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addison and kelsey are running on a path modeled by x^2+y^2-10x-18y-378=0, where the distance is in meters. what is the maximum distance between the runners at any given time
The maximum distance is the diameter of the circle, which is of 44 units.
The equation of a circle of radius r and center [tex](x_0,y_0)[/tex] is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The diameter is twice the radius, and is the maximum distance between two points inside a circle.In this problem, the circular path is modeled by:
[tex]x^2 + y^2 - 10x - 18y - 378 = 0[/tex]
We complete the squares to place it in the standard format, thus:
[tex]x^2 - 10x + y^2 - 18y = 378[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 378 + 25 + 81[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 484[/tex]
Thus, the radius is:
[tex]r^2 = 484 \rightarrow r = \sqrt{484} = 22[/tex]
Then, the diameter is:
[tex]d = 2r = 2(22) = 44[/tex]
The maximum distance is the diameter of the circle, which is of 44 units.
A similar problem is given at https://brainly.com/question/24992361
Did I do this right?
Find the measure of angles 1, 2, and 3
Answer:
angle one is 90
angle two is 115
angle 3 is 65
Step-by-step explanation:
Find the product -6(-3/2)(10
A) -60
B) -90
C) 60
D) 90
Answer:
[tex]answer = 90[/tex]
QUICK QUESTION: did I do this right?
Answer:
Yup looks correct
Step-by-step explanation:
Lol I verified using the calculator :)
8n+8=9n solve for the value of n
Answer:
n=8
Step-by-step explanation:
What is an equation of the line in slope- intercept form?
m=2 and the y intercept is (0,3)
Answer:
Y= 2x+3
Step-by-step explanation:
The Slope-Intercept formula is y=mx+b. M is the slope, b is the y intercept, x is the independent variable and y is the dependent variable. In order to write an equation for these types of problems, plug in the numbers for the variables.
What is the solution to the equation −p−13=−43p+23(5p−6)?
Answer:
p = 125/73
Step-by-step explanation:
−p − 13 = −43p + 23 (5p − 6)
−p − 13 = −43p + 115p − 138
−p − 13 = 72p − 138
+p +p
-----------------------------
-13 = 73p - 138
+138 +138
-----------------------------
125 = 73p
/73 /73
-----------------------------
125/73 = p
If you need the answer in mixed fraction, then it's --> p = 1 52/73
The solution to the given equation is p = - 1.71
To determine the solution of the given equation,
We will find the value of the variable, p, that satisfies the equation.
From the question, the given equation is
[tex]-p-13 = -43p+23(5p-6)[/tex]
To solve this,
First, Clear the brackets
[tex]-p-13 = -43p + 115p - 138[/tex]
Now, Collect like terms
[tex]-p +43p -115p = -138 + 13[/tex]
[tex]73p = -125[/tex]
Now, divide both sides of the equation by 73
[tex]\frac{73p}{73} = \frac{-125}{73}[/tex]
∴ p = - 1.71
Hence, the solution to the given equation is p = - 1.71
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whoever solves correctly gets brainliest The number of miles will be x. Next, we’ll have the inequality 8x+2<=10 then we will solve the inequality 8x+2-2<=10-2 and simplify 8x<=8. divide 8 both sides x<=1
4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.
Answer:
Step-by-step explanation:
Explain how to add integers that have like signs (all + or all -).
Answer:
Step-by-step explanation:
If there is two - signs you make it a positive
Answer:
Step-by-step explanation:
To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest. Subtract an integer by adding its opposite.
(x^2 + 2x + 2)(x + 5) = 0
Answer:
[tex] {x}^{2} + 2x + 2 = 0 \: no \: solution \\x + 5 = 0 - \: \: \: \: \: x = - 5 \\ sox = - 5 [/tex]
y apples at 0.35 each
Answer:
I don't understand your question! I would love to help, but I don't understand!
Step-by-step explanation:
Ill give brainles
Evaluate.
−11.9−1
Answer:
I think its -12.9
Step-by-step explanation:
what is the intersection of planes m and L
a. point D
b. line ab
c. line ce
d. they do not intersect
Answer:
d. they do not intersect
Step-by-step explanation:
write the slope-intercept form of the equation (no space)
through: (-1, -2), parallel to y = -2x - 1
Answer:
slope=-2
y+2=(-2)(x+1)
This is the slope intercept form
20 is 4/7 of what number?
Simplify using the distributive property:
5(n-3)=
Answer:
distributive property says x(a+b)
= xa+xb
so 5(n-3)
= 5n-15
Answer: 5n-15
Step-by-step explanation: 5(n-3). multiply n by 5 and -3 by 5 to get 5n-15
Place the decimal point in the quotient to make the division sentence true 8.94 : 0.016 = 55875
PLEASE I NEED HELP BAD​
Answer:
558.75
Step-by-step explanation:
please i need ASAPPPPP ILL GIVE BRAINLIEST!!!!
Hans baked 51 cookles. His family ate m of them. Using m, write an expression for the number of cookles that remained. + ローロ ロメロ
Answer:
[tex]51-m=n[/tex]
Step-by-step explanation:
M - Number of cookies his family ate
N - The remaining number of cookies left
To solve this question you have to use TAN COS SIN i give brainiest
Answer:
4.3Step-by-step explanation:
Use cosine:
cos = adjacent / hypotenusecos ∠L = KL/JLcos 21° = 4/xx = 4 / cos 21°x = 4.3 (rounded)Answer:
4.3Step-by-step explanation:
Here we will use cosine to find the value..
[tex] \cos = \frac{adjacent}{hypotenuse} [/tex][tex] \cos∠l = \frac{kl}{jl} [/tex][tex] \cos21° = \frac{4}{x} [/tex][tex]x = \frac{4}{ \cos21° } [/tex][tex]x = 4.3[/tex] When rounded off...How much is 1 dime and two nickels
Answer:
so 10 +5+5=20
Step-by-step explanation:
so look a dime is 10 cent a nickel is 5 cent
PLEASE HELP ME PLWASE MY LAST ATTEMPT PLEASE HELP ME!!!!!!!
9514 1404 393
Answer:
y = -3/4(x -2)
Step-by-step explanation:
You are given point (2, 0) on the new pipeline. To find the equation of it, you need to know the slope of the line on the graph. A careful look at the graph shows you the line goes through grid points that are separated by 4 units horizontally, and 3 units vertically. For a positive horizontal change, the vertical change is negative, so the slope is ...
m = rise/run = -3/4
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For m = -3/4 and (h, k) = (2, 0), the equation is ...
y = -3/4(x -2)
_____
Additional comments
If you use the distributive property to eliminate parentheses, the equation becomes ...
y = -3/4x +3/2
The slope of the red pipeline can also be determined by considering the slope of the blue pipeline. The two marked points on that line have a horizontal separation of 3 and a vertical separation of 4. Its slope is ...
m = rise/run = 4/3
The slope of the perpendicular (red) line is the opposite reciprocal of this:
-1/m = -1/(4/3) = -3/4 . . . . as we determined from the red line's graph
Raquel estimated 304,900,000,000 as 3 × 10^8. What error did she make?
The error that was made by Raquel when expressing [tex]304,900,000,000[/tex]
is that she didn't count the digit correctly, The correct digit is [tex]3 *10^{11}[/tex]
Raquel was trying to express the figure in standard form but she doesn't count the number of digit very well and that was her mistakeStandard form helps to represent digits that are very long or short in simple form and fir conveniency sakeTherefore, the correct expression in standard form is [tex]3 * 10^{11}[/tex]
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Marcos tem 44 carrinhos em sua coleção e comprou mais 13. Com quantos carrinhos Marcos ficará?
Answer:
Marcos ficará com 57 carros.
Step-by-step explanation:
44+13=57
Aliás, 57 carros é muito carro!
Luigi incorrectly solved the following equation. Explain the error in Luigi's work.
Complete your work in the space provided or upload an image of your work completed on paper.
Answer:
the error(s) is from the step 2
Step-by-step explanation:
3r - 12 = 2r - 3 +4r
3r - 4r -2r = 12 - 3
-3r = 9
r = 9 : (-3)
r = -3
--------------------------
the error(s) is from the step 2
The ordinate of a point is twice its abscissa . If its distance from the point (4,3) is √10 units ,then the coordinates of the point are ?
Answer:
(1 , 2) and (3 , 6)
Step-by-step explanation:
the point P : (x , y) -> (x , 2x) ... ordinate of P point is twice its abscissa, y = 2x
√10 = √(x-4)² + (2x-3)²
5x² - 20x + 25 = 10
x² - 4x + 3 = 0
(x-1)(x-3) = 0
x = 1 or x = 3
y = 2 or y = 6
The ages of three friends are represented by three consecutive odd numbers. The sum of their ages is 63. If the youngest is represented by x, what equation would be used to find x?
Answer:
x+(x+2)+(x+4)=63
Step-by-step explanation:
Karla is going to the store. She bought a banana for $0.67, a jar of peanut butter for $2.35 and a bottle of water for $1.50. If she paid with a $5 dollar bill, how much change will she get back? (Do not use $ in your answer)
Answer:
48 cents
Step-by-step explanation:
The model shows the addition expression 18 + 12.
(A model containing 3 rows of 6 orange squares and 3 rows of 4 blue squares)
One expression that is equivalent to this sum is _______. 1. 3 + 6 + 4 2. 3(6 + 4) 3. 3 + 6(4) 4. 3(6) + 4
Answer:
2. 3(6+4)
Step-by-step explanation:
find the value of k so that the two given lines are parallel. -5x+kx=4 2y-9x=11
The value of k so that the two given lines are parallel is; k = 22.5
First, the correct question is;
-5y+ kx = 4 and 2y-9x=11In line segment geometry;
The slopes of two or more parallel lines are equalFirst, we must determine the slope of the lines by rewriting the equations to resemble the equation of a line in the slope-intercept form; y = mx + c
Therefore, we have;
y = (k/5)x - 4/5.................eqn(1)and y = (9/2)x + 11/2....,........eqn(2)Evidently, the slope of the line in equation 2 is; 9/2.
And since the slope of parallel lines are equal;
k/5 = 9/2By cross product;
2k = 45k = 22.5
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