Ailani draws a map of her local town. She places the town hall at the origin of a coordinate plane and represents a lake
with a circle drawn on the map. The center of the lake is 19 miles east and 3 miles south of the town hall, and the
radius of the lake is 0.5 miles.
If the positive x-axis represents east and the positive y-axis represents north, which equation represents the lake?
O (x + 19)2 + (y - 3)2 = 0.5
O (x – 19)2 + (y + 3)2 = 0.5
O (x + 19)2 + y - 3)2 = 0.25
O (x - 19)2 + ( + 3)2 = 0.25
T
Answers
The equation of the lake with a center 19 miles east and 3 miles south with radius of 0.5 miles is (x + 19)² + (y + 3)² = 0.25
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The equation for a circle is given as:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle and r is the radius.
The center of the lake is 19 miles east and 3 miles south, i.e. (-19, -3) and the radius is 0.5 miles.
The equation of the lake is:
(x - (-19))² + (y - (-3))² = 0.5²
(x + 19)² + (y + 3)² = 0.25
The equation of the lake with a center 19 miles east and 3 miles south with radius of 0.5 miles is (x + 19)² + (y + 3)² = 0.25
Find out more on equation at: https://brainly.com/question/2972832
#SPJ2
Answer: D. [tex](x-19)^2+(y+3)^2=0.25[/tex]
Step-by-step explanation:
Let's review what we know:
the lake is circularthe town hall is at the originthe center of the lake is 19 miles east of the origin and3 miles south of itthe radius of the lake is 0.5 milesA circle can be depicted on the coordinate plane with the equation [tex](x-h)^2+(y-k)=r^2[/tex], where:
(h, k) is the center of the circleand r is the radius of the circle19 miles east of the origin would be 19 units to the right of the origin on the coordinate plane, as east is the rightwards direction in real life. In short, h = 19.
Let's plug in that value: [tex](x-(19))^2+(y-k)^2=r^2[/tex].
So we know that the x-coordinate defining part of the equation would have to be [tex](x-19)^2[/tex].
Meanwhile, 3 miles south of the origin would be modeled as three units underneath it, because south would be considered "downwards". The y-value (k) would be negative 3.
Putting what we have so far together, the center of the circle would be (19, -3).
Therefore, the y-coordinate defining part of the equation would be [tex](y+3)^2[/tex].
Here's what the equation looks like with the work we've completed so far: [tex](x-19)^2+(y+3)^2=r^2[/tex]
Finally, let's plug in the radius value 0.5.
0.5 * 0.5 = 0.25
Ailani would use the equation [tex](x-19)^2+(y+3)^2=0.25[/tex] to model the lake in relation to the town hall. I hope that makes sense!
Related Questions
plz help me with this math problem
Answers
Answer:
[tex]a = 9in[/tex]
Step-by-step explanation:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]
[tex]a = \sqrt{ {10.6}^{2} - {5.6}^{2} } [/tex]
[tex]a = \sqrt{112.36 - 31.36} [/tex]
[tex]a = \sqrt{81} [/tex]
[tex]a = 9in[/tex]
If x + y = –10 and x - y = 2, what is the value of x?
Answers
Answer:
y -10
x graph
Step-by-step explanation:
I know there is a very similar question already out there
but my version is requesting different functions
Cami is comparing the growth rates in the value of two items in a collection. the value of a necklace increases by 3.2% per year. the value of a ring increases by 0.33% per month.
1a) Write a function to represent the value of A of the necklace after t years, assuming the initial value of $1
1b) then write an equivalent function with a power of 12t
2a) Write a function to represent the value of B of the ring after t years with the power of 12t , assuming the initial value of $1
2b) then write an equivalent function with a power of t
so
1a) A= 1 (1+3.2/100)^t
A= $1.032
1b) ????? please help
2a) B=1 (1+0.33/100)^12t
B= $1.04
2b) ???????? please help
ty ty ty this momma is trying to help her kids and is a bit lost !
Answers
Problem 1, part (a)
t = number of years
A = value of the necklace after t years
3.2% = 3.2/100 = 0.032
If the necklace starts off being $1, then after t years, it will have this value
A = 1*(1 + 0.032)^t
A = 1.032^t
You were close, but forgot about the exponent t
------------------------------------
Problem 1, part (b)
Since t represents the number of years, this means 12t represents the number of months, because there are 12 months in a year.
The annual growth rate is 3.2%, which converts to 0.032
Divide this over 12 and we get the approximate value 0.032/12 = 0.00267
So we get this new equivalent function
A = 1*(1+0.00267)^(12t)
A = 1.00267^(12t)
=========================================================
Problem 2, part (a)
t = number of years
12t = number of months
The ring's value goes at a rate of 0.33% per month, which converts to the decimal form 0.0033
The value of the ring is
B = 1*(1 + 0.0033)^(12t)
B = 1.0033^(12t)
------------------------------------
Problem 2, part (b)
We'll take the reverse approach in what we did with part (b) of the previous problem. There we divided by 12 to go from an annual rate to a monthly rate.
We'll multiply by 12 to go from the monthly growth rate to the annual growth rate.
The monthly growth rate of 0.33% turns into the annual growth rate of 12*0.33% = 3.96%, and that turns into the decimal form 0.0396
So,
B = 1*(1+0.0396)^t
B = 1.0396^t
represents the value of the ring after t years.
Write an equation of the locus of all points equidistant from the x axis and the y axis and whose coordinates have the opposite signs.
Answers
Answer:
y=-x
Step-by-step explanation:
Since the y-axis and x-axis are intersecting lines then you need to apply the locus of intersecting lines which would be the angle bisector and since the problem is asking for the opposite signs you need to make it -x instead of x.
Hope this helps
:)
Find the shaded area
Help please
Answers
Answer:
Area= 49[tex]\pi[/tex] or 153.94 or 147 (Since Pi= 3)
Circumference= 14[tex]\pi[/tex] or 43.98 or 42 (Since Pi= 3)
Step-by-step explanation:
[tex]A=\pi rx^{2}[/tex]
[tex]C=2\pi r[/tex]
Select the correct answer
What is the range of this function?
Answers
Answer:
The answer is A.
Step-by-step explanation:
Plato
The range of the function is (A)
What is graph?
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, per the graph we can see that the range for y starts from negative infinity but it only exceeds upto +4.
Hence, the range is -∞ < y ≤ 4.
Learn more about graph here:
https://brainly.com/question/16608196
#SPJ2
Write an Integer for each situation. Moving 5 spaces back on a game board
Answers
A bag has 5 balls: 1 red (R), 1 green (G), 1 yellow (Y), 1 blue (B), and 1 orange
(0)
You randomly choose a ball. What is the sample space?
OA. (RG, Y, B, O)
OB. (R,G, Y, B, P)
Oc. (G, )
OD. (R, G, Y, B)
Answers
Answer: R,G,Y,B,O
Step-by-step explanation: Sample space is just any and all possible outcomes
The sample space of the given experiment is (R,G, Y, B, O). So option A is the correct one.
What is a Sample Space?A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.
The subset of the sample space are events.
Given experiment is that you randomly choose a ball from a bag which consists of 5 balls.
Balls are 1 red (R), 1 green (G), 1 yellow (Y), 1 blue (B), and 1 orange (O).
Each ball is of different color.
When you randomly choose a ball, the chosen ball can be any of the colors given.
So sample space = (R,G, Y, B, O)
Hence the required sample space is (R,G, Y, B, O).
Learn more about Sample Space here :
https://brainly.com/question/30206035
#SPJ7
what is the slope of the line?^
Answers
Answer:
(1/0) infinite slope if it is going wrong sorry
Can someone help me?
Answers
Answer:
Step-by-step explanation:
Because these two triangles are isoceles triangles, two angles are the same, which in this case would be 78. 78 times 2 would give us 156 for the right triangle, but since 180 - 156 does not equal 16, they are not similar nor congruent.
Please I need help
I will mark you brainliest
Answers
Answer:
60ft
Step-by-step explanation:
Using the formula shown a^2 + b^2 = c^2
5 ^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
Take the square root of both sides:
C = 13
Solve the systems of equations 9x+5y=41 and x+y=9 by combining the equations
Answers
Step-by-step explanation:
multiplying the 2nd eqn by 9 we get,
9x+9y=81
then,subtracting 1st and 2nd eqn
9x+5y=41
9x+9y=81
- - -
__________
0. -4y=-40
we get y = 10
then we get x=9-y
x=9-10
x= -1
so x is -1 and y is 10
What is the slope of the line through
(-9, 6) and (-6, -9)? Show your work.
Answers
Answer:
-5
Step-by-step explanation:
HURRY PLEASEEEEEEEEEEE. A coordinate plane. The point (5, 5) is in Quadrant . The point (3, –2) is in Quadrant . The point (–4, –4) is in Quadrant .
Answers
Answer:
point (5, 5) is in Quadrant: I (1)
point (3, –2) is in Quadrant: IV (4)
The point (–4, –4) is in Quadrant: III (3)
Step-by-step explanation:
Answer:
The point (5, 5) is in Quadrant
✔ I
II
III
IV
The point (3, –2) is in Quadrant
I
II
III
✔ IV
The point (–4, –4) is in Quadrant
I
II
✔ III
IV
Expression equivalent to 8p-3n+4q-9m
Answers
Answer:
4p-n+2q-3m is equivalent to 8p-3n+4q-9m
The expression 4(2p+ q) - 3(n+3m) is equivalent to the given expression. which is the correct answer would be an option (C).
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question following:
8p - 3n + 4q - 9m
We have to determine the equivalent expression to the given expression
As per option (C), we have
⇒ 4(2p+ q) - 3(n+3m)
Apply the distributive property of multiplication,
⇒ 4 × 2p+ 4 × q - 3 × n + 3 × m
⇒ 8p + 4q - 3n + 3m
Rearrange the terms in the above expression,
⇒ 8p - 3n + 4q - 9m
So this expression is the same as the given expression.
Therefore, the expression 4(2p+ q) - 3(n+3m) is equivalent to the given expression.
Learn more about Expressions here :
brainly.com/question/21751419
#SPJ5
The question seems to be incomplete the correct question would be:
Which expression is equivalent to 8p-3n+4q-9m
A. 0
B. 5pn - 5qm
C. 4(2p+ q)-3(n+3m)
D. 4(2p+q)-3(n-3m)
x = sin 1/2θ, y = cos 1/2θ, −π ≤ θ ≤ π (a) Eliminate the parameter to find a Cartesian equation of the curve.
Answers
Answer:
Use the form a cos ( b x− c) + d to find the amplitude, period, phase shift, and vertical shift.
x = sin ( 1 2 θ )
y = cos ( 1 2 θ )
− π ≤ θ ≤ π ( a )
Step-by-step explanation:
find the perimeter of the square on the centimeter grid
Answers
6) Solve the equation by Completing the Square. Show all the solutions.
x2 + 8x -5 = 0
Answers
I used tiger algebra cause why not. You should try it!
an acting troupe is holding a performance in an arena they are selling child tickets for $2 and adult tickets for $4 the arena can hold at most 200 people and the troupe is hoping to make atleast $400 in ticket sales graph the inequalities
Answers
Answer plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
Step-by-step explanation:
10+60t≤280
60t≤280-10
60t≤270
6t≤27
2t≤9
t≤9/2
t≤4.5
t=4 hours
first subtract $10 from$280 and you get $270
270 divided by 60 = 4.5
so the answer is four and a half hours
"I think of a number, take away 1 and multiply the result by 3."
Write it in algebraically, using x as your unknown
Answers
Answer:
(x-1)3
3x-3
Step-by-step explanation:
I came up with this.
The resultant of the expression of the given phrase as take away 1 and multiply the result by 3 will be 3x - 3.
What is an expression?An expression is a combination of some mathematical symbol such as an arithmetic operator and variable that are all constrained and create an equation.
In other meaning, expression is beneficial to determine the end or root value of constraint.
For example 3x +5y
As per the given,
take away 1 = x - 1
Multiply the result by 3 = 3(x - 1)
3(x - 1) = 3x - 3
Hence "The resultant of the expression of the given phrase as take away 1 and multiply the result by 3 will be 3x - 3".
To learn more about expression,
https://brainly.com/question/14083225
#SPJ2
creating a diagram so far this session a team has won 51 out of 68 games identify the value of a b c and d that complete the bar diagram for the situation
Answers
Answer:
a = 25
b = 100
c = 17
d = 68
Step-by-step explanation:
2/a - 6 = 12
= 12
Nejekernammd
Answers
Answer:
what's the question xjsbzbksns
Answer:
what r u asking?
Step-by-step explanation:
please help as fast as possible
Answers
Answer:
D
Step-by-step explanation:
You can divide each side length by two to get D
Answer:
The answer is D
Step-by-step explanation:
Hiroshi found that 3/5 of his class prefers vanilla ice cream, 26% prefers chocolate ice cream, and 0.14 prefers strawberry ice cream. Put the numbers in order from least to greatest. Which kind of ice cream do the least number of students prefer?
help asappp!!!
Answers
Answer:
The kind of ice cream the least number of students prefer is Strawberry ice cream.
Step-by-step explanation:
We convert all given values to decimal
Hiroshi found that:
a) For vanilla ice cream
3/5 of his class prefers vanilla ice cream
3/5 to decimal = 0.6
b) For Chocolate ice cream
26% prefers chocolate ice cream
26% to decimal = 0.26
c) For strawberry ice cream
0.14 prefers strawberry ice cream
0.14 = 0.14
Arranging the numbers in order from least to greatest, we have :
0.14, 0.26 , 0.6
The kind of ice cream the least number of students prefer is Strawberry ice cream.
A recipe calls for 2 cups of flour and 1 1/2 cup milk to make four servings. Ming has plenty of flour, but only 6 cups of milk. How many servings can he make?
Answers
1 and -1 is nonlinear or linear
Answers
Answer:
liner
Step-by-step explanation:
they look like a line on a graph
find the value of r so that the line through (8 r) and (4 5) has a slope of -4
Answers
Answer:
r = -11
Step-by-step explanation:
slope formula: (y2-y1)/(x2-x1) = slope
(5-r)/(4-8) = -4
(5-r)/ -4 = -4
5-r = 16
-r = 11
r = -11
im not sure but i beleive this is how you do it.
you find the agreegable slope, and then multiply it by the y value.
hope this helps! :)
What is the sum of 1/9, 2/3, and 5/18? A. 12/9 B.19/18 C.8/30 D.4/15
Answers
angie painted 1/20 of the fence in half an hour. how long will it take her to finish one fence?
Answers
Answer:
What are the choices
Step-by-step explanation: