Answer:
[tex]\displaystyle \boxed{ (x - 6)^2 + (y - 2)^2 = 64 }[/tex]
General Formulas and Concepts:
Precalculus
Circle Equation:
[tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
Center (6, 2)
h = 6k = 2r = 8
Step 2: Find Equation
[Circle Equation] Substitute in variables:∴ we have found the equation for the circle with given properties.
---
Topic: Precalculus
Unit: Conics
The equation of a circle is [tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex].
What is circle?A circle is a shape made up of all points in a plane that are at the same distance from a central point.
Equation of the circle [tex]\[{{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}\][/tex] where (h,k) is the coordination of the center and r is the radius
Which is the equation for the circle with center (6, 2) and radius 8?put the values of h, k and r in the equation of the circle
[tex]{{\left( x-6 \right)}^{2}}+{{\left( y-2 \right)}^{2}}={{8}^{2}}[/tex]
[tex]{{x}^{2}}+{{y}^{2}}+36+4-12x-4y=64[/tex]
[tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex]
therefore, the equation of the circle is[tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex].
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2) A band played an encore at 4 of its last 14 shows. What is the
experimental probability that the band will play an encore at its next
show?
a.2/7
b.3/7
c.4/7
d.5/7
Answer:
a. 2/7
Step-by-step explanation:
Please kindly go through the attached file for explanation
These box plots represent the number of seconds that a random sample of 100 traffic lights are red in each of two cities: Johnstown and Martinville
Answer:
The question is not complete. Attached to this answer is the diagram of the box plot and the complete question:
These box plots represent the number of seconds that a random sample of 100 traffic lights are red in each of two cities: Johnstown and Martinville
Based on the data on the two box plots, which statement about the difference in the medians of the two data sets is true?
The correct answer is:
The difference is about [tex]\frac{1}{2}[/tex] times the range of the data shown for Johnstown,and about [tex]\frac{3}{8}[/tex] times the range of data for Martinville. (D)
Step-by-step explanation:
From the box plot, it is seen that the following data can be gotten:
Cities Range Midian (mid-point)
Johnston 140 - 80 = 60 110
Martinville 120 - 40 = 80 80
Difference in medians = 110 - 80 = 30
now comparing the difference between the median and the ranges of each city, we observe that:
range for Johnston = 60 ; median difference = 30
hence difference in medians : range for Johnston = 30 : 60 = 1 : 2 = 1/2
hence difference of medians is [tex]\frac{1}{2}[/tex] times the range of Johnston.
Difference of midians : range of Martinville = 30 : 80 = 3 : 8 = 3/8
hence the difference of medians is [tex]\frac{3}{8}[/tex] times the range of Martinville.
Answer: The question is not complete. Attached to this answer is the diagram of the box plot and the complete question:
These box plots represent the number of seconds that a random sample of 100 traffic lights are red in each of two cities: Johnstown and Martinville
Based on the data on the two box plots, which statement about the difference in the medians of the two data sets is true?
The correct answer is:
The difference is about times the range of the data shown for Johnstown,and about times the range of data for Martinville. (D)
Step-by-step explanation:
From the box plot, it is seen that the following data can be gotten:
Cities Range Midian (mid-point)
Johnston 140 - 80 = 60 110
Martinville 120 - 40 = 80 80
Difference in medians = 110 - 80 = 30
now comparing the difference between the median and the ranges of each city, we observe that:
range for Johnston = 60 ; median difference = 30
hence difference in medians : range for Johnston = 30 : 60 = 1 : 2 = 1/2
hence difference of medians is times the range of Johnston.
Difference of midians : range of Martinville = 30 : 80 = 3 : 8 = 3/8
hence the difference of medians is times the range of Martinville.
Step-by-step explanation:
oel biked 9 miles east and then 12 miles north. If he biked back to his starting point using the most direct route, how many miles would he ride all together?
Answer:
36 miles
Step-by-step explanation:
(Imagine a huge triangle on a perfectly open space-- not with streets or houses or cornfields.)
The dimensions of the two sides given are multiples of a classic Pythagorean Triple: 3, 4, 5. [tex]3^{2} + 4^{2} = 5^{2}[/tex]
9 is 3x3, 12 is 3x4 so the remaining side would be 3x5 15
Add those 3 sides to get the total distance, 36 miles.
Answer:
36
Step-by-step explanation:
Which line segment is a diameter of circle F?
Answer:
AC
Step-by-step explanation:
We know that a diameter of a circle is any straight line segment that passes through the center of the circle such that whose endpoints lie on the circle. It is also be known as the longest chord of the circle.
In the given figure we can see that only AC and BE are the line segments that pass through the center of the circle such that whose endpoints lie on the circle.
Answer:
AC
Step-by-step explanation:
Which of these situations could be written as an equation with one variable?
A
Penny picked 35 apples, Ben picked 22 and Sam picked 17. They picked 74 apples all together. Who picked the most apples?
B
Harriet and Lea found 9 four-leaf clovers on the baseball field in all. Harriet found 5 of them. How many clovers did Leah find?
C
There were 45 doughnuts at the snack table today. Tanisha brought 33 of them, and Doug brought 12. Where did Tanisha buy her doughnuts?
D
Lori bought the most T-shirts of anyone in her family. She bought 1 more T-shirt than Thea and 3 more than Pino. How many shirts did Lori buy?
BACK
Answer:
b
Step-by-step explanation:
Because i dont know I just need points bro
It would be B becuase 9-x=5
P.S x=4
Determine the slope of the line below.
A. -3 B. 3 C. 1/3 D. -1/3
• Each number on a number cube is a possible result, or _______________, of rolling the cube.
Ratio or outcome maybe?
Use the distributive property to expand the following expression.
−3(2x+(−7)+5y)
Answer:
-6x +21 -15y
Step-by-step explanation:
−3(2x+(−7)+5y)
Distribute
-3*2x + -3*-7 + -3*5y
-6x +21 -15y
The coordinates of point A on a grid are (2, -5). Point A is reflected across the x-axis to obtain point B. The coordinates of point B are (2, ___). (1 point)
Answer:
(2,5)
Step-by-step explanation:
If you are flipping a point over the x-axis, multiply the y coordinate by -1, if you are flipping something over the y-axis, multiply the x coordinate by -1.
The coordinates of point B are (2,5)
How does reflection across axis work?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.
If you study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
Given that coordinates of point A on a grid are (2, -5). Point A is reflected across the x-axis to obtain point B.
Since flipping a point over the x-axis, then we have to multiply the y coordinate by -1,
And ifyou are flipping something over the y-axis, then we have to multiply the x coordinate by -1.
Therefore, the point B are (2, _5_).
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A. (7, -2), (4, -1), (3, 0), (4, 1), (7,2)
B. (-2, 1), (-1, 2), (0, 3), (1, 4) (2, 7)
C. (-2, 7), (-1, 4) (0, 3) (1, 4), (2, 7)
D. (1, -2), (2, -1), (3, 0), (4, 1), (7, 2)
Answer:
the answer is c
all work is pictured
pls help me give u a brainlest
Answer:
uhmm. lemme remember how to do that
Answer:
30 in
Step-by-step explanation:
V=Bh
Find the area of the triangle then multiply it by the height of the prism.
A 12-sided die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find the probability of rolling a 9.
Answer:
1/12
Step-by-step explanation:
Since all are equally likely, each outcome has a probability of 1/12.
P(9) = 1/12
Answer:
1/12
Step-by-step explanation:
The probability of rolling a nine is given by the number of good outcomes over the total outcomes
P(9) = number of 9's / total
=1/12
Art and PE
--------- Art No Art Total
PE A B C
No PE D E F
Total G H J
300 students in a middle school take Art, and 250 of those students also take PE. There are 250 students who do not take Art but do take PE. 125 students take neither Art nor PE. If you were to complete the two-way table shown here, which value would go in position D?
A) 50
B) 75
C) 100
D) 125
Answer:
A) 50
Step-by-step explanation:
D: Art & No PE
Art - Art&PE
300 - 250
50
Answer:
Answer is 50
Step-by-step explanation:
I just did the test on usatestprep
Finish the sentence....
FTC Flight team____________?
Answer:
Step-by-step explanation:
What it do Flight Crew FTC Flight Team Stand UPPPPPP
11) Find the length of side x. picture is above!
I will give you 20 points and
brainliest
Answer:
25m :)
Step-by-step explanation:
What is the volume of the right rectangular prism with a length of 2 millimeters, a width of 4 millimeters, and a height of 8 millimeters?
Answer:
8
Step-by-step explanation:
Answer:
64
Step-by-step explanation:
2 times 4 times 8 = 64
what is a number that when you multiply it by 4 and add 15 to the product you get 28? show your work please
Answer:2
Step-by-step explanation:
Thomas wants To find out which sport the entire 8th grade cloth on his school likes best
Answer:
Ok what are his options?
Step-by-step explanation:
Answer:
Ping Pong
Step-by-step explanation:
dunno
Can someone help me out
Answer:
m= -5/8
Step-by-step explanation:
Slope of a line containing the points,
[tex] \frac{y2 - y1}{x2 - x1} = m[/tex]
where, m is the slope
Here,
[tex]m = \frac{7 - 2}{4 - 12} = \frac{ 5}{ - 8} = \frac{ - 5}{8} [/tex]
What is the area of the following circle?
Either enter an exact answer in terms of t or use 3.14 for it and enter your answer as a decimal.
r=1
Answer:
The area is 3.14
Step-by-step explanation:
Get the radius and times it by itself then multiply it by pie and you get 3.14
What is the f?
f/5 - (-13) = 12
Step-by-step explanation:
[tex] \frac{f}{5} - ( - 13) = 12[/tex]
[tex] \frac{f}{5} + 13 = 12[/tex]
[tex] \frac{f}{5} = 12 - 13[/tex]
[tex] \frac{f}{5} = - 1 [/tex]
Now cross multiply
Therefore f = -5
Answer:
f= -5
Step-by-step explanation:
f/5-(-13)=12
remove the parenthesis and replace the negative with a positive.
f/5+13=12
multiply all by 5
f+65=60
move constant to the right
f=60-65
subtract 60 to 65
-----------------
f= -5
-----------------
factor completely 36x2 – 1.
Answer:
(6x - 1)(6x + 1)
Step-by-step explanation:
36x² - 1 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
Thus
36x² - 1
= (6x)² - 1²
= (6x - 1)(6x + 1)
You randomly draw a marble out of a bag that contains 20 total marbles. 12
What is P (draw a blue marble)?
If necessary, round your answer to 2 decimal places.
Answer:
The probability of drawing a blue marble is 1 IN 4
Step-by-step explanation:
HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP
Answer:
The first relationship have a zero slope.
Step-by-step explanation:
Because if the y-axis is the same number and that's what makes the first choice the right answer.
solve for x. 1/15+x=3/10
Answer:
x=7/30
Step-by-step explanation:
3/10-1/15
Mrs. Hanson bought 1.6 pounds of grapes. The grapes cost $2.50 per pound. How much did
she pay for the grapes?
Answer:
$4.00
Step-by-step explanation:
Multiply the 1.6 pounds of grapes by the $2.50 per pound.
Answer:
4$
Step-by-step explanation:
Multiply 2.50$ with 1.6 pounds.
You get 4$
It won't cost more than 5$ because there are less than 2 pounds of grapes.
An object is launched at 29.4 meters per
second (m/s) from a 34.3-meter tall
platform. The equation for the object's
height s at time x seconds after launch is
f(x) = -4.9x2 + 29.4x+ 34.3, where y is in
meters. What is the initial height of the
object?
29.4 meters
78.4 meters
34.3 meters
3 meters
Answer:
34.3 meters
Step-by-step explanation:
The generic equation for a movement with constant acceleration is:
S = So + Vo*t + (a*t^2)/2
Where S is the final position, So is the inicial position, Vo is the inicial speed, a is the acceleration and t is the time.
If we compare with our equation (where x is the time and f(x) is the final distance), we have that:
So = 34.3
Vo = 29.4
a = -9.8
So we have that the inicial position (So) of the object is 34.3 meters
Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 24 miles south. She then runs 10 miles west. Her trainer bikes from the health club to meet jane at the end of her run. How much farther does jane travel than her trainer?
Answer:
26 miles farther from her trainer
Step-by-step explanation:
She starts her journey at health club,
Ran 24 miles south and then 10 miles west.
The distance between her end point and her trainer who was at health club can be calculated using pythagorean theorem.
X² = y² + z²
X = her end point
Z = distance between health club 24 miles south. = 24miles
Y = 10 miles distance from the 24 miles south. = 10 miles.
(See attachment for better illustration.)
X² = 24² + 10²
X² = 576 + 100
X² = 676
X = √(676)
X = 26 miles
Jane was 26 miles farther from her trainer
Recent statistics state that the average life expectancy for an American is a little over 78 years.
The sentence above refers to
factors that can affect family responsibilities
Answer:
189
Step-by-step explanation: cause i had dis question before in england
What is the length of the diagonal of a 10 cm by 15 cm rectangle?
Answer:
18.02 cm
Step-by-step explanation:
A diagonal makes a rectangle into two right triangles. So if we use the Pythagorean theorem we can find the hypotenuse which is the diagonals.
Remember, because we know the length and width, we know the two sides.
10^2 + 15^2 = c^2
100+225 = c^2
325 = c^2
18.027 ≈ c
We can use the Pythagorean theorem to solve for the diagonal. The diagonal is the same as the hypotenuse of a triangle.
Pythagorean Theorem: a² + b² = c²
Now, solve for the diagonal.
(10)² + (15)² = c²
100 + 225 = c²
325 = c²
√325 = √c²
18.0277... = c
Round if necessary.
18.0277... = 18.03
Therefore, the diagonal of the rectangle is approximately 18.03cm.
Best of Luck!