Answer:
X=3
Step-by-step explanation:
We have two linear functions which intersect at a point. This point is shown in the attached graph. Linear functions are lines which are made of points that satisfy the function or relationship. This means at the intersection, this point (3,-1), both functions have the same values. An input of x=3 produces y=-1 in both functions.
Final answer:
To find the input value that yields the same output for both functions f(x) = -2/3x + 1 and g(x) = 1/3x - 2, we set the functions equal, combine like terms, and solve for x, getting the result x = 3.
Explanation:
The question asks which input value produces the same output value for the two functions f(x) = -2/3x + 1 and g(x) = 1/3x - 2. To find this value, we need to set the two functions equal to each other and solve for x.
Here are the steps to find the input value:
Set f(x) equal to g(x):
-2/3x + 1 = 1/3x - 2
Combine like terms:
-2/3x - 1/3x = -2 - 1
Combine the x coefficients on the left side and constants on the right side:
-1x = -3
Divide both sides by -1 to solve for x:
x = 3
Therefore, the input value that produces the same output value for both functions is x = 3.
These are just like the last ones please help.
8.
Statement Reason
1. A'F is perpendicular bisector of JK 1. Given
2. JA ≅ KA 2. Dfinition of perp bisector
3. ∠JAF and ∠KAF are right angles 3. Dfinition of perp bisector
4. A'F ≅ A'F 4. Reflexive Property
5. ΔJFA ≅ ΔKFA 5. SAS Theorem
6.
(ANGLE): It is given that ∠AMD ≅ ∠EDM
(SIDE): MD ≅ MD by the Reflexive Property
Which angle would satisfy AAS? ∠MAD ≅ ∠ DEM
NOTE: If you chose the other angle, it would satisfy ASA
Janine has 93 beads. She uses 7 beads for each bracelet. She makes as many bracelets as possible. How many beads will Janine have left over?
Which functions are even? Select all that apply
Answer:
The even functions are options 2, 3, and 5
Step-by-step explanation:
Please, see the attached file.
Thanks.
Answer:
Options B, C and E are even functions.
Step-by-step explanation:
If f(x) = f(-x) then function is called to be even.
A). f(x) = ∛8x
f(-x) = ∛8(-x) = (∛8)(∛(-x) = 2∛(-x)
Therefore f(x) ≠ f(-x)
So function is not an even function.
B). [tex]f(x)=log_{9}x^{6}[/tex]
[tex]f(-x)=log_{9}(-x)^{6}[/tex]
[tex]=log_{9}(x)^{6}[/tex]
f(x) = f(-x)
So this function is even.
C). [tex]f(x)=\frac{1}{x^{8}+7x^{7}}[/tex]
[tex]f(-x)=\frac{1}{(-x)^{8}+7(-x)^{6}}[/tex]
= [tex]\frac{1}{x^{8}+7x^{6}}[/tex]
f(x) = f(-x)
Therefore given function is even.
D). f(x) = [tex]e^{x^{8}-x }[/tex]
[tex]f(-x)=e^{(-x)^{8}-(-x)}=e^{x^{8}+x}[/tex]
Therefore f(x) ≠ f(-x)
So the given function is not even.
E). f(x) = |8x| - 3
f(-x) = |8(-x)| - 3
= |8x| - 3
f(x) = f(-x)
Therefore, function is even.
F). [tex]f(-x)= -9(-x)^{10}+5(-x)^{4}-12(-x)[/tex]
[tex]f(-x)= -9(x)^{10}+5(x)^{4}+12(x)[/tex]
f(x) ≠ f(-x)
Therefore the given function is not an even function.
Options B, C and E are even functions.
Given that f(x) = 1-x x . What is the domain of f-1(x)? A) R B) R, x ≠ 0 C) R, x ≠ 1 D) R, x ≠ -1
Answer:
The required domain is [tex]x\ne -1[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1-x}{x}[/tex]
We need the inverse of this function.
We first of all have to let [tex]y=f(x)[/tex].
This implies that,
[tex]y=\frac{1-x}{x}[/tex]
Next, we interchange [tex]x[/tex] and [tex]y[/tex] to obtain,
[tex]x=\frac{1-y}{y}[/tex]
We make y the subject to get,
[tex]xy=1-y[/tex]
[tex]xy+y=1[/tex]
[tex](x+1)y=1[/tex]
[tex]y=\frac{1}{1+x}[/tex]
The inverse function is
[tex]f^{-1}(x)=\frac{1}{1+x}[/tex]
The domain of this function is
[tex]x+1\ne 0[/tex]
[tex]\Rightarrow x\ne -1[/tex]
The correct answer is D
The population of Henderson City was 3,381,000 in 1994, and is growing at an annual rate of 1.8%. If this growth rate continues, what will the approximate population of Henderson City be in the year 2000?
Answer:
3746148
Step-by-step explanation:
i know you probably just want the answer but hear me out it is just simple math and can be resolved with a quick search. Find or search 1.8% of 3,381,000 and multiply it times the years progressed.
60858 x 6 = 3746148
Final answer:
Using the exponential growth formula, the approximate population of Henderson City in the year 2000 is calculated to be around 3,769,706 if the annual growth rate remains constant at 1.8%.
Explanation:
To calculate the approximate population of Henderson City in the year 2000, we can use the formula for exponential growth. The formula is
[tex]A = P(1 + r)^t[/tex]
where A is the amount of the final population, P is the initial population, r is the growth rate expressed as a decimal, and t is the time in years. In this case:
P (initial population) = 3,381,000r (annual growth rate) = 1.8% or 0.018t (time from 1994 to 2000) = 6 yearsSo the equation becomes:
A =[tex]3,381,000(1 + 0.018)^6[/tex]
Calculating this gives us the approximate population, A:
A ≈[tex]3,381,000(1.018)^6[/tex]
A ≈ 3,381,000(1.1155)
A ≈ 3,769,706
Therefore, the approximate population of Henderson City in the year 2000 would be 3,769,706 residents if the growth rate remains constant at 1.8%.
How wide is a rectangular strip of land with a length of 3/4 miles and an area of 1/2 square mile?
The width of the rectangular strip of land is 2/3 miles whose the width of the rectangular strip of land is 2/3 miles.
To find the width of the rectangular strip of land, we can use the formula for the area of a rectangle, which is:
Area = Length × Width
Given that the length of the rectangular strip of land is 3/4 miles and the area is 1/2 square mile, we can plug these values into the formula and solve for the width (W):
Area = 1/2 square mile
Length = 3/4 miles
1/2 = (3/4) × Width
To solve for the width (W), divide both sides by 3/4:
Width = (1/2) ÷ (3/4)
When dividing by a fraction, you can multiply by its reciprocal:
Width = (1/2) × (4/3)
Now, multiply the numerators and denominators:
Width = 4/6
The fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
Width = 2/3
So, the width of the rectangular strip of land is 2/3 miles.
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Find the coordinates of the midpoint of the segment whose endpoints are H(5, 13) and K(7, 5). (12, 18) (9, 7) (2, 8) (6, 9)
Answer: D. (6, 9)
Step-by-step explanation:
Midpoint is the "average" of the x's and y's:
Given: (5, 13) and (7, 5)
Midpoint: [tex](\dfrac{5+7}{2},\dfrac{13+5}{2})[/tex]
= [tex](\dfrac{12}{2},\dfrac{18}{2})[/tex]
= (6, 9)
Answer: (6, 9)
Step-by-step explanation:
What is the graph of this function?
Answer:
See attachment.
Step-by-step explanation:
The main part of the function is an absolute value function and so it forms a V with the center of the V at (0,0). The sides of the V go up and over 1 unit at a time. However, since 2 is added to the it outside of the absolute value, the center of the V moves from (0,0) to (0,2). The sides stay the same. The division by 2 changes the sides. The sides move from up and over 1 unit to up 1 unit and over two units. It spreads or widens the graph. Lastly, the interval selects a specific part of the graph only from 0 to 6 on the x-axis. This takes just one side of the V and looks like a line segment. See attachment.
Answer:
We are given a function,
[tex]y=\frac{|x|+2}{2}[/tex] if 0 ≤ x < 6
We need to draw the graph of the function.
We know that Parent function of the given function is Modulus function | x |.
Consider given function,
[tex]y=\frac{|x|+2}{2}[/tex]
[tex]y=\frac{|x|}{2}+\frac{2}{2}[/tex]
[tex]y=\frac{|x|}{2}+1[/tex]
So, the given function is translated 1 unit upward and compressed by factor of 1/2.
So the obtained graph is attached.
Select the true statement plzzzz need help ASAPPPPP
Answer:
Correct choice is B
Step-by-step explanation:
All three functions are increasing when x is increasing. You can find values of each function when x is "enough large". For example, at x=100,
1. linear function: [tex]y=10\cdot 100=1,000.[/tex]
2. exponential function: [tex]y=5^{100}\approx 0.8\cdot 10^{70}.[/tex]
3. quadratic function: [tex]y=4\cdot 100^2+5\cdot 100=40,500.[/tex]
As you can see, when x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.
Also you can use graphical method to get from the attached diagrams result. When x approaches positive infinity, the exponential function will exceed both the linear and the quadratic functions.
Correct choice is B.
20 POINTS!!!Which ray is a bisector of angle ABC? BC BD BA BF
Answer:
The answer is BD is the bisector angle
Find the 20th term of the arithmetic sequence
Answer:
-99
Step-by-step explanation:
Given :
Arithmetic sequence : 15 , 9 ,3 , -3 , ........
To Find : 20th term .
Solution :
Formula of nth term in Arithmetic mean : [tex]a_{n} = a+(n-1)*d[/tex] ---(A)
where
a = first term of sequence
n = term position
d = common difference
[tex]a_{n}[/tex] = the term you want to find
Thus in the given sequence:
a = 15 ( first term )
n = 20 th term ( given )
d = 9-15 = 3-9 = -6(common difference)
Putting values in (A)
⇒[tex]a_{20} = 15+(20-1)*(-6)[/tex]
[tex]a_{20} = 15-114[/tex]
[tex]a_{20} = -99[/tex]
Hence the 20th term is -99 i.e. option 1
Ava is saving for A new computer that cost 1218 she has already saved half of the money Ava earns $14 per hour how many hours must a work in order to save the rest of the money
Ava must work 43.5 more hours in order to save the rest of the money
Further explanationMoney is any item that generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. In math, it can be defined as the medium of exchange such as notes, coins, and demand deposits, to pay for commodities and services.
If you're self-employed, it's unwise to work more than 40 hours a week on a regular basis because, you'll get a burst of productivity, the extra hours have diminished returns over time and within any time period.
Ava is saving for A new computer that cost 1218 she has already saved half of the money
[tex]\frac{1218 }{2} = 609[/tex] $, hence she has already saved half of the money ($609), so she needs $609
Ava earns $14 per hour
Hence [tex]\frac{609}{14} = 43.5[/tex] hours
Ava must work 43.5 more hours in order to save the rest of the money
Hope it helps!
Learn moreLearn more about hours https://brainly.com/question/2645145Learn more about work https://brainly.com/question/10711591Learn more about computer https://brainly.com/question/2901657Answer details
Grade: 5
Subject: math
Chapter: hours
Keywords: hours, money, saved, order, Ava
What is the approximate solution to the equation 3t=29 ? 0.3263 3.0650 3.3672 9.6667
ASAP
Answer:
9.6667
Step-by-step explanation:
3t=29
Divide each side by 3
3t/3 = 29/3
t = 29/3
Three goes into 29 nine times (3*9 = 27 ) with 2 left over
t = 9 2/3
We know 1/3 = .3 repeating
so 2/3 = .6 repeating
t = 9 .6 repeating
Answer: 3.0650
Step-by-step explanation:
K-12
A card is chosen at random from a deck of 52 cards. It is replaced, and a second card is chosen. What is the probability that both cards chosen are jacks?
A.) 1/26
B.) 1/13
C.) 1/169
D.) 2/13
Answer:
C.) 1/169
Step-by-step explanation:
There are 4 jacks in a deck of 52 cards
The probability the first card is a jack
4/52 = 1/ 13
Since we replace the card
The probability the second card is a jack
4/52 = 1/ 13
To get the probability that we get a jack then a jack, we multiply the probabilities
1/13 * 1/13 = 1/169
Find an equation of variation where y varies directly as x and y = 15 when x = 5, find y when x is 19.
Answer:
[tex]y=3x[/tex]
y=57, when x is 19.
Step-by-step explanation:
We are asked to write an equation of variation where y varies directly as x.
Since we know that a directly proportional equation is in form: [tex]y=kx[/tex], where k is the constant of proportionality.
Upon substituting x=5 and y= 15 in our equation of variation we will get,
[tex]15=k*5[/tex]
[tex]k=\frac{15}{5}[/tex]
[tex]k=3[/tex]
Upon substituting k=3 in the standard equation of variation we will get our desired equation of variation as: [tex]y=3x[/tex].
Now let us find y, when x is 19.
[tex]y=3*19[/tex]
[tex]y=57[/tex]
Therefore, y equals 57, when x is 19.
Please answer this question! 20 points and brainliest!
Answer:
[tex]x>-3[/tex]
Step-by-step explanation:
To solve equations, we use inverse operations. Normally, we use PEMDAS to simplify an equation. To solve it, we use the inverse of each in this order SADMEP. Solving an inequality is the same except for step. When dividing by a negative, the sign of the inequality changes.
We have [tex]5x+7>2(x-1)\\5x+7>2x-2[/tex] in simplified form. We begin by subtracting or adding constants across the equal sign. Then doing the same with the variable terms. We finish by dividing by the coefficient of the variable term.
[tex]5x+7>2x-2\\5x+7-7>2x-2-7\\5x>2x-9\\5x-2x>2x-2x-9\\3x>-9\\x>-3[/tex]
To graph, we draw a number line, draw an open circle at -3.
Since it is not equal to, we do not fill it in. We leave it open. We also draw an arrow to the right of -3
Need help ASAP! Brainliest promised!
Lines y and z are parallel.
What is the measure of angle 2?
Answer:
28 degrees
Step-by-step explanation:
180 = 10x + 5 + 65 because they are supplementary. x = 11.
Angle 2 = 180 - (Angle 1 + (4x - 7))
Angle 2 = 180 - ((180 - 65) + 4x - 7)
Angle 2 = 180 - (115 + 4x - 7)
Angle 2 = 180 - 152
Angle 2 = 28 degrees
A car travels 6 kilometers in 3.75 miles. How many miles will it travel in 40 kilometers?
Answer:
25 miles
Step-by-step explanation:
[tex]\frac{6}{40} :\frac{3.75}{y} \\y=25[/tex]
Answer: In the question, 3.75 miles is equal to 6 kilometers (that's rounding in a real life situation. It would actually be about 3.72... but who cares?! :)). So, if you divide 3.75/6... you get 0.625. Now, you multiply 40 by 0.625. After so, you get 25. 40 kilometers is equal to 25 miles!
Carlos can type 228 words in 4 minutes. Which equation represents the number of words Carlos types per minute?
Answer:
see explanation
Step-by-step explanation:
For words per minute divide 228 by 4
words per minute = [tex]\frac{228}{4}[/tex] ( = 57 )
Final answer:
To find the number of words Carlos types per minute, set up an equation and solve for 'x'.
Explanation:
To find the number of words Carlos types per minute, we can set up an equation using the given information. Let's assume that the number of words Carlos types in 1 minute is 'x.' We know that Carlos can type 228 words in 4 minutes. So, the equation would be:
228 words in 4 minutes = x words in 1 minute
To solve this equation, we can cross-multiply and divide:
(228 words) x (1 minute) = (4 minutes) x (x words)
Simplifying further:
x = (228 words) / (4 minutes)
Therefore, the equation that represents the number of words Carlos types per minute is:
x = 228 / 4
Help me with these math questions.......
Answer: 118.40, 300, $18,000
Step-by-step explanation:
a) p(x) = [tex]-\frac{1}{5} (8) + 120[/tex]
p(8) = [tex]-\frac{8}{5} + 120[/tex]
= -1.60 + 120
= 118.40
b) R(x) = x * p(x)
= [tex]x(-\frac{1}{5}x + 120)[/tex]
= [tex]-\frac{1}{5}x^{2} + 120x[/tex]
a=[tex]-\frac{1}{5}[/tex], b=120
x = [tex]\frac{-b}{2a}[/tex]
= [tex]\frac{-120}{-\frac{2}{5}}[/tex]
= [tex]\frac{-120(5)}{-2}[/tex]
= 300
c) R(x) = [tex]-\frac{1}{5}x^{2} + 120x[/tex]
R(300) = [tex]-\frac{1}{5}(300)^{2} + 120(300)[/tex]
= -18,000 + 36,000
= 18,000
***********************************************************************
sec θ = [tex]\sqrt{6}[/tex]
[tex]\frac{hypotenuse}{adjacent} = \frac{\sqrt{6}}{1}[/tex]
adjacent² + opposite² = hypotenuse²
1² + opposite² = (√6)²
1 + opposite² = 6
opposite² = 5
opposite = √5
csc θ = [tex]\frac{hypotenuse}{opposite} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{30}}{5}[/tex]
cot θ = [tex]\frac{adjacent}{opposite} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}[/tex]
sin θ = [tex]\frac{opposite}{hypotenuse} = \frac{\sqrt{5}}{\sqrt{6}} = \frac{\sqrt{30}}{6}[/tex]
cos θ = [tex]\frac{adjacent}{hypotenuse} = \frac{1}{\sqrt{6}} = \frac{\sqrt{6}}{6}[/tex]
tan θ = [tex]\frac{opposite}{adjacent} = \frac{\sqrt{5}}{1} = \sqrt{5}[/tex]
**********************************************************************
Answer: 144°
Step-by-step explanation:
[tex]\frac{\pi}{180}=\frac{4\pi}{5(x)}[/tex]
π(5x) = 180(4π)
x = [tex]\frac{180(4\pi)}{5\pi}[/tex]
= 36(4)
= 144
2. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Adelia had 4 dollars. She found 50 cents and then bought a snack. She ended up with 6 quarters. Which expression equals the number of dollars Adelia spent on the snack?
Answer:
3 Dollars
Step-by-step explanation:
$4+.50cents=4.50
6 quarters is $1.50
4.50-1.50=3 dollars
So, I got this question for my Imagine Math, and here is what I got;
4+0.50−1.50.
Why; I got this because 4+0.50 is 4.50 and then 4.50-1.50 is 3.
Hopes this helps.
A famer had 612 tomatoes. He put them in baskets of 100. How many baskets did he fill completely. How many tomatoes where left over.
Answer:
6 baskets were filled and 12 tomatoes were left
Step-by-step explanation:
Just do 612/100= 6
Camilla borrows a book from the library for d days. The library charges a late fee 0.10 dollars per day that the book is late. If Camilla returns the book more than 21 days after she borrowed it, the expression 0.10(d?21) represents the total late fee Camilla owes. What does (d?21) represent in this context?
Answer: (d-21) represent in this context
The number of days the book is late
Step-by-step explanation:
The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
Camilla borrows a book from the library for d days.
The library charges a late fee 0.10 dollars per day that the book is late.
If Camilla returns the book more than 21 days after she borrowed it.
Then the expression will be 0.10d.
The total amount is given as
Total amount = 0.10 d
Total amount = 0.10 x 21
Total amount = $2.1
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Xander goes to the movies with his family. Each family member buys a ticket and two boxes of popcorn. If these are five members of his family,let t represent the cost of a ticket and p represent tye cost of a box of popcorn. Write two different expressions that represents the total amount his family spent.
Final answer:
The total cost can be expressed as 5t + 10p or (5t) + (5 × 2p), representing the combined cost of five movie tickets and twice the amount of popcorn boxes for each of the five family members.
Explanation:
The total amount Xander's family spent on movie tickets and popcorn can be expressed with two different algebraic expressions. The cost for one family member is the cost of one ticket plus the cost of two boxes of popcorn. Since there are five members in the family, we multiply the cost of one person by five.
The first expression is 5t + 10p, which represents the cost of five tickets (5t) and ten boxes of popcorn (2 boxes per person), therefore, 5 times 2 boxes of popcorn (10p).
An alternative expression is (5t) + (5 × 2p), which explicitly shows the cost of five tickets (5t) plus the cost of two boxes of popcorn for each of the five members (5 × 2p).
David and Jillian are playing a board game together. Jillian wants to trade her wool cards for David's ore cards. The double number line shows that David will trade 33 ore cards to Jillian for 66 wool cards. Based on the ratio shown in the double number line, how many wool cards does Jillian need to trade for 44 ore cards?
Answer:8
Step-by-step explanation:6%3=2
4x2=8
I swear its 8 check if i'm wrong I dare you
Banu is 20 years older than binu. In 5 years, Banu will be twice as old as binu. Find their present age.
Answer:
15?
Step-by-step explanation:
If Binu is 15, in 5 years they will be 20. And if Banu is 20 years older, in 5 years they will be 40 (becuase 15 + 20 = 35 and then + the 5 years) Thats twice Binu's age. So Binu is 15 I would assume?
What is 6,3.6,2.16,1.296,...
a common ratio of r
Answer:
r=0.6
Step-by-step explanation:
Consider geometric sequence
[tex]b_1=6,\\ \\b_2=3.6,\\ \\b_3=2.16,\\ \\b_4=1.296,...[/tex]
In geometric sequence
[tex]b_i=b_{i-1}\cdot r,[/tex]
then
[tex]b_2=b_1\cdot r[/tex]
and
[tex]3.6=6r,\ r=\dfrac{3.6}{6}=0.6.[/tex]
Note that
[tex]2.16=3.6\cdot 0.6,\\ \\1.296=2.16\cdot 0.6.[/tex]
This means that ratio r=0.6.
Write the equation in standard form. Identify the important features of the graph:
x^2+y^2-9x+10y+15=0
Answer:
Standard form: [tex]\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]
This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]
Step-by-step explanation:
Consider expression [tex]x^2+y^2-9x+10y+15=0.[/tex]
First, form perfect squares:
[tex](x^2-9x)+(y^2+10y)+15=0,\\ \\\left(x^2-9x+\dfrac{81}{4}\right)-\dfrac{81}{4}+(y^2+10y+25)-25+15=0,\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=10+\dfrac{81}{4},\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.[/tex]
This equation represents the circle with the center at the point [tex]\left(\dfrac{9}{2},-5\right)[/tex] and the radius [tex]r=\dfrac{11}{2}.[/tex]
PLEASE SHOW ALL STEPS!!!!
find the center and radius of the circle.
x2 −2x + y2 − 6y = 26
Answer:
Center (1,3) and radius 6
Step-by-step explanation:
We must complete the square to find the center and radius of the circle.
First make sure the x and y squared terms have 1 as their coefficients. We also make sure x and y terms together.
[tex]x^2-2x+y^2-6y=26[/tex]
We now create space between the x and y terms with parenthesis.
[tex](x^2-2x)+(y^2-6y)=26[/tex]
We complete the square by taking the middle terms -2x and the -6y - divide each and square them.
[tex]\frac{-2}{2} =(-1)^{2} =1[/tex]
[tex]\frac{-6}{2} =(-3)^{2} =9[/tex]
We add the squares to both sides.
[tex](x^2-2x+1)+(y^2-6y+9)=26+1+9[/tex]
Simplify.
[tex](x^2-2x+1)+(y^2-6y+9)=36[/tex]
And write the quadratics in factored form.
[tex](x-1)^{2} +(y-3)^{2} =36[/tex]
The center is (h,k) or (1,3). The radius is the square root of 36 which is 6.