What are the coordinates of the point (-9, 4) after a 90 degree rotation followed by a translation 3 units right?
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)
Learn more about rotation of a point with respect to origin here:
https://brainly.com/question/18856342
k12 students help please!!!!!!!!!!!!
Answer:
[tex] 35 \: {units}^{2} [/tex]
Step-by-step explanation:
Area of the triangle
[tex] = \frac{1}{2} \times 14 \times 5 \\ \\ = 7 \times 5 \\ \\ =35 \: {units}^{2} [/tex]
the speed of light is approximately 3 x 10 to the 8th power meters per second, while the speed of sound is approximately 3.4 meters per second. How many times faster is the speed of light than the speed of sound?
Answer:
The speed of light is 8.8x10⁵ times faster than the speed of sound.
Step-by-step explanation:
We can find how many times faster (R) is the speed of light than the speed of sound as follows:
[tex] R = \frac{c}{v_{s}} [/tex]
Where:
c: is the speed of light = 3x10⁸ m/s
[tex]v_{s}[/tex]: is the speed of sound = 340 m/s (the value given in the statement, 3.4 m/s, is wrong)
[tex]R = \frac{3 \cdot 10^{8} m/s}{340 m/s} = 8.8 \cdot 10^{5}[/tex]
Hence, the speed of light is 8.8x10⁵ times faster than the speed of sound.
I hope it helps you!
Choose the inequality that represents the following graph. It's On khan academy
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Thats a closed dot, which means its greater than or equal to
Lin has a scale model of a modern train. The model is created at a scale of 1 to 48. The height of the model train is 102 milliliters. What is the actual height in meters?
Answer:
The actual height is 4.896 m
Step-by-step explanation:
Given
[tex]Ratio= 1 : 48[/tex]
[tex]Scale\ Height = 102mm[/tex]
Required
Determine the actual height in metres
Represent the actual height with x.
So, the ratio of Scale Height to Actual Height as:
[tex]Ratio = 102mm : x[/tex]
To calculate x, both ratios must be equal
[tex]1 :48 = 102mm:x[/tex]
Convert to fraction
[tex]\frac{1}{48} = \frac{102mm}{x}[/tex]
Cross Multiply
[tex]x * 1 = 48 * 102mm[/tex]
[tex]x = 4896mm[/tex]
Convert mm to metres
[tex]x = 4896 * 0.001m[/tex]
[tex]x = 4.896m[/tex]
The actual height is 4.896 m
Answer first and I will mark brainliest
Answer:
A 6660 it decreases by 820 so 8,300-820=7480 and then 7480-820=6660
$6,660
Answer: The cost after 7 years should be $5740.
Step-by-step explanation:
If you find the ammoun that the value decreases each year, and multiply that by your 7 years you get your answer.
Joe has a picture that measures 8 centimeters by 12 centimeters. He creates four enlargements of the picture. The
table below shows the width and the length of each enlargement.
What is the constant of proportionality between the width and the length of the pictures?
Answer:
1.5
Step-by-step explanation:
Because 15 divided by 10 equals 1.5
if someone could help me with this that would be great!!! TYSM
Answer:
1005 ft squared (B)
Step-by-step explanation:
The far left area:
30*15=450
The middle area:
-Since there is an eight feet being subtracted it is:
22*15=330
The last side:
-Since there is two 15's at the bottom we must subtract 30 from 45:
15*30*1/2=225
Add the area together:
450+330+225=1005
1005 ft squared
Solve the equation and show all of your steps!
8 + 3x = 14
Answer:
x=2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Step-by-step explanation:
This is a linear equation, and we will need to get the variable by itself.
Let's calculate!
[tex]8+3x=14\\3x=14-8\\3x=6[/tex]
Now we divide both sides by 3. Dividing 3 by 3 is just 1, and we don't need to write the 1, and 6 divided by 3 is two! So your equation will look like this:
[tex]3/3x = 6/3\\x=2\\[/tex]
Hope that helps! :)
A computer salesman gets a commission for each sale he makes. If he makes 1.0% commission on a sale of $2,000, how much commission does he make?
A) $2,020
B) $200
C) 20
D) $2,000
morganville and newton are 24, miles apart. on a map. the two cities are 3 inches apart? What is the map scale?
Answer:
Step-by-step explanation:
we have 24/3=8
1 inch is 8 miles
1in:8miles
What is the solution to this system of linear equations?
2x + y = 1
3x - y = -6
A. (-1,3)
B. (1,-1)
C. (2,3)
D. (5,0)
Answer:
A. (-1 , 3)
Step-by-step explanation:
2x + y = 1
plus 3x - y = -6
------------------------------
5x = -5
x = -1
y = 1 - (2*-1) = 3
PLZZZZZ HALP FOR 50 POINTS AND BRAINLIEST
Which steps should you follow to write an equivalent ratio to find 120% of 700?
Answer:
D
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
HELP ME PLZ THIS IS SO IMPORTANT
Answer:
4
Step-by-step explanation:
4(6)/ 3+3
24/6
=4 Jushsgsghss
Answer:
11
Step-by-step explanation:
hope that helps :)))))
A football team lost 5 yards on one play and gained 12 yards on the next play. Find the overall change in field position.
Answer:
60 yards
hope that helps
Step-by-step explanation:
ASAPPPP WITH EXPLANATION!!!
If Adam and his family travel for 8 hr. at a constant rate of 50 mph, how many miles will they drive on the first day of their vacation?
A. 120 mi.
B. 400 mi.
C. 660 mi.
D. 800 mi.
Answer:
B. 400 Miles
Step-by-step explanation:
Just take 8hrs and multiply it by 50mph to get an answer of 400.
Hope this helps :)
Answer:
B 400
Step-by-step explanation:
50 x 8 = 400
help me with this please
Answer:
The answer is 2 3/4
If you simplify 2 3/4 then its 5/6
Hope this helps
PLSS HELPP The question is in the picture!
Answer:
3.20
Step-by-step explanation:
who makes taxes 300 or even 30 dollars
9. Each share of a certain stock lost a total of $1.50 in value over several weeks. Over how many weeks, w, did the stock lose value if each week it lost $0.25 per share? *
Answer:
Did you ever get the answer?
Step-by-step explanation:
Answer:
6 weeks
Step-by-step explanation:
your welcome :) Hope this helps you!
please mark me as brainliest if you can
Please Help !!!!!!!!!!!
Answer:
its A the cost increases $2.50
Step-by-step explanation:
K12 students help !!!!!!!!!!!!
Answer:
D i think
Step-by-step explanation:
One leg of a right triangle is 3.2 centimeters long. The length of the second leg is 5.7 centimeters.
What is the length of the hypotenuse? Round to the nearest tenth if necessary.
A ) 2.5 cm
B ) 4.7 cm
C ) 8.9 cm
D ) 6.5 cm
The mass of an electron is approximately 9.1 x 10^-31 kilograms.
The mass of a proton is approximately 1.7 x 10^-27 kilograms.
Approximately how many times greater is the mass of a proton than the mass of a electron?
A. 5,500
B. 1,900
C. 19,000
D. 55,000
Answer:
1900
Step-by-step explanation:
hello bro how r u i think answer is 1835 but there is no option
The required mass of the proton is 1900 times the mass of the electron. Option B is correct.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
The mass of an electron is approximately e = 9.1 x 10⁻³¹ kilograms.
The mass of a proton is approximately p = 1.7 x 10⁻²⁷ kilograms.
Now
p/e = 1.7 x 10⁻²⁷/9.1 x 10⁻³¹
p/e ≈ 1900
p = 1900e
Thus, the required mass of the proton is 1900 times the mass of the electron.
Learn more about proportionality here: https://brainly.com/question/22620356
#SPJ5
Jada had some dimes and quarters that had a total value of $12.50. The relationship between the number of dimes, d, and the number of quarters, q, can be expressed by the equation
01.d + 0.25q = 12.5.
1. If Jada has 4 quarters, how many dimes does she have?
2. If Jada has 10 quarters, how many dimes does she have?
3. Is the number of dimes a function of the number of quarters? If yes, write a rule (that starts with d =...) that you can use to determine the output, d, from a given input, q. If no, explain why not.
Answer:
1. 115. If q=4, then the equation tells us that 0.1d+(0.25)⋅4=12.5. Subtracting 1 from both sides gives 0.1d=11.5, so d=115.
2. 100. If q=10, then the equation tells us that 0.1d+(0.25)⋅10=12.5. Subtracting 2.5 from both sides gives 0.1d=10, so d=100.
3. Yes. If you know the number of quarters, then you can determine the number of dimes from the equation. We can even write the equation in a way that shows this: d=125−2.5q. The expression 125−2.5qrepresents the output—it is the rule that determines the output d from a given input q.
can somebody pls help me with this question I dont get it
Answer:
1. 195=6.50·c
2. 30
Step-by-step explanation:
195=6.5·c
Divide both sides by 6.5
30=c
what in the world.......
Answer:
Y=0.99+x
Step-by-step explanation:
Answer:
y = 0.99x
Step-by-step explanation:
For each donut that costs $0.99 each as stated in the question, you want to multiply that number by x in which x is the amount of donuts that may be bought in which y = 0.99x is your correct answer.
PLLSSSSS HELLLP
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 6 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 6) would represent a height of 6 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burnt was 0.3 inches per hour instead of 0.5 inches per hour, will the relation continue to be a function? Explain your answer using input and output values. (3 points)
Answer:
Part A: 0,6 1, 5.5 2,5.0 3,4.5 4,4.0 5,3.5 6,3.0
Step-by-step explanation:
Part B: This would be a function, it has a constant rate of change.
Part C: 0,6 1,5.7 2,5.4 3,5.1 4,4.8 5,4.5 6,4.2, this would still be a function, just at a slower rate of speed.
A department store offered a 15% discount off the regular price of a shirt. The amount of the discount is $3. What is the regular price of the shirt?
Answer: $3.53
Step-by-step explanation: 15 percent off can be thought of as 85% of the original value because 100-15 is 85. this means that if x is the value of the original shirt, .85x=3
divide by .85
x=3.5294
which is about $3.53
Answer:
You will pay $12 for a item with original price of $15 when discounted 20%. In this example, if you buy an item at $15 with 20% discount, you will pay 15 - 3 = 12 dollars.
Step-by-step explanation:
Help ASAP
Which of the following correctly simplifies the expression 2 to the power of 2 multiplied by 6 to the power of 0 whole over 7, the whole cubed.? (5 points)
Question 4 options:
1)
2 to the power of 2 multiplied by 1 whole over 7, the whole cubed. = 2 to the power of 5 multiplied by 1 cubed over 7 cubed. = 32 over 343.
2)
2 to the power of 2 multiplied by 0 whole over 7, the whole cubed. = 2 to the power of 6 multiplied by 0 over 7 cubed. = 0
3)
2 to the power of 2 multiplied by 1 whole over 7, the whole cubed. = 2 to the power of 6 multiplied by 1 cubed over 7 cubed. = 64 over 343.
4)
2 to the power of 2 multiplied by 0 whole over 7, the whole cubed. = 2 to the power of 5 multiplied by 0 over 7 cubed. = 0
Answer:
(2^2 * 6^0) / 7)^3 =
(2^6 * 1^3) / 7^3 =
(64 * 1) / 343 =
64/343
Step-by-step explanation:
I hope this helps!