List the coordinates of the image after a rotation of the figure below of 180° about the origin. 20 points
(__ , __)
(__ , __)
(__ , __)
(__ , __)
Find the measures of the segment and its image:
AD = √___, A'D' = √___
Answers
B' (-5,-4)
C' (-7,-2)
D' (-4,0)
AD = sqrt(2)
A'D' = sqrt(2)
Answer: The co-ordinates of the image quadrilateral areA'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
Step-by-step explanation: We are given to list the co-ordinates of the image after a rotation of the figure below of 180° about the origin.
From the figure, we note that
the co-ordinates of the vertices of quadrilateral ABCD are A(3, 1), B(5, 4), C(7, 2) and D(4, 0).
We know that
the co-ordinates of the image of a point (x, y) after rotation of 180° about the origin is given by (-x, -y).
Therefore, after rotating the quadrilateral ABCD through an angle of 180° about the origin, then the co-ordinates of the image A'B'C'D' are
A(3, 1) ⇒ A'(-3, -1),
B(5, 4) ⇒ B'(-5, -4),
C(7, 2) ⇒ C'(-7, -2)
and
D(4, 0) ⇒ D'(-4, 0).
And, the lengths of the line segments AD and A'D' can be calculated using distance formula as follows :
[tex]AD=\sqrt{(4-3)^2+(0-1)^2}=\sqrt{1+1}=\sqrt{2}~\textup{units},\\\\A'D'=\sqrt{(-4+3)^2+(0+1)^2}=\sqrt{1+1}=\sqrt 2~\textup{units}.[/tex]
Thus, the co-ordinates of the image quadrilateral are A'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
Related Questions
What happens to the surface area of a rectangular prism when each of the dimensions is doubled? (1 point) i?
Answers
Final answer:
The surface area of a rectangular prism increases by four times when each of the dimensions is doubled because surface area scales in proportion to the square of the linear dimensions.
Explanation:
When the dimensions of a rectangular prism are doubled, the surface area of the prism increases by a factor of four. This is because the surface area is proportional to the square of the linear dimensions. If the length, width, and height of the prism are doubled, the new surface area (A') compared to the original surface area (A) is calculated as follows:
A' = 2l × 2w + 2l × 2h + 2w × 2h
A' = 4(lw + lh + wh)
A' = 4A
Thus, if each dimension is doubled, the surface area increases by four times.
Someone please help me find x and y for problems #19 and 20!!! Please explain if you can
Answers
19) you have 40 for one leg, 10 for another leg and 50 for a hypotenuse. To find x, the altitude, you need to set up the ratio, 10/x=x/40. You can multiply x by both sides. 10=x^2/40. You can also multiply 40 by both sides. 400=x^2. Square root both sides. 20=x. You now have one variable, let's solve for y now :0. Using the biggest triangle, we have 50 as the hypotenuse. You can use the Pythagorean Theorem to help you out. We first need to find the value of one of the legs, so 40^2+20^2=c^2. This gets me to 2000=c^2. Take the square root of both sides. I get c=44.72 (be aware that I'll always round to the nearest hundredth for every ANSWER! It's a bit more accurate). Now to find the leg of the biggest triangle. y^2+44.72^2=50^2 which is y^2+1999.8784=2500. Subtract 1999.8784 from both sides to get y^2=500.1216. Take the sqrt or square root of both sides. (It's rounded) y=22.36. That's question 19 for ya.
20) Look at this now! Doesn't it look familiar? Let's start with y. Start with the ratio '21/y=y/4'. Use my ways from before to get (you can pretend the same thing is happening from prob. 19)), '21=(y^2)/4' '84=y^2' 'y=9.17'. That's y, now x. Let's find the leg of the big triangle first. PYTHAGOREAN THEOREM!!! 21^2+9.17^2=c^2, 441+84.0889=c^2,
c^2=525.0889, c=22.91. We can finally figure out x. 22.91^2+x^2=25^2, 524.8681+x^2=625, x^2=100.1319, x=10.01.
Hope you've enjoyed this learning experience about geometric means and whatnot!!! :3
helppppp meeee with thisssss
Answers
slope is 1 and the y intercept is -5
remember the equation y=mx+b
we have just x, so the slope is 1
Based on the given information, choose the abbreviation of the postulate that supports the conclusion that ΔWAS ΔNOT.
AHH! HELP!!
If the conclusion cannot be drawn from the given information, then choose "not possible."
Given:
WS = NT, AS = OT, S = T.
Answers
If you mark what you know in the diagram, you will see that you have a SIDE, then an ANGLE, and finally another SIDE.
Therefore, you can use ASA to prove that they two triangles are congruent.
Good luck,
MrEQ
Which statement best describes how to determine whether f(x) = x3 + 5x + 1 is an even function?
Answers
→ Even: f(x) = f(-x) → Odd: -f(x) = f(-x)
If -f(x), then -f(x) = -x³ + 5x If x = -x, then f(-x) = -x³ + 5x
Since -f(x) = f(x), the function is therefore odd.
The answer is B) Determine whether (–x)^3 + 5(–x) + 1 is equivalent to x^3 + 5x + 1
Check my answers please?
1. What are the first five terms of the sequence given by the formula a_n=6n+1
a. 7,13,19,25,31
b.1,7,13,19,25
c. 6,12,18,24,30 <---
d.13,19,25,31,37
3. Write an explicit definition for the sequence -3, 1, 5, 9,...
a. a_n=-3+4(n-1)
b. a_n=-3+ 4n <---
c. a_n= -3+(n-1)
d. a_n= -3+4(n+1)
7. what is the 12th term of the sequence 20,16,12,...
a. -30
b. -20
c. -28
d. -24 <----
8. Find the missing term of the arithmetic sequence 20, __, 32,...
a.42
b.18
c.34 <----
d. 36
10. what is the 10th term of the sequences 625,125,25,...
a. 1/3,125
b. 1/
Answers
3. Correct answer is a (a(n)=-3+4(1-1)=-3).
7. The pattern is to reduce the previous value by 4, thus the 12th term of the sequence is -24 (a(n)=20 - 4(n-1)=20 - 4(12-1)=-24).
8. Missing term is 26 (32+20=52; 52/2=26).
10. Pattern is 625/1=625; 625/5=125; 125/5=25; 25/5=5, thus. the 10th term is 1/3125 (answer a).
William works at a nearby electronics store. He makes a commission of 6 % 6%6, percent on everything he sells. If he sells a computer for $ 7 6 4 . 0 0 $764.00dollar sign, 764, point, 00, how much money does William make in commission?
Answers
$ 764 ----> 100%
$ x --------> 6%
We clear the value of x:
x = (6/100) * (764)
x = 45.84 $
Answer:
William makes $ 45.84 in commission
Answer:
x = 45.84 $
late but i need points
Step-by-step explanation:
Probabilities are between 0 and 1. A probability of 0 means that an event occur or that it is for the event to occur. If it is unlikely that the event will occur, then the probability of that event is . If it is equally likely that the event will occur or that the event will not occur, then the probability is . If it is very likely that the event will occur, then the probability of that event is . If the event will definitely occur, then the probability of that event is . A sample space has probability when all of the possible outcomes of the sample space have probabilities.
closer to zero equal to one impossible real numbers one-half will not closer to one uniform equal
Answers
Final answer:
Probability measures the likelihood of an event occurring, with values between 0 (impossible) to 1 (certain). A probability closer to 0 implies unlikeliness, one-half means equal likelihood, and closer to 1 suggests high likelihood. The probabilities in a uniform sample space are equal for all outcomes.
Explanation:
Probabilities are mathematical measures between 0 and 1. A probability of 0 means an event will not occur, or it is impossible for the event to happen. Conversely, if the probability is equal to one, it means the event will definitely happen. When it's unlikely that the event will occur, the probability is closer to zero. If there's an equal chance the event will occur or not, the probability is one-half (0.5). For events that are very likely to occur, the probability is closer to one. A sample space is considered uniform when all the possible outcomes have equal probabilities.
To calculate the probability of an event A in a uniform sample space, count the number of outcomes for event A and divide by the total number of outcomes in the sample space. This is the theoretical probability of A. For example, when tossing a fair coin, there is an equal likelihood of landing on heads or tails, which are mutually exclusive events, each with a probability of 0.5, and together they form the sample space with a total probability of 1.
n a recent survey of 50 10-year olds, it was discovered that 14 liked both McDonald's and Burger King. Overall, 36 of the children surveyed liked McDonald's and 24 liked Burger King. How many of the children surveyed did not like either restaurant? Please show your statistical thinking to support your answer.,
Answers
A family on vacation drives 123 miles in 2 hours, then gets stuck in traffic and goes 4 miles in the next 15 minutes . The remaining 191 miles of the trip take 3 3/4 hours. What was their average rate of speed to the nearest tenth of a mile per hour ?
Answers
The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance.
Total distance traveled = 123 miles + 4 miles + 191 miles = 318 miles
Total time taken = 2 hours + 15 minutes + [tex] 3\frac{3}{4} [/tex] hours
= 2 hours + [tex] \frac{15}{60} [/tex] hour + [tex] \frac{15}{4} [/tex] hours
= [tex] 2+\frac{1}{4}+\frac{15}{4} [/tex] hours
=[tex] 2+\frac{16}{4} [/tex] hours
= 6 hours
Average speed = Total distance [tex] \div [/tex] Total time
= [tex] \frac{318}{6} [/tex] mile per hour
= 53 mile per hour.
The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance.
Total distance traveled = 123 miles + 4 miles + 191 miles = 318 miles
Total time taken = 2 hours + 15 minutes + [tex] 3\frac{3}{4} [/tex] hours
= 2 hours + [tex] \frac{15}{60} [/tex] hour + [tex] \frac{15}{4} [/tex] hours
= [tex] 2+\frac{1}{4}+\frac{15}{4} [/tex] hours
=[tex] 2+\frac{16}{4} [/tex] hours
= 6 hours
Average speed = Total distance [tex] \div [/tex] Total time
= [tex] \frac{318}{6} [/tex] mile per hour
= 53 mile per hour.
What is the simplest form of root 3.025
Answers
Explanation:
1) By convention if you do not mention the index of the root it is square root.
2) By definition the square root of a number x is the numberwhose square is the original number, i.e.
√3025 = 55 because 55^2 = 3025.
3) 3025 is a perfect square because it is the square of a whole numbe.
4) It is easy to find the square root of a perfect square, but if the number is not easily reknownm as a perfect square you will have to probe with several numbers until finding the square root.
For example, you might easily realize that 50^2 is 2500, and that 60^2 is 3600, so you start testing numbers greater thatn 50 and less than 60 until you get 55^2 = 3025.
5) How can you simplify a radical? If you know the properties of radicals you can simplify a radical easily.
You start by decomposing 3025 into its prime factors.
That will result into:
[tex]3025 =5^2{11}^2[/tex]
Then, by radical properties:
[tex] \sqrt{5^2{11}^2} = \sqrt{5^2} \sqrt{{11}^2} =(5)(11)=(55)[/tex]
So, the simplest form of √3025 is 55.
Which calculation can be used to find the value of y in the equation y^3 = 27?
y equals 27/3
y equals cube root of 27
y equals square root of 27 divided by 3
y equals square root of 27
Answers
another answer is
y equals square root of 27 divided by 3
Provided it is square root of (27 divided by 3)
HELP!!!
Draw a tree diagram illustrating the events, two cards are drawn in succession with replacement from a standard deck of 52 and its suit is observed.
I got 50 branches but it's wrong and I'm not sure what I'm doing incorrectly.,
Answers
In a statistics class there are 11 juniors and 6 seniors; 2 of the seniors are females; 6 of the juniors are males. if a student is selected at random, what is the probability that the student is either a junior or a female?
enter your answer as a fully reduced fraction.
Answers
The tricky portion of this question is the phrasing using the word "or".
The fact that it is looking for either a female "or" a junior, let's us know that the selection can't be both. In mathematics, we would need the term "and/or" in order to include those that are both.
So, given that information, we know we have 11 juniors, 6 of which are males and 5 of which are females. We would include the males in our selection.
We also know there are 6 seniors, 2 of which are female and 4 of which are males. We would include the 2 females.
This would give us a selection size of 8. There are 17 total kids, so we divide the 8 by 17 for the answer of 8/17.
Answer: [tex]\dfrac{13}{17}[/tex]
Step-by-step explanation:
Given: Number of juniors = n(J)= 11
Number of seniors = 6
Total students n(S)=[tex]11+6=17[/tex]
Number of seniors are which are females =2
Number of juniors are which are males =6
Then, number of juniors which are females = [tex]11-6=5[/tex]
Now, total females n(F)=[tex]2+5=7[/tex]
such that number of juniors which are females n(J∩F) = [tex]5[/tex]
Now, the number of students either a junior or a female is given by :_
[tex]n(J\cup F)=n(J)+n(F)-n(J\cap F)\\\\\Rightarrow n(J\cup F)=11+7-5=13[/tex]
Now, the probability that the student is either a junior or a female is given by :-
[tex]P(J\cup F)=\dfrac{n(J\cup F)}{n(S)}=\dfrac{13}{17}[/tex]
How much would Kendra have in her account after three years if she started with $500 and earned 2 percent interest compounding annually?
Answers
A time period of 3 years would be $30.
I hope I helped you!
Answer:530.6
Step-by-step explanation:
Plutonium -25 has a half live of 6 hours . George has 5000 grams of plutonium -25 . How much plutonium-25 will hearse have after 4 days
Answers
.. a(d) = 5000*(1/2)^(4d)
.. a(4) = 5000*(1/2)^(4*4) = 5000/2^16 ≈ 0.076 . . . grams
George will have about 0.076 grams after 4 days.
Find two numbers, if
Their sum is 3/5 and their difference is 7 1/5
Answers
.. x + y = 0.6
.. x - y = 7.2
Add these equations to get
.. 2x = 7.8
.. x = 3.9
Then you can find y from
.. y = 0.6 -3.9 = -3.3
The two numbers are -3.3 and 3.9.
Answer:
3.9 and -3.3
Step-by-step explanation:
Does 6(x+2)>x-3 have a solution
Answers
To see if this has a solution, we can simplify it.
6x + 12 > x - 3
5x + 12 > -3
5x > -15
x > -3
Yes, there are solutions to this problem. Any number greater than -3 would match the inequality requirements.
Hope this helps!
Corey is out on the roads doing a long run, and also doing some mental calculations at the same time. corey's pace is 3 strides per second, and each stride covers 5 feet. (a) how much time does it take corey to cover a mile? (b) if corey's stride increased to 5.5 feet per step, how much time would be needed to cover a mile? (c) at five feet per step, how many steps would corey need to run the marathon distance, which is 26 miles and 385 yards?
Answers
B. 320 seconds or 5 minutes and 20 seconds
C. 27687 steps
There are 5280 feet per mile. In A, 3 strides per second at 5 feet gives us 15 ft per second. 5280/15 = 352 seconds. In B, 3 strides per second at 5.5 feet gives us 16.5 feet per second. 5280/16.5 = 320 seconds. In C, we calculate the total feet to divide by 5 per step. multiply 26 miles by 5280 to get feet per mile and multiply 385 by 3 to get the feet per yard. Add them together. then divide by 5. 26(5280) + 385(3) =138435. 138435/5 = 27687 steps
PLZ HELP QUICKLY AND CORRECT GETS BRAINLY!
Solve for x: −3|x − 3| = −6
Answers
A triangular playground has angles with measures in ratio 8: 3: 9 what is the measure of the smallest angle
Answers
20x = 180
x = 180/20
x = 9
The smallest angle is: 3×9 = 27 degrees
Note: 180 degrees is the sum of angles in a triangle
Answer:
The measure of the smallest angle is 27°
Step-by-step explanation:
The triangle has angles with measure ratio 8:3:9, so the sizes of the angles are going to change depends on the ratio.
Let’s name the common value as “α”.
Basing on the angle-sum property, we already know that the sum of the angle in a triangle is 180°.
The measure of each one are:
8α, 3α, 9α
The sum of these is 180°.
Then,
8α + 3α + 9α = 180°
Let’s sum similar values:
20α =180°
α= 180°/20
α= 9
Replacing values, we going to find the measure of each angle:
8(9) = 72°
3(9) = 27°
9(9) = 81°
The measure of the smallest angle is 27°
HELP!!! WILL MARK BRAINLIEST IF YOUR RIGHT!!! LOOK AT THE IMAGE FOR THE QUESTION AND ANSWER CHOICES
Answers
√3 ≈1.732, 17/10=1.7
convert all the fraction into decimals, you'll see C is the closest to 1.732
you owe $1,945.61 on a credit card that has an 11.2% APR. the minimum payment due is $156.00. you decide to pay $300.00. how much do you save in interest by paying more than the minimum, assuming you make both payments at the beginning of the month?
$,
Answers
Answer:
$1.344
Step-by-step explanation:
APR represents annual percentage rate, and it specifies the amount of interest that would accrue on a loan over a specified period.
Extra amount paid = $300 - $156 = $144
Annual interest that would have been paid on the extra $144 = $144 * 11.2/100= $16.128
this amount on monthly basis is $16.128/12 = $1.344
Your weekly allowance is $25.you spent 6% of the budget on a new video game . how much did you spend on the video game ?\
Answers
Allowance
----------------------------------------------------------
$25
----------------------------------------------------------
Video Game
----------------------------------------------------------
6% 0f 25
= 0.06 x 25
= $1.50
----------------------------------------------------------
Answer: $1.50 were spent on video game
----------------------------------------------------------
Use the Law of Sines to find the missing angle in the triangle. Find m
Answers
(13) / (sin (40)) = (19) / (sin (C))
Clearing the angle C we have:
sin (C) = (19/13) * (sin (40))
C = Asin ((19/13) * (sin (40)))
C = 69.96086904
Rounding:
C = 70 degrees
Answer:
The missing angle in the triangle using the Law of Sines is:
70 degrees
option 4
During a basketball game, the East Middle School Tigers scored 42 points from two-point baskets. How many two-point baskets did they make?
84
14
21
42
Answers
Answer:
21 two point basket.
Step-by-step explanation:
It is given that During a basketball game, the East Middle School Tigers scored 42 points from two-point baskets. It means
Total score = 42 points
Score for each basket = 2 point
Let total number of two-point baskets be x. So,
Total score = 2x points.
[tex]2x=42[/tex]
Divide both sides by 2.
[tex]\dfrac{2x}{2}=\dfrac{42}{2}[/tex]
[tex]x=21[/tex]
Hence, they make 21 two point basket.
factor each polynomial 9x-6 a.9(x-6) b.3(3x-2) c.6(3x-1) d.3x
Answers
The correct answer is b) 3(3x - 2)
In order to factor this, you have to find the greatest common factor of 9x and 6. Since 6 does not have an x in it, we cannot pull out an x. Instead we have to look for the biggest whole number that goes into 9 and 6, which is 3.
Next, to take the 3 out, we need to divide each term by 3.
9x/3 = 3x
-6/3 = -2
So the 3 comes out and the results above go together in the parenthesis.
3(3x - 2)
[tex] 9x-6=3(3x-2)\implies\text{B} [/tex]
I need help with this one
Answers
So this is False
Hey
PLEASE HELP ME
Limited time!!!!
Blank 1: 38,35,65,15
Blank 2: purchasing 12 apps, purchasing 35 apps, spending $35, spending $12
Blank 3: Has 12 new on her phone , Has $35 remaining on her card , Has 35 new apps , Has $12 remaining on her card.
CHOOSE ONE ONLY FOR EACH BLANK.
THX
Answers
a(12) = 50 - 1.25(12) = your answer for blank 1
For blank 2: because x represents the number of apps on her phone, and x is given 12 for this problem, she bought 12 apps.
For blank 3: You would mention how many apps she got twice, so not the first option or the third option. It should be the answer from the first blank because the equation represents how much money is in her account.
n quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply. ML ∥ NO ML ⊥ LO LO ≅ MN ML ≅ LO MN ⊥ NO
Answers
Answer: The correct options are
(A) ML ∥ NO,
(C) LO ≅ MN.
Step-by-step explanation: Given that in quadrilateral LMNO, LO ∥ MN.
We are to select the correct additional information that would be sufficient along with the given information to conclude that LMNO is a parallelogram.
PARALLELOGRAM: A parallelogram is a quadrilateral if ine of the following conditions are satisfied:
(i) Two pairs of opposite sides parallel
or
(ii) one pair of opposite sides parallel and congruent.
The given condition is
LO ∥ MN.
So, the other additional sufficient condition will be
either the other pair of opposite sides parallel, i.e., ML ∥ NO,
or
the same pair of parallel sides are congruent, i.e, LO ≅ MN.
Thus, the correct statements are ML ∥ NO and LO ≅ MN.
Option (A) and (C) are correct.
Answer:
a and c
Step-by-step explanation: