The maximum distance between them is the diameter of the circle, which is of 44 units.
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r 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 on the same circle.
They are running on a circular path, modeled by:
[tex]x^2 + y^2 - 10x - 18y = 378[/tex]
Completing the squares, the equation is:
[tex](x - 5)^2 + (y - 9)^2 = 378 + 5^2 + 9^2[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 378 + 25 + 81[/tex]
[tex](x - 5)^2 + (y - 9)^2 = 484[/tex]
Then, the radius is: [tex]\sqrt{484} = 22[/tex], which means that the maximum distance between the runners at any given time is of 44 units.
A similar problem is given at https://brainly.com/question/25008198
Vani signed up for a streaming music service that costs $12 per month. The service allows Vani to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1.25 per song. How much total money would Vani have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded s songs?
Answer:
49.5$
Step-by-step explanation:
first you need to multiply 1.25*30 which will give you 37.5 then from there add the monthly cost which is 12$ giving you the total of 49.5$
Brittany bought 3 bracelets and 2 necklaces for $21. Each bracelet cost $5. The necklaces were all the same price. What is the cost for 1 necklace?
Answer:
The cost for 1 necklace is $3.
Step-by-step explanation:
With the information provided, you can say that the amount spent in bracelets and necklaces is equal to the price per bracelet for the number of bracelets plus the price per necklace for the number of necklaces, which is:
c=3x+2y, where:
c is the total cost
x is the price per bracelet
y is the price per necklace
Now, you can say that c=21 and x=5 and solve for y to find the price per necklace:
21=(3*5)+2y
21=15+2y
21-15=2y
6=2y
y=6/2
y=3
According to this, the answer is that the cost for 1 necklace is $3.
What is 5g+7g and g(5+7)?
Answer:
12g and 12g
Step-by-step explanation:
5g + 7g = 12g
g(5+7) = g(12) = 12g
What is the simplest form of the fraction below?
24/36
Answer:
2/3
Step-by-step explanation:
A rectangular tank with length 50 cm and width 30 cm contains 36 litres of water. Find the depth of the water.
Answer:
24cm
Step-by-step explanation:
Given data
Length=50cm
Width= 30cm
Volume = 36liters
=36000cm^3
We know that the expression for volume is
V= L*W*H
substitute
36000=50*30*H
36000= 1500*H
H= 36000/1500
H= 24cm
Hence the height is 24cm
Each quadrilateral below is a parallelogram . find the missing measures .
Answer:
AD = 8
DC = 15
m∠A = 112°
m∠B = 68°
m∠C = °
Step-by-step explanation:
If we're working with parallelograms, we can assume that each line and it's opposite are perfectly parallel.
To find AD, all you need to do is look to the opposite line, BC. Since This is a parallelogram, AD = BC, so AD is 8.
To find DC, you do the exact same. Find the opposite line that it is parallel to, in this case that's AB, and since AB = DC, you know that DC = 15.
To find m∠A, let's look at m∠D. Since m∠D = is 68°, We can use that knowledge to find m∠A. Since the two angles are right beside each other on the same line, together they would equal 180° if you added them up. But since you don't know what m∠A is, you just have to subtract 68 from 180.
180 - 68 = 112.
To find m∠B, We simply look back to m∠D. Since m∠B is directly opposite to m∠D, That means they have the same value, 68°.
And finally, to find m∠C, we do the same thing we did to find m∠B. m∠C is directly across from m∠A - we have already found m∠A, and we know that it is 112°. Therefore, m∠C is 112° as well.
I WILL GIVE YOU 58 POINTS!!!!!!!!!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Input(x) Output(y) 32 20 14 2 ? − 6 -2 -14 -10 ? Complete the function table and write the function rule.
Answer:
3rd box = 6
6th box = -22
y=x-12
output = input-12
Step-by-step explanation:
The input value correspond to output value = -6 is +6
The output value correspond to input value = -10 is -22
What is function Rule?A function rule is the relationship between the dependent and independent variables in the form of an equation.
As per the given data if we follow the pattern we get a relation between Output and Input as:
Output= Input-12
or, input= Output + 12
So, we have to find the input when output= -6
Input = -6+12
=+6
Now, to find the output when input is -10
output= -10-12
=-22
Learn more about function rule here:
https://brainly.com/question/20527725
#SPJ2
Time Remaining56:19m:s When I have walked 20 % of the way to school, I have 1200 metres more to walk than when I have 20 % of the walk remaining. How far, in metres, is it from my home to my school?
Answer:
x = Total distance from your home to school = 1,500 meters
Step-by-step explanation:
Let
x = Total distance from your home to school
When you walked 20% of the way to school, you still have 1200 meters more to walk
Walked distance = 20% of x
= 20/100 * x
= 0.2 * x
= 0.2x
Total distance - walked distance = 1200 meters
x - 0.2x = 1200
0.8x = 1200
x = 1200 / 0.8
x = 1,500 meters
x = Total distance from your home to school = 1,500 meters
what is1 00 + 84 – 62x = 494
100 points!
At what point(s) do these graphs intersect? y=x^2 = 3x-5
y=4x+1
Seth’s solution:
y=x^2 +3x-5
y=4x+1
x^2 =3x-5=4x+1
x^2 -x-6=0
(x-3)(x+2)=0
x=3 and x=-2
The graphs intersect at (-2,0) and (3,0).
Is Seth's solution correct? Explain.
Answer:
Solution is correct till finding the roots:
x = 3, x = -2Then Seth should find the respective y- points using either equation:
y = 4*3 + 1 = 13and
y = -2*4 + 1 = -7Correct solution is:
(3, 13) and (-2, -7)Answer:
Seth's answer is incorrect.
Step-by-step explanation:
He is correct with all of his steps until he reaches the roots... the correct roots are, y = 4(3) + 1 = 13 y = 4(-2) + 1 = -7
So the correct answer would actually be: The graphs intersect at the coordinates (3,13) and (-2,-7)
Keion is calculating his expenses from his work trip to San Francisco. Below is the expense log he kept while traveling.
Expense Amount of Expense
Airfare $379.00 round trip minus $15.00 movie on plane
Hotel $154.00 per night × 3 nights
Dinner $65.00 plus $13.00 tip
Car Mileage $0.55 per mile × 63 miles
Keion will submit all of the expenses to his company for reimbursement except for the movie on the plane. How much will he be reimbursed for?
A
$784.65
B
$923.65
C
$925.65
D
$938.65
Answer:
D
Step-by-step explanation:
379.00 - 15.00 + 154.00 x 3 + 65.00 + 13.00 = 904
0.55 x 63 = 34.65
34.65 + 904 = 938.65
Answer:
Your answer is D
Step-by-step explanation:
because 379-15+154x3+65+13+0.55x63=938.65
What is the 15th term in the sequence with the given formula?
An = 7n – 10
The Smiths spend 8% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $3,920 on entertainment. What was their total budget last year?
Answer:
4.8
Step-by-step explanation:
Jamie sees a sale at the Gaming Store where all games are the same price. He buys 3 video games. His sister talks him into also buying two $1.50 candy bars and a $2.00 drink for a total of $57.50. Write an equation to find the price of one video game.
Answer: 3x + 5 = 57.50
Step-by-step explanation:
Assume that the price of one video game is x. Jamie bought 3 video games so the expression will be:
= 3x
His sister talked him into buying two $1.50 candy bars and a $2.00 drink. The total of this is:
= 1.50 + 1.50 + 2.00
= $5.00
The total amount spent on both the video game and the snacks is $57.50. Equation will therefore be:
3x + 5 = 57.50
un refresco tiene una concentración de 3.8 x 10-4 de iones H+. determina el valor de PH de ese refresco
Answer:
El pH del refresco es 3.42.
Step-by-step explanation:
Se puede calcular el pH del refresco usando la siguiente fórmula:
[tex]pH = -log([H^{+}])[/tex]
En donde:
[H⁺]: es la cocentración de los iones H⁺ de la solución
Entonces, el pH es:
[tex]pH = -log([H^{+}]) = -log(3.8\cdot 10^{-4}) = 3.42[/tex]
El resutlado obtenido nos permite concluir que ese refresco es ácido.
Por lo tanto, el pH del refresco es 3.42.
Espero que te sea de utilidad!
Usando su fórmula, se encuentra que el valor de PH de ese refresco es dado por 3.42.
Cual es la fórmula para el valor de PH?Es dada por:
[tex]pH = -\log{H^{+}}[/tex]
Onde [tex]H^+[/tex] es la concentración.
En este problema, hay que la concentración es de [tex]H^+ = 3.8 \times 10^{-4}[/tex], por eso:
[tex]pH = -\log{H^{+}}[/tex]
[tex]pH = -\log{3.8 \times 10^{-4}}[/tex]
[tex]pH = 3.42[/tex]
El valor de PH de ese refresco es dado por 3.42.
Puede-se aprender mas sobre el valor de PH en https://brainly.com/question/16146414
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
2:3
Step-by-step explanation:
You can divide 6:9 by 3
6/3=2
9/3=3
So, therefore the answer is 2:3.
What is the solution to this system of linear equations?
Answer: To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.
Step-by-step explanation: hope this helps
5(-7)+9(4) I am confused on this problem
Answer:
the answer is 1
Step-by-step explanation:
Answer:
It's really easy, just need to multiply and add the symbol of the multiplication, the answer is: 1
-35+36=1
A new car has a sticker price of $25750, while the invoice price paid on it was 21950, what is the percentage?
Answer:
24750/21950 = 1.12756 or 112.756% of the original price. 12.76% is the correct answer.
Step-by-step explanation:
Answer:
24750 ÷ 21950 = 17.31% as the original price
Step-by-step explanation:
Which inequality represents this situation?
The number of students, s, who ride in a bus is less than 30.
s< 30
s> 30
S 30
ss 30
Answer:
s<30
Step-by-step explanation:
s is the number of students. the staement says the number of students is less than 30
PLEASE HELP
Is th function shown a linear function?
EXPLAIN PLZZ
NO LINK
Need help with this asap!
Answer:
Step-by-step explanation:
area circle = πr² or π(d/2)² but how to find the diameter?
The only angles I can see to calculate is in the small right triangle
The smaller angle on the right is ...
sin Ф = opp/hyp = 6/10 Ф = 36.87°
This angle is the same as the small angle on the LARGE right triangle
So now I want to calculate the side (diameter) opposite the smaller angle
sin Ф = opp/hyp = diameter/300 = sin 36.87°
diameter = 300 sin 36.87°
= 300 (6/10)
= 180 ft
area circle = πr² or π(d/2)²
area circle = π(180/2)²
area circle = 25446 ft² which is close to answer A 25434 ft²
There is actual no need to find the sin Ф wasted step
just use 6/10 small triangle is similar to diameter/300 the large triangle
opp / hyp small 6/10 = diameter/300 diameter = 180
area circle = π(180/2)² = 25446
❗❗❗PLS I NEED HELP ON THIS I DON'T UNDERSTAND PLS HELP❗❗❗❗❗❗
❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗❗
Answer:
3) H' = (-5,-4) I' = (-2,2) J' = (-2,-4)
4) K' = (-8,-3) L' = (-8,-8) M' = (-6,-8)
5) N' = (2,1) O' = (1,6) P' = (-2,3)
6) Q' = (0,3) R' = (-1,-2) S' = (3,1)
Step-by-step explanation:
All you have to do is exactly what the directions tell you to do. First, plot the original image of the triangle (The letters without the apostrophe (') behind it), and then recreate it on the opposite side of whatever axis it tells you to. The x-axis is the horizontal line, and the y-axis is the vertical line.
When you're doing this, think of it as a mirror. The mirror is whatever line it tells you to reflect the image across. The final product will be the exact same image, but reversed to the opposite of the axis chosen.
Let me know below in a comment if something confused you in my explanation, I'll try my best to re-word it better so you can understand :)
(HELP I BEG U THERE IS 20 MIN LEFT I NEED SLEEP AND I WILL GIVE BRAINLY )
Answer:
your answer is number 3 or 4 I believe it is both
write 19/41 in lowest forms
Answer:
19/41
Step-by-step explanation:
this fraction cannot be simplified since 19 is a prime number.
Which graph best represents the equation 2x + 4y = -8?
Answer:
y = -1/2x - 2
Step-by-step explanation:
2x + 4y = -8
4y = -2x - 8
y = -1/2x - 2
Name an outcome that has a probability between 0 and 0.5.
Program the VR Robot to drive in a square. Make each side of the square 3 grid squares long. What is the area of your square in mm? Use a calculator and/or pencil and paper to find out.
Answer:
9 mm squared
Step-by-step explanation:
hope this helps, lol :b
A composite shape consists of a square with a semicircle sitting on top of it. The dimension of the square (which is
also the dimension on the half circle) is 20 yards. What is the area of this composite shape?
Answer:
40m i think
Step-by-step explanation:
jane leaves her bicycle at 8:00 AM, traveling at an average speed of 15mph. her brother frank leaves home in his car at 10:30 AM, traveling the same route as Jane at an average speed of 40 mph. at what time will they meet? i will give brainliest
Answer: 11:00
Step-by-step explanation:
Answer: 11:00
Step-by-step explanation: