well, the distance from the center of a circle to any point "on" the circle is simply just its radius, thus
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{center}{(\stackrel{x_1}{11}~,~\stackrel{y_1}{6})}\qquad (\stackrel{x_2}{17}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(17-11)^2+(12-6)^2}\implies r = \sqrt{36+36}\implies r=\sqrt{72} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{11}{ h},\stackrel{6}{ k})\qquad \qquad radius=\stackrel{\sqrt{72}}{ r} \\\\\\ (x-11)^2+(y-6)^2=(\sqrt{72})^2\implies (x-11)^2+(y-6)^2=72[/tex]
Final answer:
The equation of the circle with center (11, 6) that passes through the point (17, 12) is (x - 11)² + (y - 6)² = 72.
Explanation:
To find the equation of the circle with center (11, 6) that passes through the point (17, 12), we first determine the radius of the circle. The radius can be found by calculating the distance between the two points using the distance formula: √[(x2-x1)² + (y2-y1)²]. Plugging in the coordinates, we get √[(17-11)² + (12-6)²] = √[6² + 6²] = √[36 + 36] = √72. The squared radius (r²) is therefore 72.
The general form for the equation of a circle is: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle. Substituting the center (11, 6) and the squared radius 72 into this equation, we get: (x - 11)² + (y - 6)² = 72, which is the desired equation of the circle.
Question number 34 ?
Figured out how to do the graph portion now confused on this one
Ahonswer:
Step-by-step explanation:
his season, Lisa's lacrosse team has won $\frac 23$ of their home games (games played at Lisa's school), but just $\frac 25$ of their away games (games played at other schools). In total, Lisa's team has won $26$ games out of $49$ games they have played. How many home games has Lisa's team played?
Solution:
Let "h" be the number of home games
Let "a" be the number of away games
The total number of games is 49
Therefore,
h + a = 49 ---------- eqn 1
They won 2/3 of the home games and 2/5 of the away games
There were 26 games won
Thus we get,
[tex]\frac{2}{3}h + \frac{2}{5}a = 26\\\\10h + 6a = 26 \times 15\\\\10h + 6a = 390\\\\[/tex]
10h + 6a = 390 --------- eqn 2
Multiply eqn 1 by 6
6h + 6a = 294 ----------- eqn 3
Subtract eqn 3 from eqn 2
10h + 6a = 390
6h + 6a = 294
( - ) ------------------
4h = 96
h = 24
Thus 24 home games were played
At a recent audition school play, 1 out of 3 students who auditioned were asked to come to a second audition . After the second audition ,75% of those asked to the second audition were offered parts. If 18 students were offered parts , how many students were offered to the first audition
Answer:
The total students appearing in first audition = 72
Step-by-step explanation:
As given in the question:
1 out of 3 students were asked to come for second audition.
Let us assume the TOTAL STUDENT who came to first audition = m
So, [tex](\frac{1}{3}) m[/tex] appeared for the SECOND ROUND.
Now, 75% of students appearing in second audition were offered parts.
Calculating 75% of [tex](\frac{1}{3}) m[/tex]
[tex]\frac{75}{100} \times\frac{1}{3} m = 0.25 m[/tex]
Also, as said 18 students were offered parts.
⇒ 0. 25 m = 18
Now, solving for m, we get:
m = 18/0.25 = 72
or, m = 72
Hence, the total students appearing in first audition = 72
Final Answer:
- 24 students were asked to attend the second audition.
- 72 students auditioned initially for the first audition.
Explanation:
Let's tackle the problem step by step.
1. **Find the number of students asked to the second audition.**
We know that 18 students were eventually offered parts after the second audition. We're also given that 75% of those who were asked to the second audition were offered parts. To find out how many students were asked to the second audition, we can set up the following equation:
[tex]\[ \text{Number of students offered parts} =[/tex] [tex]\text{Percentage offered parts} \times \text{Number of students at the second audition} \][/tex]
From the given information:
[tex]\[ 18 = 0.75 \times \text{Number of students at the second audition} \][/tex]
Solving for the number of students at the second audition gives us:
[tex]\[ \text{Number of students at the second audition} = \frac{18}{0.75} = 24 \][/tex]
So 24 students were asked to the second audition.
2. **Find the total number of students who auditioned initially.**
If 1 out of 3 students who auditioned were asked to the second audition, we can infer that the ratio of students asked to the second audition to the total number of students who auditioned is 1:3.
Let's let X represent the number of students who auditioned initially. According to the ratio, we can write:
[tex]\[ \frac{1}{3} \times X = \text{Number of students at the second audition} \][/tex]
We've already solved for the number of students at the second audition, which is 24. Thus:
[tex]\[ \frac{1}{3} \times X = 24 \][/tex]
Solving for X, we get:
[tex]\[ X = 24 \times 3 = 72 \][/tex]
So 72 students auditioned initially for the first audition.
To summarize:
- 24 students were asked to attend the second audition.
- 72 students auditioned initially for the first audition.
the test scores for 10 students were 61,67,81,83,87,88,89,90,98, and 100. which frequency table represents this data set?
Answer:
below only shows up once
Step-by-step explanation:
mark: tally: frequency:
61 I I
67 I I
81 I I
83 I I
87 I I
88 I I
89 I I
90 I I
98 I I
100 I I
40 points at the game . Darnell scored 15%
Answer:
6
Step-by-step explanation:
40*15%=6
What is the solution to the inequality 6x−5>−29? x<−4 x>−4 x<4 x>4
Answer:x>-4
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
Answer: x>-4
Step-by-step explanation: I took the test.
Forty-two of the students in band own their instrument.
if this is $37.5% of the Students in the band, how many total
students are in the band?
Answer:
112 students
Step-by-step explanation:
Let T be the total number of students in the band.
From the question,
We were told that 37.5% of the total owns their individual instruments and this amount to 42 students
The total number of students can calculated for as follows:
37.5% x T = 42
37.5/100 x T = 42
Cross multiply to express in linear form
37.5 x T = 100 x 42
Divide both side by 37.5
T = (100 x 42) /37.5
T = 112
Therefore, there are 112 students in the band
KNOWLEDGE CHECK: ALEKS
a and b: decreasing
b and c: constant
c and d: decreasing
d and e: increasing
Answer:
a and b: decreasing
b and c: constant
c and d: decreasing
d and e: increasing
Step-by-step explanation:
What is the distance between S( -9, 8) and T(8 , -6) ?
Answer:
[tex] \sqrt{ {(- 9 - 8)}^{2} + {(8 + 6)}^{2} } [/tex]
[tex]\sqrt{ {(- 17)}^{2} + {(14)}^{2} } [/tex]
[tex] \sqrt{289 + 196} [/tex]
[tex] \sqrt{485} [/tex]
[tex]22.02[/tex] units
The five-number summary for a set of data is 10, 14, 15.5, 21, 25 what is the interquartile range of the data?
Answer:
7
Step-by-step explanation:
Q1 = 14
Q3 = 21
Take 21 - 14 and it gives you the interquartile range of 7.
Final answer:
The interquartile range (IQR) for the data set with a five-number summary of 10, 14, 15.5, 21, 25 is 7, calculated as the difference between the third quartile (Q3) and the first quartile (Q1), which are 21 and 14 respectively.
Explanation:
The interquartile range (IQR) of a data set is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Given the five-number summary of 10, 14, 15.5, 21, 25, where 14 is Q1 and 21 is Q3, the IQR can be found using the formula:
IQR = Q3 - Q1
In this case:
IQR = 21 - 14
IQR = 7
Therefore, the interquartile range for this data set is 7.
Find the MAD:
58, 38, 54, 48, 26, 36
Answer:
10.166666666667
Step-by-step explanation:
Answer:
(add up all the number and divide it by 6, cause there are about 6 numbers in the list)
58 + 38 + 54 + 48 + 26 + 36 = 260 ÷ 6 = 43.3
(subtract the mean {43.3} with the same listed numbers)
43.3 - 58 = 14.7
43.3 - 38 = 5.3
43.3 - 54 = 10.7
43.3 - 48 = 4.7
43.3 - 26 = 17.3
43.3 - 36 = 7.3
(add up all the difference and divide it with 6 again)
14.7 + 5.3 + 10.7 + 4.7 + 17.3 + 7.3 = 60 ÷ 6 = 10
so our MAD (mean absolute deviation) would be 10!
~hope this helps, have a good day/afternoon/nigh~
An animal reserve has 28,000 elk. The population is at a rate of 15% per year. How long will it take for the population to reach 56,000?
Answer: In 5 years time the population will reach to 56,000.
Step-by-step explanation:
This can be calculated using yearly compound interest formula
Formula for yearly compound interest
CI = P(1+R/100)ⁿ
CI = 56,000
P = 28,000
R = 15%
n= number of years
Now,
56,000 = 28,000 (1+15/100)ⁿ
56,000 = 28,000 (1+.15)ⁿ = 28,000 (1.15)ⁿ
log (56,000/28,000) = n log(1.15)
log 2 = n log (1.15)
n = log 2/log 1.15
n≅ 5
Someone help please
Answer I DONY KNOW SO LIKE BRUH
Step-by-step explanation: GOOD LUCK
:
Joe will go to the swimming pool on 20 different days this month.
• A one-day pass to the pool is $2.25.
• A monthly pass to the pool is $30.00.
How much money will Joe save by buying a monthly pass?
Answer:
He will save $15.00
Step-by-step explanation:
You multiply $2.25 by 20 days and that is equal to 45
So $45.00 - $30.00 that would be $15.00
If Joe buys a one-day pass for each of the 20 days he goes to the swimming pool this month, it will cost him $45.00. However, if he buys a monthly pass for $30.00, he will spend less money. Joe can save $15.00 by buying a monthly pass instead of a one-day pass each day.
Explanation:The subject of this question is mathematics as it involves arithmetic calculations to compare the cost of two possible options.
If Joe goes to the swimming pool 20 different days this month and buys a one-day pass for $2.25 every day, it would cost him 20 * $2.25 which equals to $45.00.
However, if Joe buys the monthly pass for $30.00, he would spend less money compared to buying a one-day pass every day. To find out how much Joe will save by buying the monthly pass, subtract the cost of the monthly pass from the total cost of buying one-day passes for 20 days. Therefore, $45.00 - $30.00 equals to $15.00.
So, Joe will save $15.00 by buying the monthly pass instead of a one-day pass each day he goes to the swimming pool.
Learn more about Cost calculation here:
https://brainly.com/question/34783456
#SPJ2
What are not rational numbers
Step-by-step explanation:
Numbers that cannot be written as a simple fraction are Irrational (i.e not rational) numbers.
Some examples are :
π = 3.14159...........
or
√2 = 1.41421.............
or
e = 2.718218...........
A road falls 10 m for every 200 horizontal
metres.
Multiplying Polynomials, Simplify with Work Shown.
(2x-10) (6x + 7)
20 Point offer for real, complete answer.
-4t=15=-1 what is t
Answer:
-4
Step-by-step explanation:
-4t+15=-1
Subtract 15 on both sides:
-4t=-16
Divide -4 on both sides:
t=-4
Why does (x-2)^2+9=0 have no real solutions?
Answer:
see explanation
Step-by-step explanation:
Given
(x - 2)² + 9 = 0 ( subtract 9 from both sides )
(x - 2)² = - 9 ( take the square root of both sides )
x - 2 = ± [tex]\sqrt{-9}[/tex]
[tex]\sqrt{-9}[/tex] yields no real solutions
There is no real number when multiplied by itself gives - 9
In fact the solutions to [tex]\sqrt{-9}[/tex] are said to be imaginary, that is ± 3i
where i = [tex]\sqrt{-1}[/tex]
If interested investigate further.
Which property is demonstrated in the equation (4×7)×10 = 4×(7×10)
A associative
B symmetric
C commutative
D distributive
Answer:
A: Associative
Step-by-step explanation:
Which shows a difference of squares?
10y^2−4x^2
16y^4−x^2
8x^2−40x+25
64x^2−48x+9
A difference of squares must be a binomial, so we want two terms. This rules out the third and fourth options.
If we look at the first two, we must check that both terms are perfect squares.
Look at the first one: [tex]4x^2[/tex] is a perfect square (it's [tex](2x)^2[/tex]), but [tex]10y^2[/tex] is not a perfect square, because 10 is not a perfect square.
On the other hand, if we look at the second option, [tex]16y^4[/tex] is the square of [tex]4y^2[/tex], and [tex]x^2[/tex] is clearly the square of [tex]x[/tex]. So, this is the difference of two squares.
a car travels 90 miles in the same amount of time that a car traveling 10 mph slower travels 60 miles. find the speed of each car
Speed of the first car is 30 mph and that of the second car is 20 mph.
Step-by-step explanation:
Step 1: Let the speed of the first car be x mph. Then the speed of the second car = x - 10 mph. Distance traveled by the second car = 60 miles. Find the time taken by the second car to travel this distance.Time = Distance/Speed
= 60/x - 10 ------ (1)
Step 2: Find the time taken by the first car to travel given distance of 90 miles.Time = 90/x ------- (2)
Step 3: Given that both cars take the same amount of time, equate the 2 equations. (1) = (2)⇒ 60/x - 10 = 90/x
⇒ 60x = 90(x-10)
⇒ 2x = 3(x - 10)
⇒ 2x = 3x - 30
⇒ -x = -30
∴ x = 30 mph
⇒ x - 10 = 30 - 10 = 20 mph
The table below describes a sequence of transformations that justify that two figures are similar. Which sentence below shows that two figures are similar, not congruent.
Answer:
dilation
Step-by-step explanation:
whenever the shape is dilated, or scaled by a factor of any number, the shape will change size and will become similar rather than congruent. congruent shapes have the same dimensions as the parent or original shape.
answer:
dilation
Step-by-step explanation:
whenever the shape is dilated, or scaled by a factor of any number, the shape will change size and will become similar rather than congruent. congruent shapes have the same dimensions as the parent or original shape.so it dilation so ez
Help me find the missing angles
Answer:
b) 105°
d) 130°
Step-by-step explanation:
An external angle has the same measure as the sum of the remote internal angles.
b) ? = 25° +80° = 105°
d) ? = 35° +95° = 130°
_____
This should be fairly obvious if you consider that the adjacent internal angle together with the external angle totals 180°, and the adjacent internal angle together with the other two internal angles totals 180°.
If the two "remote" angles are A and B, and the adjacent internal angle is C, then we have in symbols ...
A + B + C = 180° = ? + C
If we subtract C, then we find ...
A + B = ? . . . . . . the fact we used above
The powers of 2 that are in the range 2 through 1,000 are 2, 4, 8, 16, 32, 64, 128, 256, and 512. Find all the powers of 3 that are in the range 3 through 1,000.
Final answer:
The powers of 3 that fall within the range of 3 through 1,000 are 3, 9, 27, 81, 243, and 729.
Explanation:
To find all the powers of 3 that are in the range 3 through 1,000, we need to calculate successive powers of 3 until the result exceeds 1,000. These calculations give us 31=3, 32=9, 33=27, 34=81, 35=243, 36=729, and 37=2187. However, since 2187 is greater than 1,000, we exclude it from our list. Therefore, the powers of 3 that fall within the specified range are 3, 9, 27, 81, 243, and 729.
111 = 14a This part is for the extra characters
The value of a = 7.93 or left as the fraction 111/14.
The question asks us to solve an algebraic equation for a single variable, specifically, solving 111 = 14a. This involves isolating the variable on one side of the equation to find its value. To do this, we divide both sides of the equation by 14, the coefficient of a.
Dividing both sides by 14, we get a = 111 / 14.
Thus, a = 7.928571429. However, for simplicity, we could round this to a = 7.93 or left as 111/14.
Point G’ has coordinates (- 5, 2) If it was reflected across the y-axis, what were the coordinates of its pre image?
a.) (- 5, - 2)
b.) (5,2 )
c.) (2, - 5)
d.) (5, - 2)
Answer:
B. (5,2)
Step-by-step explanation:
Answer: b. 5, 2
Step-by-step explanation: got it right :p
Which equation represents “nine less than k is three”?
Answer:
k - 9 = 3
And k = 12
Jake eats 1/4 of a. box of cereal in 1/8 of a month. How many boxes will Jake eat in a month?
Jake can eat 2 boxes of cereal in a month as per the given conditions.
What is the rate of change?Rate of change is defined as the change in value with rest to the time is called rate of change.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Jake eats 1/4 of a. box of cereal in 1/8 of a month.
The number of boxes of cereal jake can eat in a month is given as,
= 1/4 / [1 / 8]
= 8 / 4
= 2 cereal boxes
Thus, jake can eat 2 boxes if cereal in a month as per the given conditions.
Learn more about the rate of change here: https://brainly.com/question/13103052
#SPJ2