Given:
The endpoints of a diameter are (0,0) and (4,-6).
To find:
The equation of the circle.
Solution:
The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(-6-0)^2+(4-0)^2}[/tex]
[tex]d=\sqrt{36+16}[/tex]
[tex]d=\sqrt{52}[/tex]
[tex]d=2\sqrt{13}[/tex]
Now, radius is half of the diameter.
[tex]r=\dfrac{2\sqrt{13}}{2}[/tex]
[tex]r=\sqrt{13}[/tex]
Center of the circle is the midpoint of the endpoints of a diameter.
[tex]Center=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Center=\left(\dfrac{0+4}{2},\dfrac{0+(-6)}{2}\right)[/tex]
[tex]Center=\left(\dfrac{4}{2},\dfrac{-6}{2}\right)[/tex]
[tex]Center=\left(2,-3\right)[/tex]
Standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, (h,k) is center and r is radius.
The center of the circle is (2,-3) and radius is [tex]\sqrt{13}[/tex]. So,
[tex](x-2)^2+(y-(-3))^2=(\sqrt{13})^2[/tex]
[tex](x-2)^2+(y+3)^2=13[/tex]
Therefore, the standard form of the circle is [tex](x-2)^2+(y+3)^2=13[/tex].
Four friends share the profit of a lawn care service equally. The friends charge $45 per lawn and spend $30 of their total earnings on gasoline for the lawnmowers each week. Which inequality can be used to find m, the number of lawns they need to mow next week so that each person earns at least $275? A. 45m - 30/4 _> 275 B. 45m/4 - 30 _>275 C. 45m - 30/4 _< 275 D. 45m/4 - 30 _< 275
Answer:
The answer is actually A) 45m-30/4 ≥ 275
Step-by-step explanation:
It says, "of the total earnings", so after they took off the 30 dollars, they split it between themselves. Hope this helps ;)
Which value is the same as 6 tenths?
Answer:
6/10 or 0.6
Step-by-step explanation:
Answer:
0.6 or 60%
Step-by-step explanation:
What is 10 divided by 5/8
Answer:
its 16 lol
Step-by-step explanation:
I just did the math
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
First you put all the variables with a negative exponent to the opposite side of the fraction, with the answer of 45m^2p^2v^16/15m^6p^8. You then simplify, or cancel out until the variable only remains on one side of the fraction. 3v^16/m^4p^6. So your answer is B
HELP ME FAST PLEASE I NEED THIS VERY SOON!!! you’d be a lifesaver omg
There are 600 seats in the auditorium. This is 112 less than the number of seats in the gymnasium. How many seats are in the gymnasium?
712 is the answer of this question
Help please.
state the scale factor.
Answer:
1.25
Step-by-step explanation:
Answer:
1.25
Step-by-step explanation:
It is 1.25 because take two of the same sides, I will use 15.5 and 12.4 as an example. If you divide 15.5 by 12.4, you get 1.25. To check the answer just do the same for another side. <3
Expand the following:
a) x(x + 6)
b) x(5x - 1)
c) 3x(6x + 5)
d) 4x(2x – 3y)
Answer:
a) x(x + 6) = x · x + x · 6 = x² + 6x
b) x(5x - 1) = x · 5x - x · 1 = 5x² - x
c) 3x(6x + 5) = 3x · 6x + 3x · 5 = 18x² + 15x
d) 4x(2x – 3y) = 4x · 2x - 4x · 3y = 8x²-12xy
a - 48 = 18
What is a?
Answer:
A=66
Step-by-step explanation:
Answer:
a=66
Step-by-step explanation:
You do an inverse operation to find your answer, in this case it is addition, so you add 48 and 18 to get 66!
Suppose that the functions q and r are defined as follows.
q(x) = -x-1
r(x) = 2x² – 2
Find the following.
(q*r)(-5) =
(r*q) (-5) =
Step-by-step explanation:
r(-5) = 2*25 - 2 = 48
Q(-5) = 5 - 1 = 4
Compute the mean of the following population values:
6, 3, 5, 7, 6.
Answer:
The mean (average) is 5.4 or 5 if you're rounding.
Step-by-step explanation:
Mean is the average of all of the numbers.
Add them up: 6+3+5+7+6 = 27
Divide 27 by the amount of numbers you have(5): 27/5
Solve: 5.4
The mean of the given values 6, 3, 5, 7, and 6 will be 5.4.
What is mean?mean is the average of a data set. Mean gives us the idea of that how much amount of overall data have.
Mean = sum of data / Number of data
For example, if you have marks in 5 subjects like 40,45,44,46,48 then the mean will be
( 40 + 45+ 44 + 46 + 48) /5 = 44.6.
Given the data set;
6, 3, 5, 7, 6
Mean = (sum of data) / (number of data)
Mean = (6 + 3 + 5 + 7 + 6)/5
Mean = 27/5
Mean = 5.4
Hence the mean will be 5.4.
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Find parametric equations which describe each curve. No particular orientation is required.
a. The line containing the points (1, 2) and (-3,8).
b. The circle with radius 3 and center (4,1).
Answer:
The equation of the line is [tex](x(t),y(t))=(1-4t,2+6t)[/tex] and the equation of the circle is [tex]F(t)= (3cos(t)+4,3sin(t)+1)[/tex].
Step-by-step explanation:
(a) Given: The given points are [tex](1,2)[/tex] and [tex](-3,8)[/tex].
To find: The parametric equation of line containing points [tex](1,2)[/tex] and [tex](-3,8)[/tex].
We know that the parametric equation of line containing [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is given by [tex](x(t),y(t))=(x_{1}+(x_{2}-x_{1})t,y_{1}+(y_{2}-y_{1})t)[/tex] where [tex]t[/tex]∈[tex][0,1][/tex].
Now, [tex]x(t)=1+(-3-1)t[/tex]
i.e, [tex]x(t)=1-4t[/tex]
And, [tex]y(t)=2+(8-2)t[/tex]
i.e, [tex]y(t)=2+6t[/tex]
Hence, the required parametric equation of the line is [tex](x(t),y(t))=(1-4t,2+6t)[/tex].
(b) Given: The radius of circle is 3 and centre is [tex](4,1)[/tex].
To find: The parametric equation of circle with radius 3 and centre [tex](4,1)[/tex].
We know that parametric equation of circle with radius [tex]r[/tex] and centre [tex](h,k)[/tex] is given by [tex]F(t)= (x(t),y(t))[/tex] where [tex]x(t)=rcos(t)+h[/tex] and [tex]y(t)=rsin(t)+k[/tex].
Now, [tex]x(t)=3cos(t)+4[/tex]
[tex]y(t)=3sin(t)+1[/tex]
So, the parametric equation of circle having radius 3 and centre [tex](h,k)[/tex] is [tex]F(t)= (3cos(t)+4,3sin(t)+1)[/tex].
Hence, the required equation of the circle is [tex]F(t)= (3cos(t)+4,3sin(t)+1)[/tex].
Mr. George has 5 bookcases in his classroom. Each bookcase has 3 shelves. Each
shelf has 20 books. How many total books are on Mr. George's 5 bookcases?
CLEAR
SUBMIT
300 books
160 books
100 books
60 books
Answer:
300
Step-by-step explanation:
What is the perimeter of polygon LMNPQ
Answer: c for maps
Step-by-step explanation:
17.66 units is the perimeter of the polygon.
What is Perimeter?The perimeter of a two-dimensional form is the space surrounding it. It represents the total length of the shape's sides. The units used to measure the sides of the form, such as meters, centimeters, inches, or feet, determine the units used to measure the perimeter.
To find the perimeter of the polygon LMNPQ, we need to add up the lengths of all the sides.
The distance formula for finding the distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y-2 - y-1)^2)[/tex]
Using this formula, we can find the lengths of each side of the polygon:
[tex]LM = \sqrt{(2 - 4)^2 + (4 - 2)^2} = \sqrt{8}\\MN = \sqrt{(5 - 2)^2 + (8 - 4)^2} = \sqrt{25}\\NP = \sqrt{(8 - 5)^2 + (4 - 8)^2}= \sqrt{25}\\PQ = \sqrt{(6 - 8)^2 + (2 - 4)^2} = \sqrt{8}\\QL = \sqrt{(4 - 6)^2 + (2 - 2)^2} = 2[/tex]
Therefore, the perimeter of the polygon LMNPQ is:
Perimeter = LM + MN + NP + PQ + QL
= √8 + √25 + √25 + √8 + 2
≈ 2.83 + 5 + 5 + 2.83 + 2
≈ 17.66
So, the perimeter of the polygon LMNPQ is approximately 17.66 units.
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please help! which expression is equivalent to (-√-1)?
A: i^31
B: i^29
C: i^24
D: i^18
Answer:
Here Is Your Answer i^31
The length of a football playing field is 100 yards between the opposing goal lines. What is the length of the football field in feet? Use the conversion equivalency of 3 feet = 1 yard.
a.
33.3 feet
b.
300 feet
c.
200 feet
d.
600 feet
Answer:
33.3
Step-by-step explanation:
100 divided by 3
the length of a living room is 12 fert and its width is 10 1/2 feet. the length of the room is being expanded by x feet. select all the expressions that represent the area of the living room in square feet
Answer:
vbhjnkmlnkbjvhcgfdxgcvhbjnncnng
Step-by-step explanation:
cxvcxbvcbcvbvcbcvbvcvbb
Answer:
thanks
Step-by-step explanation:
Please help I suck at this kind of math
I really only need help with number three but if you could do it ll that would be awesome
On the coordinate plane shown below, points G and I have coordinates (6,4) and (3,2), respectively.
1 Design a strategy in which the Pythagorean theorem is used to calculate the straight line distance between points G and I on a coordinate plane. Use complete sentences to describe the strategy.
2 Use the Pythagorean theorem to determine the distance between the two points on the coordinate plane. In your final answer, include all of your calculations.
3 Use the distance formula and the coordinates of points G and I to prove that the Pythagorean theorem is an alternative method for calculating the distance between points on a coordinate plane. In your final answer, include all of your calculations.
Answer:
I am sorry, I am only in middle school... I am learning about like the questions I have been asking
Step-by-step explanation:
I really hope you get the question answered and get it correct
Round the following numbers to 2 decimal places.
b)
562.6783
Answer:
b is the correct answer i know it is
solve the inequality
Answer:
x>-1
Step-by-step explanation:
Subtract 0.7 from both sides
Which expression shows the result of applying the distributive property of 3(2x – 6)?
(NEED ANSWER QUICK!)
52 - 3
20 – 18
62 - 6
6.2 – 18
Answer:
6x - 18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Step-by-step explanation:
Step 1: Define
3(2x - 6)
Step 2: Expand
Distribute 3: 3(2x) + 3(-6)Multiply: 6x - 18Step-by-step explanation:
[tex] \huge3(2x - 6) = 6x - 18[/tex]
(6x-18) is the right answer.How many ways can a person toss a coin 14 times so that the number of tails is between 11 and 13 inclusive
Answer:
Step-by-step explanation:
Probability is the possibility for an event to occur or not to occur.
The formula for a combination is:
n choose r = n! / (r! x (n-r)!)
Given
n=14
r= 11 to 13
Hence, we shall add up the cases for 11 through 13.
nCr
14C11 + 14C12 + 14C13
14!/11!(14-11)! + 14!/12(14-12)! + 14!/13(14-13)!
= 14!/11!•3! + 14!/12!•2! + 14!/13!•1!
= 14*13*12*11!/11!•(3*2*1) + 14*13*12!/12!•(2*1) + 14*13!/13!•(1*1)
= 2184/6+182/2+14/1
= 364+91+14
= 469 ways
Step-by-step explanation:
469 ways are the ways to I think so if the answer is correct plz make ma the brainliest
PLS HELP WILL GIVE BRAINLIEST ANSWER
Answer:
8
Step-by-step explanation:
2(20-8x)=5x-2
40-16x=5x-2
42=21x
x=2
HK=5x-2 = 5(2)-2 = 10-2 = 8
if we just passed a sign which says that harrison is 25 miles away and turkey is 40 miles ahead, how far will we have to go to be halfway between turkey and harriso
Answer:
You will need to go 7.5 miles to be halfway between Harrison and Turkey
Step-by-step explanation:
If you see a sign saying that Harrison is 25 miles away and that Turkey is 40 miles ahead, then the distance from Harrison to Turkey must be 40 miles - 25 miles = 15 miles.
If you drive up to be halfway between Harrison and Turkey, then you need to travel 15/2 = 7.5 miles.
You will need to go 7.5 miles to be halfway between Harrison and Turkey
Percy buys tomatoes that cost $0.56 per pound. He pays $2.52 for the tomatoes.
Part 1 out of 3
Percy estimates he bought 5 pounds of tomatoes. Is Percy's estimate reasonable? Complete the explanation.
Use compatible numbers to estimate how many pounds of tomatoes he can buy.
{Answer choices: 25, 5, 35} tenths divided by {Answer choices: 5, 25, 10} tenths is __. His estimate {Answer choices: is reasonable, is not reasonable}
Answer:
1) We know that tomatoes cost 56c per the pound, and he estimates that he bought 5 pounds of tomatoes. If we multiply 5 by 0.56 we get 2.8, which means that if he purchased 5 pounds of tomatoes, he would have spent only 20c more than he did, which is pretty close. So yes, his estimate is reasonable
2) Well, i dont hav any clear amount of money he can spend so, just remember, if you have 3 pounds per say, you multiply 3 by 0.56. And then you can find your answer
Hope that this helped to some extent!
Answer:
Step-by-step explanation:
Answer choices: 25, 5, 35} tenths divided by {Answer choices: 5, 25, 10} tenths is __. His estimate {Answer choices: is reasonable, is not reasonable}
write a polynomial in factored form with solutions of
Answer:
The factored form of a polynomial means it is written as a product of its factors. The factors are also polynomials, usually of lower degree.
Suppose the heights (in inches) of adult males in the United States are normally distributed with a mean
of 71 inches and a standard deviation of 3 inches.
Find the percent of men who are no more than 65 inches tall.
The percent of men who are 65 inches tall or below is
%.
Please answer right brineliest to wover right
Answer:
10
15
-5
-35
-30
0
Step-by-step explanation:
Step-by-step explanation:
A: 10 degrees
B: 15 degrees
C: -5 degrees
D: -35 degrees
E: -30 degrees
F: 0 degrees
Marco recorded the cost of jeans at several stores in the mall:
$45, $65, $75, $45, $97, $88, $52, $67, $99, $35
Find the mean price of jeans at the mall.
i think the answer is sixty-five
Help me with this pls!!
Answer:
5 3/4 hours
Step-by-step explanation:
They drove 3 1/2 hours then 2 1/4 hours. We need to find the total of these to find how long this part of the trip was
(3 + 1/2) + (2 + 1/4) = 5 + 1/2 + 1/4
For 1/2, we can multiply both the numerator and denominator by 2 to get
1/2 = 2/4
Substituting that in, we get
5 + 2/4 + 1/4
= 5 + 3/4 hours
In ΔIJK, k = 26 cm, ∠I=135° and ∠J=11°. Find the length of i, to the nearest centimeter.
Answer:
33 cmStep-by-step explanation:
GivenTriangle IJK with:
Side k = 26 cm, ∠I = 135°, ∠J = 11°To findThe length of side iSolutionFind angle K:
∠K = 180° - (135° + 11°) = 34°Use the low of sines to findthe value of i:
i/sin I = k/sin Ki = k sin I / sin Ki = 26 * sin 135° / sin 34° = 33 cm (rounded to the whole number)