Answer:
The statement is now presented as:
[tex]\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}[/tex]
In other words, this mathematical statement can be translated as:
There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r.
Step-by-step explanation:
Let [tex]C = (h,k)[/tex] the coordinates of the center of the circle, which must be transformed into [tex]C'=(h', k')[/tex] by operations of translation and reflection. From Analytical Geometry we understand that circles are represented by the following equation:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
Where [tex]r[/tex] is the radius of the circle, which remains unchanged in every operation.
Now we proceed to describe the series of operations:
1) Center of the circle is translated 4 units to the right (+x direction):
[tex]C''(x,y) = C(x, y) + U(x,y)[/tex] (Eq. 1)
Where [tex]U(x,y)[/tex] is the translation vector, dimensionless.
If we know that [tex]C(x, y) = (h,k)[/tex] and [tex]U(x,y) = (4, 0)[/tex], then:
[tex]C''(x,y) = (h,k)+(4,0)[/tex]
[tex]C''(x,y) =(h+4,k)[/tex]
2) Reflection over the x-axis:
[tex]C'(x,y) = O(x,y) - [C''(x,y)-O(x,y)][/tex] (Eq. 2)
Where [tex]O(x,y)[/tex] is the reflection point, dimensionless.
If we know that [tex]O(x,y) = (h+4,0)[/tex] and [tex]C''(x,y) =(h+4,k)[/tex], the new point is:
[tex]C'(x,y) = (h+4,0)-[(h+4,k)-(h+4,0)][/tex]
[tex]C'(x,y) = (h+4, 0)-(0,k)[/tex]
[tex]C'(x,y) = (h+4, -k)[/tex]
And thus, [tex]h' = h+4[/tex] and [tex]k' = -k[/tex]. The statement is now presented as:
[tex]\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}[/tex]
In other words, this mathematical statement can be translated as:
There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r.
Answer:
the same area as
Step-by-step explanation:
When a circle is translated and reflected, the center of the circle will change; however, its area, circumference, radius and diameter remain the same.
This is so because, translation and reflection only affect the positioning of the circle not the size.
Considering the above analysis, we can conclude that option d answers the question correctly.
PLZ HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER!!!!
Which of the following is equivalent to the expression below?
3 5/4 (mixed number faction)
Answer:
4 1/4
Step-by-step explanation:
3 5/4 as a mixed number =
4 1/4
Answer:
3 5/4 could become an improper fraction which would be 17/4.
Step-by-step explanation:
Hey everyone I need help with this. Will mark brainliest as soon as two people answer my question right
Answer:
I think it's (3,1)
9 × ⅓ = 3
3 × ⅓ = 1
HELP ASAP!! The choices are..
-slope
- Y intercept
- X coordinate
- Y coordinate
What is the slope of y = -2x and what does this mean?
Answer:
-2 is the slope
Step-by-step explanation:
Answer:
The slope is -2.
The slope represents the rate of change an object moves in either increasing, decreasing or constant rate.
Utiliza la información del siguiente diagrama para determinar la altura del asta de
la bandera.
1 m
2 m
4 m
¿Cuál es la altura en metros del asta de la bandera en el diagrama
de arriba?
A store sells 3 different sizes of the same juice. The 8 ounce bottle costs $2.96, the 16 ounce bottle costs $5.44, and the 24 ounce bottle costs $9.36. Which size bottle is the better buy?
Answer:
24 ounce bottle.
Step-by-step explanation:
8 Ounce bottle=2.7 for each ounce
16 ounce bottle=2.9 for each ounce
24 ounce bottle=2.6 for each ounce
Translate 2(5+t)=8 into verbal phrase
2(5+t)=8
Step-by-step explanation:
2×5+2t=8
10+2t=8
collect like terms
10-8=2t
2 =2t
divide both sides by 2
2 = 2t
2/2 =2t/2
1 = t
t = 1
Question on a picture
Answer:
c = 0
Step-by-step explanation:
Step 1: Write equation
15 - 5(4c - 7) = 50
Step 2: Solve for c
Distribute -5: 15 - 20c + 35 = 50Combine like terms: -20c + 50 = 50Subtract 50 on both sides: -20c = 0Divide both sides by -20: c = 0Step 3: Check
Plug in c to verify it's a solution.
15 - 5(4(0) - 7) = 50
15 - 5(-7) = 50
15 + 35 = 50
50 = 50
For questions 18-20, if l \\ m, find the values of x and y
Answer:
Step-by-step explanation:
18). l║m and a transverse is intersecting these lines.
(11y - 32)° = (6x + 7)° [Vertical angles]
-6x + 11y = 39 -------(1)
(3x - 16)° + (6x + 7)°= 180° [Same side exterior angles]
9x - 9 = 180
9x = 189
x = 21
Now substitute the value of x in the equation (1)
-6(21) + 11y = 39
11y = 39 + 126
y = 15
19). l║m and a transversal is intersecting these lines.
(8x - 14)° + (5y + 16)° = 180° [Linear pair of angles]
8x + 5y = 178 --------(1)
(8x - 14)° = (5x + 34)° [Alternate exterior angles]
8x - 5x = 48
3x = 48
x = 16
From equation (1)
8(16) + 5y = 178
128 + 5y = 178
5y = 178 - 128
y = 10
20). From the figure attached,
m∠CAB = (5y - 23)°
Since sum of interior angles of a triangle is 180°
m∠CAB + m∠ACB + m∠ABC = 180°
(5y - 23)° + (2x + 13)° + (47)° = 180°
2x + 5y = 143 ------(1)
(5y - 23)° = 3x°
3x - 5y = -23 -----(2)
Equation (1) + Equation (2)
(2x + 5y) + (3x - 5y) = 143 - 23
5x = 120
x = 24
From equation (1)
2(24) + 5y = 143
48 + 5y = 143
5y = 95
y = 19
Samir begins riding his bike at a rate of 6 miles per hour. Twelve minutes later, Chris leaves from the same point and bikes along the same route at 9 miles per hour. How long after Chris begins riding does he catch up to Samir? 4 min 12 min 24 min 40 min
Answer:
The correct option is C) 24 min.
Step-by-step explanation:
It is given that:
Speed of Samir riding his bike = 6mph
Speed of Chris riding his bike = 9 mph
Let the time taken by Chris be x min. Then the time was taken by Samir be x+12
We know that the formula for the distance is
Where d is the distance, t is the time and r is the rate.
According to the question:
[tex]9x=6(x+12)\\9x=6x+72\\9x-6x=72\\3x=72\\x=24[/tex]
Hence, after 24 minutes Chris will catch up to Samir.
Therefore the correct option is C) 24 min.
Answer:C
Step-by-step explanation: edge 2020
Honon spent 3 1/4 hours on homework yesterday while Sequoia spent 2 5/6 hours on homework. How much more time did Honon spend on jomeworm than sequoia
Answer:10/24 = 5/12
Step-by-step explanation:
Identify all of the roots of the function f(x) = x^3 - 5x^2-2x+24
The roots are -2, 3 and 4.
What are roots?A solution to an equation, usually expressed as a number or an algebraic formula.
Given:
x³-5x²-2x+24
As, x+2 divides the x³-5x²-2x+24 gives quotient x²−7x+12.
Now,
x²−7x+12.
=x²− 4x -3 x+12.
=x(x-4) - 3(x-4)
=(x-4)(x-3)
Hence, the roots are -2, 3 and 4.
Learn more about roots here:
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6. In the expression shown prepresents a rational number. 4 p What value of p makes the expression equal a number less than 4?
Answer:
4 - p
Step-by-step explanation:
hope this helped :)
Graph the line with the equation y = x + 6.
Answer:
Hi there!
Your answer is:
Based off the equation we know that the slope is 1 and the y intercept is 6. We know that slope is rise/run so it goes UP one unit for every unit it goes RIGHT! We must start at the point (0,6) because that is the y intercept
1. A candy company used 18 pints of chocolate to make 3 boxes of candy. What is the rate of chocolate per box?
2. A bouquet had 6 flowers and sold for $30, which is a rate of $___ per flower.
3.A carpenter installed 60 sheets of drywall in 10 minutes. What is the rate per minute?
4.A fair owner made 8 dollars when a group of 2 people entered, which is a rate of ___ dollar per person.
5. An industrial machine is able to make 30 pens in 5 seconds. What is the rate made per second?
need answers today
Answer:1. 6 pints per box 2. $5 per flower 3. 6 sheets a minute 4. 4 dollars a person 5. 6 pens a second
Step-by-step explanation:
Please if correct give brainliest :)
Answer:
1) 6 pints of chocolate per box,2) $5 per flower,3)6 sheets of drywall in ten minutes,4) 4$ dollars per person,5) 6 six pens made in 6 seconds
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST
Answer:
1.) 2/3
2.)2 3/17
3.) 16/27
4.)8
5.)1/2
6.)3 3/32
7.) 20/31
8.)1/7 0r 0.142857
Step-by-step explanation:
Need help now please
Answer:
f(13)=105
f(4)=58
f(6)=-5
f(7)=26
Step-by-step explanation:
Good luck
Container A and container B have leaks. Container A has 600 ml of water, and is leaking 5 ml per minute. Container B has 750 ml, and is leaking 7 ml per minute. How many minutes, x, will it take for the two containers to have the same amount of water?
Answer:
si papi
Step-by-step explanation:
square root of -100= _+_
Answer:
The answer i belevie should be 10i
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
I hope this helps
Answer:
-10i
Step-by-step explanation:
Working together ,Ann and Jane painted a total of 480 square feet in 3 hours they each painted the same num of sq feet what is the average rate that ann and Jane each painted in square feet per hour
The average rate that Ann and Jane each painted is 80 square feet per hour.
What is rate of change?A rate of change is a rate that describes how one quantity changes in relation to another quantity.
Now it is given that,
Total area painted by Ann and Jane = 480 square feet
Time taken in painting 480 square feet = 3 hours
Now let x and y be the amount painted by Ann and Jane.
Since,they each painted the same number of sq feet
⇒ x = y
Therefore, Total area painted = x + y = 2x
or, 2x = 480 square feet
⇒ x = 240 square feet
So, the same num of sq feet painted by both is 240 sq feet each
Now average rate = num of sq feet painted by each/time taken
⇒ average rate = 240/3 square feet per hour
or, average rate = 80 square feet per hour
Thus, The average rate that Ann and Jane each painted is 80 square feet per hour.
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PLEASE ANSWER QUICK!!!What are the slope and the y-intercept of the linear function that is represented by the table?
X
-3
0
3
Y
18
12
6
0
a.The slope is -2, and the y-intercept is 6.
b.The slope is -2, and the y-intercept is 12.
c.The slope is 2, and the y-intercept is 6.
d.The slope is 2, and the y-intercept is 12.
Answer:
b
Step-by-step explanation:
the y intercept is at 12 and it slopes down
Answer:
B. the slope is -2, and the y-intercept is 12.
Step-by-step explanation:
i cant really explain stuff that well but basically you have to find the slope. you have to subtract 18-12 and you would get 6. then subtract -3-0 and that would be -3.
you then have to divide 6 (-3) and you would get -2. i never knew how to get 12 tho- sorry lol
WILL DO A BRIANLY! The system inequalities is partially graphed. The only missing portion is the shading. Which area labeled in the diagram should be shaded to represent the solution?
A) A
B) B
C) C
D) D
Answer:
C
Step-by-step explanation:
The Diagonal line is y < = 2, and the horizontal line is y < = x. Since both signs are less than signs, you shade below each line, which would be area c.
Michael wants to buy a new car the car dealership has six read new cars five red used cars three silver new cars and seven silver used cars in how many ways can Michael choose a car if he wants either use a used car a silver car
Answer:
Step-by-step explanation:
6 new red cars
5 used red cars
3 new silver cars
7 used silver cars
Out of all the cars
10/21 (47.6%) chance of picking a silver car
3/21 (14%) of picking a NEW silver car
7/21 (33%) of picking a USED silver car
Out of the Silver cars
3/10 (30%) of picking a NEW used silver car
7/10 (70%) of picking a USED silver car
What is the square root of -16
-8i
-4i
4i
8i
Pls explain tooo
A pool estimate that 43% of likely voters are in favor of additional restrictions on teen drivers the Poll has a margin of error of plus or minus 4%. Write and solve the absolute value equations to find the minimum and maximum percent of voters that support the restriction
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Estimated number of voters in favor of additional restriction = 43%
Margin of Error = ±4%
Write and solve the absolute value equations to find the minimum and maximum percent of voters that support the restriction:
Minimum percentage of voters = 4% lesser than the estimated number of voters
Maximum percentage of voters = 4% greater than the estimated number of voters
Let number of voters = v
|v - 43%| = ±4%
v = - 4% + 43% = 39% = minimum percentage
v = +4% + 43% = 47% = maximum percentage
39% ≤ v ≤ 47%
Round $19.623 to the nearest cent.
Answer:
do wu round it to 6 or 2 ?
Step-by-step explanation:
help, please............!!
Answer:
Simplified or Evaluated Expression:
-52u + 16
Step-by-step explanation:
Answer:
-52u+16
Step-by-step explanation:
of 100 children 3 quarters have pets 40 kids have a dog and 18 have a cat how many kids have other kinds of pets
Answer:
17 kids have other kinds of pets
Please help. The picture is below
Answer:
yea you got it right its c
Step-by-step explanation:
PLZ HELP ASAP WILL MARK BRAINLIEST
Answer:
A value is 6.
Step-by-step explanation: