The grid shows figure Q and its image figure Q' after a transformation: Figure Q is a pentagon drawn on a 4 quadrant grid with vertices at 2, 4 and 4, 2 and 5, 4 and 7, 5 and 3, 7. Figure Q prime is a pentagon drawn with vertices at negative 4, 2 and negative 2, 4 and negative 4, 5 and negative 5, 7 and negative 7, 3. Which transformation was applied on figure Q?
Answers
we notice that for every pair (x, y) in Q, there is a point (-y, x) in Q',
this means that the transformation is a 90° counterclockwise rotation around the origin.
The transformation can be also noticed by sight in the figure.
Answer: 90° counterclockwise rotation
Both algebraic analysis and visual inspection affirm that the transformation applied to Figure Q is a 90° counterclockwise rotation around the origin, evident in the corresponding coordinates and the visual alignment of vertices.
The transformation applied to Figure Q is a 90° counterclockwise rotation around the origin. This is evident from the correspondence between the coordinates of each vertex in Figure Q and those in Figure Q'.
Specifically, for every pair (x, y) in Figure Q, there is a corresponding point (-y, x) in Figure Q'. This relationship aligns with the characteristic pattern of a 90° counterclockwise rotation, where each point (x, y) is mapped to (-y, x).
Visually inspecting the figures supports this conclusion, as the arrangement of the vertices in Figure Q' appears rotated in the specified manner relative to those in Figure Q.
Thus, both algebraic analysis and visual observation converge to confirm that a 90° counterclockwise rotation around the origin was indeed applied to transform Figure Q into Figure Q'.
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Related Questions
A rope 10 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing the area of both square and circle as a function of the length of one side of the square.
Answers
(10-x)/(2π)=r
A=π(100-20x+x^2)/(4π^2)
A=(x^2-20x+100)/(4π)
...
x/4=s, x=4s using this in the area of a circle we get:
A=(16s^2-80s+100)/(4π)
A=(4s^2-20s+25)/π
And of course the area of a square is s^2
A=(4s^2+πs^2-20s+25)/π
The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.
Let's denote:
- [tex]\( x \)[/tex] as the length of one side of the square (in feet).
- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.
1. Area of the Square [tex](\( A_s \))[/tex]:
The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].
2. Area of the Circle [tex](\( A_c \))[/tex]:
The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:
[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]
Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]
The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].
Substituting the value of [tex]\( r \)[/tex], we get:
[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]
[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]
A parachutist's speed during a free fall reaches
207
kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 5 seconds of free fall?
Answers
207km/h = 57.5m/s
2) Use the rate from question 1.
Make an equation and cross multiply to solve for x.
57.5/1 = x/5
x = 57.5(5)
x = 287.5
So he fell 287 meters in just 5 seconds
Solve each system:
80x+60y=85
100x-40y=20
Answers
x= 1/2 (fraction)
You have ten fewer quarters than dimes and 5 fewer nickles than quarters. The total value of the coins is $4.75. How many quarters, nickles, and dimes do you have?
Answers
d = q + 10
n = q - 5
0.05(q - 5) + 0.10(q + 10) + 0.25q = 4.75
0.05q - 0.25 + 0.10q + 1 + 0.25q = 4.75
0.40q + 0.75 = 4.75
0.40q = 4.75 - 0.75
0.40q = 4
q = 4 / 0.40
q = 10 <=== quarters
d = q +10
d = 10 + 10
d = 20 <== dimes
n = q - 5
n = 10 - 5
n = 5 <== nickels
d=q+10 and n=q-5
.25q+.1d+.05n=4.75, then using d and n from above, this becomes:
.25q+.1(q+10)+.05(q-5)=4.75 perform indicated multiplications
.25q+.1q+1+.05q-.25=4.75 combine like terms
.4q+.75=4.75 subtract .75 from both sides
.4q=4 divide both sides by .4
q=10, since d=q+10 and n=q-5
d=20, n=5
So you have 10 quarters, 20 dimes, and 5 nickels.
If (x,y) are the coordinates of a point p in the xy-plane, then x is called the _______ of p and y is the _______ of p.
Answers
and the second coordinate of a point P is called the y-coordinate of P.
So
"x is called the ___x-coordinate____ of p and y is the ___y-coordinate____ of p."
Answer:
x-coordinate
y-coordinate
In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
Explanation:In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
For example, in the point (3, 5), the x-coordinate is 3 and the y-coordinate is 5.
Together, the x and y coordinates specify the precise location of a point in the xy-plane.
What is the length of the hypotenuse of a right triangle if each of the two legs is 4 units? square root of 8 units 4 units square root of 32 units 8 unit?
Answers
Answer:
Well if you still need the answer around 4 years later LOL its √32
Step-by-step explanation:
Answer:
√32
Step-by-step explanation:
Because this is totally helpful 4 years later
The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
The four angles of the quadrilateral are °, °, °, and °, respectively.
Answers
Answer:
The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Step-by-step explanation:
Given : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
To find : The four angles of the quadrilateral are °, °, °, and °, respectively.
Solution : We have given that The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
Let the angle of the quadrilateral is x
Then all the angles are x , 2x , 5x ,4x
Complete angle formed by circle is 360 °
Sum of all the angle are 360
x + 2x + 5x + 4x = 360 .
12 x = 360 .
On dividing both sids by 12.
x = 30 .
Then
2x = 60
5x = 5 * 30 = 150 .
4x = 4 *30 = 120 .
Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Answer:
for plato users the answers are 45,75,135,105
Step-by-step explanation:
What would you look for in a word problem that might indicate that you need to use an absolute value inequality?
Answers
At maximum speed, an airplane travels 2,400 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours. Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
Answers
x + y = 2400/5 = 480 - flying with the wind
adding the 2 equations
2x = 880
x = 440
Speed of the plane with no wind = 440 mph
Answer: The speed of the plane with no wind is 440 miles per hour.
Step-by-step explanation:
Let the maximum speed of the plane be 'x'.
Let the maximum speed of the wind be 'y'.
Since we have given that an airplane travels 2400 miles against the wind in 6 hours.
As we know that
Downstream is given by
[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]
Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.
As we know tha t
Upstream is given by
[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]
We just need to find the speed of the plane with no wind.
Using the elimination method,
[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]
Hence, the speed of the plane with no wind is 440 miles per hour.
find the GCF 12, 18, 24
Answers
18= 2*3*3
24= 2*2*2*3
The GCF would be equal to the product of all common multiples.
2*3=6
Final answer: 6
round 0.9144 to the nearest tenth of a yard
Answers
hope this helps:)
A panel containing four on-off switches in a row is to be set. assuming no restrictions on individual switches, use the fundamental counting principle to find the total number of possible panel settings.
Answers
_ _ _ _, where you can put one of two marks (off or on) on any _.
So, the number of different ways will be 2 * 2 * 2 * 2 = 16
Answer: 16 possible settings.
In the formula that gives the circumference of a circle, which quantity is multiplied by 2Ï€ ?
A. Diameter
B. Radius
C. Area
D. Circumference
Answers
The circumference of an object is the total length of the line that forms the object. For a circle, the formula is:
C = 2 π r
We can see that in the formula, what is multiplied by 2 π is the radius (r).
Therefore the answer to this is
B. Radius
3/8 of people at a fun fair were children 3/4 of the remaining people were men there were 140 more children than women how many people went to the fun fair
Answers
The remaining fraction was 1-3/8=5/8
the fraction of men was 3/4*5/8=15/32
the fraction of women=1/4*5/8=5/32
given that the there were 140 more children than women, the fraction represented by this is:
3/8-5/32
=7/32
thus the total number of people who were there was:
1/(7/32)*140
=640
The answer is 640
Four times the complement increased by forty-six is the same as twice the supplement. find the measures of the angle, the complement, and the supplement
Answers
supplement: 180 - x
Four times the complement increased by forty-six = 4(90-x) + 46
twice the supplement: 2(180 - x)
so
Four times the complement increased by forty-six is the same as twice the supplement
4(90-x) + 46 = 2(180 - x)
360 - 4x + 46 = 360 - 2x
2x = 46
x = 23
answer
measure of angle x = 23
measure of complement = 90 - 23 = 67
measure of supplement = 180 - 23 = 157
what is the distance between the points (3,7) and (15,16) on a coordinate plane?
Answers
distance = Sqrt((x2-x1)^2 +(y2-y1)^2)
15-3 =12
16-7=9
12^2 = 144
9^2 = 81
144+81 = 225
square root of 225 = 15
the distance is 15
[tex]\sqrt{(15 - 3)^2 + (16 - 7)^2} \\ \\ \sqrt{12^2 + 9^2} \\ \\ \sqrt{144 + 81} \\ \\ \sqrt{225} \\ \\ 15[/tex]
So, 15 units is the answer.
Color of car. a. Qualitative/Ordinal b. Qualitative/Nominal c. Quantitative/Discrete d. Quantitative/Continuous
Answers
4⋅10 6 4, dot, 10, start superscript, 6, end superscript is how many times as large as 1\cdot10^41⋅10 4 1, dot, 10, start superscript, 4, end superscript?
Answers
The given problem is very confusing since it was copy pasted directly from the source so the equations look scrambled and plus it was one words. After my own translation, I believe the given numbers are:
4 ⋅ 10^6
and
1 ⋅ 10^4
The symbol ⋅ means that the two numbers are multiplied while the symbol ^ means an exponent of. Now we are asked to find how much the 1st number is larger than the 2nd number. To solve this, we simply have to divide the bigger number by the smaller number. Since 4 ⋅ 10^6 has bigger exponent than 1 ⋅ 10^4 then it is the bigger number.
Ratio = 4 ⋅ 10^6 / 1 ⋅ 10^4
Ratio = 4 ⋅ 10^2 = 400
Therefore 4 ⋅ 10^6 is 400 times bigger than 1 ⋅ 10^4.
Answer:
400 times
Having knowledge about potencies we will find that the final value will be greater than 400 times.
Recalling the properties of powers we find:
Multiplication of powers with the same base.Division of powers with the same base.Power of potency. Potency of a product.Quotient power.Then we can write the two given powers as:
[tex]4 *10^6\\1 * 10^4[/tex]
We know that we have a multiplication and a power, so solving for each of them, we find:
[tex]Ratio = 4 *10^6 / 1 * 10^4\\Ratio = 4 * 10^2 = 400[/tex]
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$1,100 at 8%, for 15 years, compounded annually. Total Amount = $ Interest Amount = $
Answers
A=p (1+r)^t
A future value?
P present value 1100
R interest rate 0.08
T time 15 years
A=1,100×(1+0.08)^(15)
A=3,489.39
To find the interest amount the formula is
I=A-p
I=3,489.39−1,100
I=2,389.39
Final answer:
Compound interest plays a crucial role in determining the final amount of an investment over time, showcasing the power of compounding. In this scenario, with an initial amount of $1,000, an interest rate of 10.1%, and 47 years of compounding annually, the total interest earned would be $91,045.80.
Explanation:
Compound interest is calculated on the principal amount plus the interest earned over time. In this case, with an initial amount of $1,000, an interest rate of 10.1% compounded annually, and an end amount of $92,045.80 after 47 years, compound interest plays a significant role in determining the final amount.
To calculate the total interest earned over the 47 years, you subtract the initial principal amount of $1,000 from the end amount of $92,045.80. This gives you the total interest earned. In this scenario, the total interest earned would be $92,045.80 - $1,000 = $91,045.80.
Compound interest is crucial in understanding how investments grow over time, and it showcases the power of compounding when money is invested wisely and for a long period.
PLEASE HELP IM RUNNING OUT OF TIME!!!!!
Which of the following radical expressions has an absolute value symbol in its simplified form?
I hope i wrote these right
MY CHOICES ARE:
a. 16x^4−−−−√4
b. 81x−−−√4
c. −125x^3−−−−−−√3
d. 64x^3−−−−√3
Answers
(16x^4)^(1/4) = 2*abs(x)
Martin bought 30 shares of microsoft at the close price of $24.53. in a few years, martin sells all of his shares at $33.71. how much money did martin make?
Answers
Answer:
Money that Martin make is $ 275.9
Step-by-step explanation:
Number of shares Martin Bought = 30
Cost Price of a share = $ 24.53
Total Cost price of all share = 30 × 24.53 = $ 735.9
Selling Price of a share = $ 33.71
Total Selling Price of all shares = 30 × 33.71 = $ 1011.3
Profit money that Martin make = 1011.3 - 735.9 = $ 275.9
Therefore, Money that Martin make is $ 275.9
Ivanna deposits $600 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 2 years?
Answers
Principle [P] = $600
Rate [R] = 3
Time [T] = 2
We know,
[tex]Simple Interest = \frac{Principle * Rate * Time}{100} [/tex]
[tex]= \frac{600*3*2}{100} = 36[/tex]
Can someone help me figure this out: Factor 12y^2-27? I keep getting the steps confused.
Answers
3(4y^2-9)
The binomial inside is a perfect square so keep factoring.
3(2y+3)(2y-3)
The pair of binomials cannot be further factored so stop there.
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2 , and a vertical shift up 3 units.
Answers
y = A sin(Bx + C) + D
where
A = amplitude
B = frequency
C = shift on starting angle
D = shift of wave on the y-axis
From the given problem, A = 1 and D = 3. There is no value for C because there is no mention of any shift in angle. About the frequency, you can obtain this by getting the reciprocal of the period. Thus, B = 2/π. The complete equation is
y = sin(2x/π) + 3
Answer:
y = sin(4x) + 3
Step-by-step explanation:
y = Asin(Bx + C) + D
A is amplitude = 1
B = 2pi/period = 2pi / (pi/2) = 4
C does not mention.
D: shift up or down = 3
=> y = sin(4x) + 3
At the beginning of the month a store had a balance of −$554. During the month the store lost another $600. What is the current balance?
Answers
So the stores current balance is $-1,154.
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Consider the equation 5/3v +4 +1/3v =8 What is the result of the equation after the first step in the solution
Answers
first step would be to simplify...
2v + 4 = 8 <==
Can some PLEASE help me with 8 and 9!!????
Answers
Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price. How much does she have left to pay after making the down payment?
A.$80
B.$135.20
C. $1040.00
D. $904.80
Answers
1,040×0.13=135.2
So the amount she has to pay after making the down payment is
1,040−135.2=904.8
It's d
Downpayment is the percent amount paid from a sum of money. The amount left after the downpayment is $904.80
Downpayment on a priceDownpayment is the percent amount paid from a sum of money. If Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price, the amount he have left is;
Amount left = (100 - 13)% * 1040
Amount left .= 87% of 1040
Amount left = 0.87 * 1040
Amount left = $904.80
Hence the amount left after the downpayment is $904.80
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An urn holds 5 white and 3 black marbles. if 2 marbles are to be drawn at random without replacement and x denotes the number of white marbles, find the probability distribution for x
Answers
i = [tex]p(0) = \frac {3} {8} x \frac {2} {7} = \frac {3} {28} ; p (1) = \frac {3} {8} x \frac {5} {7} + \frac {5} {8} x \frac {3} {7} = \frac {15} {28}; p (2) = \frac {5} {8} x \frac {4} {7} = \frac {5} {14} [/tex]
(a) i. The probability mass function of X is 5 / 14
Hypergeometric Distribution is the probability distribution of a hypergeometric random variable.
The hypergeometric distribution is used to calculate the statistical importance of having drawn a specific k successes (out of n total draws) from the aforementioned population in the hypergeometric test uses.
ii. Please see attached image for the answer.
To find the probability distribution for x, consider the possible values of x and calculate the probability of each value. When 2 marbles are drawn without replacement, there are two possible outcomes. The probability distribution for x is P(x = 0) = 3/28, P(x = 1) = 15/56, and P(x = 2) = 5/14.
Explanation:To find the probability distribution for x, we need to consider the possible values of x and calculate the probability of each value.
Since there are 5 white marbles and 3 black marbles in the urn, the total number of marbles is 8.
When 2 marbles are drawn without replacement, there are two possible outcomes: (1) both marbles are white and (2) one marble is white and one marble is black.
Let's calculate the probabilities:
P(x = 0) = P(both marbles are black) = (3/8) * (2/7) = 6/56 = 3/28
P(x = 1) = P(one marble is white and one marble is black) = (5/8) * (3/7) = 15/56
P(x = 2) = P(both marbles are white) = (5/8) * (4/7) = 20/56 = 5/14
Therefore, the probability distribution for x is:
P(x = 0) = 3/28
P(x = 1) = 15/56
P(x = 2) = 5/14
A student must choose to participate in two different events during field day. There are four track events, two academic events, and six team sports events. What is the approximate probability that the student will choose to participate in two team sports?
0.114
0.227
0.273
0.545
Answers
Answer:
.227
Step-by-step explanation:
Answer:
0.227
Step-by-step explanation: