In a colder area a local wind would preferably be placed.
Answer:
All wind is caused by the uneven heating of the earth's surface, which sets convection currents in motion, convection currents on a large scale cause global winds: convection currents on a small scale cause local winds.
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
On a math test, 4 out of 20 students received an A. Two students are randomly selected without replacement, and the first student has an A. What is the probability of the second student having an A?
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Answer:
Step-by-step explanation:
The answer should be 20% chance
Two students selected without replacement, and the first student and second student having is 16/95
Probability-based problem:What information do we have?
Number of total students = 20
Number of students having A = 4
Two students selected without replacement, and the first student has an A = 4/20 × 16/19
Two students selected without replacement, and the first student has an A = 64 / 380
Two students selected without replacement, and the first student has an A = 16 / 95
Probability of the second student having an A = 16/20 × 4/19
Probability of the second student having an A = 64 / 380
Probability of the second student having an A = 16 / 35
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Answer:
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Answer:
Probability can best be seen as the total number of “successful” outcomes (non blue pants) divided by the total number of possible outcomes (all pants). Normally, you express probability as a fraction (6/10), a ratio (6:10), or a percentage (60%). You could also express the probability as .6, or 6 out of 10.
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3 x 2.5 =
2 x 3.4 =
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Answer:
7.5
6.8
Step-by-step explanation:
hope it helped :-)
Answer:
7.5
6.8
Step-by-step explanation:
because 3x 2.5 is 7.5 and 2x3.4 is 6.8
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Answer: X= -1/4
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Answer:
yes
Step-by-step explanation:
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Factor the following expression using the GCF: 42pr – 3p.
3p(14r)
p(42r – 3)
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Simplify the expression all the way down.
−5(1+2k)−8(−4+5k)
Question 1 options:
-50k+27
-30k+37
-5-10k+32-40k
32-5-40k
Answers
Answer:
-50k+27
Step-by-step explanation:
=(−5)(1)+(−5)(2k)+(−8)(−4)+(−8)(5k)
=−5+−10k+32+−40k
Combine Like Terms:
=−5+−10k+32+−40k
=(−10k+−40k)+(−5+32)
=−50k+27
mewooooooooooooooooooooo
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Answer:
Step-by-step explanation:
2 5
4 10
8 15
10 25
i think lol
Ms. Li gave her students a quiz that was supposed to take 6 minutes to complete. She asked her students to record the amount of time, to the nearest minute, that it took them to complete the quiz. Ms. Li wants to create a data display that will summarize the data and show how many students took 6 minutes to complete the quiz. Which data display should she create?
A. a box plot
B. a dot plot
C. a histogram with intervals 1-3, 4-6, 7-9, and 10-12
D. a histogram with intervals 1-4, 5-8, and 9-12
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Answer:
b
Step-by-step explanatits b
its b
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Answer:
the answer is 2
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Answer:
the correct answer is 2
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vocabulary is a repeating decimal a rational number?
a. no because it cannot be written in form of a/b where a and b are intergers and b=0
b. no because it cannot be written in form a b where a and b are integers.
c. yes because it can be written in the form a/b where a and b are integers are b=0
d yes because it can written in the a.b where a and b integers.
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if not d, it’s probably c, but the denominator for a repeating decimal (b) shouldnt always be 0, it could be 1. ex: .333/1
Yes, because it can be written in the form a/b where a and b are integers are b = 0. Then the correct option is C.
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The vocabulary is a repeating decimal a rational number will be given as,
Yes, because it can be written in the form a/b where a and b are integers are b = 0.
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Answer:
ma'am or sir... there is no picture attached... but whats the question?
Step-by-step explanation: