Answer:
the answer is 18m3n3
Step-by-step explanation:
Answer:
the answer is 18m3n3
Step-by-step explanation: :)) good luck!!
The perimeter of a rectangle is 320mm. If its length increases by 10mm and its breadth decreases by 10mm then it its area will be 32 less. Calculate the length and breadth of the original rectangle. (20)
Answer:
The length of the original rectangle is 73.4 mm.
The breadth of the original rectangle is 86.6 mm.
Step-by-step explanation:
Given : The perimeter of a rectangle is 320 mm. If its length increases by 10 mm and its breadth decreases by 10 mm then it its area will be 32 less.
To find : Calculate the length and breadth of the original rectangle ?
Solution :
The area of the rectangle is [tex]A=L\times B[/tex]
Let the length of the rectangle be 'x'
The breadth of the rectangle be 'y'
The area is [tex]A=xy[/tex]
Now, length increases by 10 mm i.e. L=x+10
breadth decreases by 10 mm i.e. B=y-10
The new area is [tex]A_n=(x+10)(y-10)[/tex]
According to question,
[tex]A-A_n=32[/tex]
[tex]xy-(x+10)(y-10)=32[/tex] ......(1)
The perimeter of a rectangle is 320 mm.
i.e. [tex]P=2(L+B)[/tex]
[tex]320=2(x+y)[/tex]
[tex]x+y=160[/tex]
[tex]x=160-y[/tex] .....(2)
Substitute the value of y from eqn (2) in (1),
[tex]y(160-y)-(160-y+10)(y-10)=32[/tex]
[tex]160y-y^2-(170-y)(y-10)=32[/tex]
[tex]160y-y^2-(180y-1700-y^2)=32[/tex]
[tex]160y-y^2-180y+1700+y^2=32[/tex]
[tex]1700-20y=32[/tex]
[tex]20y=1732[/tex]
[tex]y=\frac{1732}{20}[/tex]
[tex]y=86.6[/tex]
Substitute in (2),
[tex]x=160-86.6[/tex]
[tex]x=73.4[/tex]
The length of the original rectangle is 73.4 mm.
The breadth of the original rectangle is 86.6 mm.
graph y < x and x > 5
A box of 12" drafting scales weighs 3 3/4 lbs. A dealer has 20 1/2 boxes in stock. What is the total weight of the scales?
Answer:
[tex]76\frac{7}{8}\ lb[/tex]
Step-by-step explanation:
we know that
One box of 12'' weighs 3 3/4 lb
so
To find out the weight of 20 1/2 boxes, multiply the weight of one box by the total number of boxes
[tex]3\frac{3}{4}(20\frac{1}{2})[/tex]
Convert mixed number to an improper fraction
[tex]3\frac{3}{4}\ lb=\frac{3*4+3}{4}=\frac{15}{4}\ lb[/tex]
[tex]20\frac{1}{2}\ boxes=\frac{20*2+1}{2}=\frac{41}{2}\ boxes[/tex]
substitute
[tex]\frac{15}{4}(\frac{41}{2})=\frac{615}{8}\ lb[/tex]
Convert to mixed number
[tex]\frac{615}{8}\ lb=\frac{608}{8}+\frac{7}{8}=76\frac{7}{8}\ lb[/tex]
Bentley is going to invest $98,000 and leave it in an account for 7 years. Assuming
the interest is compounded daily, what interest rate, to the nearest tenth of a percent,
would be required in order for Bentley to end up with $114,000?
Answer:
The rate of interest for compounded daily is 2.1 6
Step-by-step explanation:
Given as :
The principal investment = $ 98,000
The Time period for investment = 7 years
Let The rate of interest compounded daily = R %
The Amount at the end up = $ 114,000
From compounded method
Amount = Principal × [tex](1+\dfrac{rate}{365\times 100})^{365\times Time}[/tex]
Or, $ 114,000 = $ 98,000 × [tex](1+\dfrac{R}{365\times 100})^{365\times 7}[/tex]
Or, [tex]\frac{114000}{98000}[/tex] = [tex](1+\dfrac{R}{36500})^{2555}[/tex]
or, 1.16326 = [tex](1+\dfrac{R}{36500})^{2555}[/tex]
or, [tex](1.16326)^{\frac{1}{2555}}[/tex] = 1 + [tex]\frac{R}{36500}[/tex]
1.00005919 - 1 = [tex]\frac{R}{36500}[/tex]
or, 0.00005919 = [tex]\frac{R}{36500}[/tex]
∴ R = 0.00005919 × 365000 = 2.16
Hence the rate of interest for compounded daily is 2.1 6 Answer
-7x- 8y=9
4x +9y=-22
Answer:
(95/31, -118/31)
Step-by-step explanation:
-7x-8y=9
4x+9y=-22
----------------
4(-7x-8y)=4(9)
7(4x+9y)=7(-22)
-----------------------
-28x-32y=36
28x+63y=-154
-----------------------
31y=-118
y=-118/31
-7x-8(-118/31)=9
-7x+944/31=9
-7x=9-944/31
-7x=279/31-944/31
-7x=-665/31
7x=665/31
x=(665/31)/7
x=(665/31)(1/7)
x=665/217=95/31
x=95/31, y=-118/31
There are 454 tiles in a row.
About how many tiles are there in 12 rows?
Answer:
227/6
Step-by-step explanation:
454/12=227/6
3x+8=15 find try the value of x
Answer:
x = 7/3
Step-by-step explanation:
To find the of x, isolate it from the other numbers (moving everything to the other side)
What you do to one side, you must do to the other:
3x + 8 = 15
3x + 8 - 8 = 15 - 8 (subtract 8 on both sides to rid of the "+ 8")
3x = 7
3x/3 = 7/3 (divide by 3 on both sides to rid of the 3 attached to "x")
x = 7/3
Answer:
x=2.3
Step-by-step explanation:
15-8=7
Divide 3 on each side (3x=7)7 divided by 3 is 2.3
so X=2.3
Which of the following is the area of a trapezoid whose dimensions are base one = 10 cm, base two = 5 cm, and height = 2 cm?
30 squared cm
30 cm
15 cm
15 squared cm
Answer:
The correct answer is D. 15 squared centimeters.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Base one = 10 centimeters
Base two = 5 centimeters
Height = 2 centimeters
2. Let's find out the area of the trapezoid, using the following formula:
Area = 1/2 (Base one + Base two) * Height
Replacing with real values:
Area = 1/2 (10 + 5) * 2
Area = 1/2 (15 * 2) = 1/2 (30)
Area = 15 centimeters ²
The correct answer is D. 15 squared centimeters.
Note: Same answer provided to question 14021584, answered by me.
Samuel can do 120 jumping jacks in two minutes.
What is the ratio?
What is the unit rate?
What is the rate?
Answers:
What is the ratio? 120:2
What is the unit rate? 60:1
What is the rate? 60 jumping jacks per minute
===================================================
Further Explanation:
To find the ratio of jumping jacks to minutes, you just write the two values 120 and 2 separated by a colon. That's how we get 120:2 as our first answer.
--------
Once we have 120:2, we divide both parts by 2 to get 60:1
120/2 = 60
2/2 = 1
The reason why we do this is so that the "2 minutes" turns into "1 minute". A unit ratio has the time value in unit increments so we can see how many jumping jacks Samuel can do. Writing "60:1" means "60 jumping jacks in 1 minute"
-------
Saying "60 jumping jacks in 1 minute" is the same as saying "60 jumping jacks per minute", which is similar to a car's speed of something like 60 miles per hour. The unit "X per Y" is the template for speed, where X is the number of items you get done and Y is the unit of time. In this case, X = 60 jumping jacks and Y = 1 minute.
What number must you add to complete the square?
x2 + 24x = 17
Answer:
144
Step-by-step explanation:
x^2+24x=17
b=24
(b/2)^2=(24/2)^2=12^2=144
-3x - y = 2 and 12x – 4y = 4
Answer:
x = (-4/3)
y = (-5)
Step-by-step explanation:
there ya go, I think this was the answer you were looking for. :)
Caroline is going to bake a cake. It takes her 5 minutes to gather the ingredients, 15 minutes to mix the ingredients and 25 minutes to bake the cake. If she started preparing the cake at 8:05 A.M., what time will the cake be ready?
Answer:
8:50 A.M
Step-by-step explanation:
You have to add all the numbers.
Example:
5+15+25=45
45 Minutes + 5 Minutes= 50 Minutes=
8:50 A.M
Answer: 8:55AM
Step-by-step explanation:
8:05 AM - 8:10 AM : gather the ingredients
8:10 AM - 8:25 AM: mix the ingredients
8:25 AM - 8:50 AM: bake the cake
5+15+25=45 minutes + 8:05 AM = 8:50 AM
parallel to 6x+5y= -5 and passes through the point (5,-4)
For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have the following equation:
[tex]6x + 5y = -5\\5y = -6x-5\\y = - \frac {6} {5} x- \frac {5} {5}\\y = - \frac {6} {5} -1[/tex]
Thus, the slope is: [tex]m = - \frac {6} {5}[/tex]
By definition, if two lines are parallel then their slopes are equal.
Thus, a line parallel to the given line will have a slope: [tex]m = - \frac {6} {5}.[/tex]Therefore, the equation will be of the form:
[tex]y = - \frac {6} {5} x + b[/tex]
We substitute the given point and find "b":
[tex]-4 = - \frac {6} {5} (5) + b\\-4 = -6 + b\\-4 + 6 = b\\b = 2[/tex]
Finally, the equation is:
[tex]y = - \frac {6} {5} x + 2[/tex]
Answer:
[tex]y = - \frac {6} {5} x + 2[/tex]
The half-life of uranium-238 is 4.5x10^9 years. The half-life of uranium-234 is 2.5x10^5 years. How many times greater is the half-life of uranium-238 that of uranium-234
Answer:
Half-life of uranium-238 [tex]18 \times 10^{3} \text { times greater }[/tex] that of uranium-234
Explanation:
Half time of uranium-238 = [tex]4.5\times 10^9[/tex] years
Half time of Uranium-234 = [tex]2.5\times 10^5[/tex] years
To find how much times greater the half life of uranium-238 is from uranium-234
= [tex]\frac{\text { Half life of Uranium-238 }}{\text { Half time of Uranium - 234 }}[/tex]
=[tex]\frac{4.5 \times 10^{9}}{2.5 \times 10^{5}}[/tex]
=[tex]18 \times 10^{3} \text { times greater }[/tex]
Hence Uranium-238 is [tex]18 \times 10^{3} \text { times greater }[/tex] than Uranium-234
Final answer:
The half-life of uranium-238 is 18,000 times greater than the half-life of uranium-234, determined by dividing the half-lives.
Explanation:
The half-life of uranium-238 is 4.5x10⁹ years, and the half-life of uranium-234 is 2.5x10⁵ years. To determine how many times greater the half-life of uranium-238 is than that of uranium-234, we divide the half-life of uranium-238 by the half-life of uranium-234:
(4.5x10⁹ years) / (2.5x10⁵ years) = 4.5/2.5 x [tex]10^{9-5[/tex] = 1.8 x 10⁴
Therefore, the half-life of uranium-238 is 18,000 times greater than the half-life of uranium-234.
Find m∠DEC (the picture is not drawn to scale).
Answer:
M∠DEC equals 123º.
Step-by-step explanation:
The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.
180 - {(x - 45)+(x - 12)} = m∠DEC
m∠DEC + x = 180
(x - 45) + (x - 12) = x
Solving for x:
(x - 45) + (x - 12) = x
x - 45 + x - 12 = x Remove parenthesis
2x - 57 = x Combine like terms
2x = x + 57 Add 57 to both sides
x = 57 Subtract x from both sides
Finding m∠D:
x - 45 = ?
57 - 45 = 12º
Finding m∠C:
x - 12 = ?
57 - 12 = 45º
** (Checking x: 12 + 45 = 57) **
Finding m∠DEC:
AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:
180 - 57 = 123º
Hope this helps,
❤A.W.E.S.W.A.N.❤
The Jurassic Zoo charges $15 for each adult admission and $6 for each child. The total bill for the 185 people from a school trip was $1569. How many adults and how many children went to the zoo?
Answer:
The number of adults visiting the zoo = 51
The number of children visiting the zoo = 134
Step-by-step explanation:
Let us assume the number of adults going to the zoo = m
Total number of people visiting the zoo = 185
SO, the number of children visiting the zoo = 185 - m
Now, the cost of 1 adult ticket = $15
So, the total cost of m adult tickets = m x ( cost of 1 adult ticket)
= m x ( $15) = 1 5 m
And, the cost of 1 children ticket = $6
So, the total cost of ( 185 - m) adult tickets
= ( 185 - m) x ( cost of 1 children ticket) = (185 - m ) x ( $6) = 6( 185 - m)
Also, the combined cost of all tickets = $ 1569
⇒ The cost of ( Adult's tickets + Children's Tickets) = $1569
or, 15 m + 6( 185 - m) = $1569
or, 15 m + 1110 - 6 m = 1569
or, 9 m = 459
⇒ m = 459/9 = 51 , or m = 51
Hence the number of adults visiting the zoo = m = 51
The number of children visiting the zoo = 185 -m = 134
Three friends go to the movies. Each ticket costs $7. They also buy popcorn for $6, candy for $4 and a drink for $2. The friends want to split the total cost evenly. Write a numerical expression to represent this situation and determine how much each friend owes.
Answer:
7+7+7+6+4+2=33
Each friend will have to pay $11
Step-by-step explanation:
Darnells car used 8 gallons to travel 340. Miles after a machanic worked on the car it used 7 gallons of gasoline to travel 350 miles if the price of gasoline was approximately $4.00 per gallon how much less to the nearest cent per mile did it cost to run the car after the mechanic worked on it
Answer:
What we are going to do for this case is find the cost for each case:
Cost to run the car before the mechanic worked on it:
Cost to run the car after the mechanic worked on it:
The difference between both cases is:
Answer:
It cost to run the car after the mechanic worked on it 0.01 $ / mile less than before the mechanic worked on it.
Read more on Brainly.com - https://brainly.com/question/2528459#readmoreStep-by-step explanation:
0.6(4 - 2x) = 20.5-(3x + 10)
find the solution in slope-intercept form y+7=-3(x-1) and 3x+y=-4
The solution in slope-intercept form for:
y + 7 = -3(x - 1) is y = -3x - 4
3x + y = -4 is y = -3x - 4
Solution:We have been given two equations
y + 7 = -3(x - 1) and 3x + y = -4
we have been asked to simplify these equations in slope intercept form.
The slope intercept form can be written as follows:
y = mx + b
Where, m is the slope of the line and b is the y-intercept.
The y-intercept of this line is the value of y at the point where the line crosses the y axis
Now, let us write the first equation in slope intercept form as follows:
y + 7 = -3(x - 1)
y + 7 = -3x + 3
y = -3x + 3 - 7
y = -3x - 4
The slope intercept form for the first equation is y = -3x - 4
Now, let us write the second equation in slope intercept form.
This can be done as follows:
3x + y = -4
y = -3x - 4
Therefore, the slope intercept form for the second line is y = -3x - 4
Which could be used to evaluate the expression -6(4 2/3)
Final answer:
To evaluate -6(4 2/3), convert 4 2/3 to an improper fraction, then multiply it by -6 and simplify the result.
Explanation:
To evaluate the expression -6(4 2/3), we need to simplify the expression inside the parentheses first. 4 2/3 can be converted to an improper fraction as follows: (4 * 3 + 2) / 3 = 14 / 3. Then, we multiply -6 by 14/3 to get: -6 * 14/3 = -84/3. The final step is to simplify -84/3, which is -28.
ng the Zero Product Property
Warm-Up
Which are solutions of the equation (x + 5)(x-3) = 0?
For this case we have a factorized quadratic equation. We equal each factor to zero and thus find the roots:
[tex]x + 5 = 0[/tex]
Subtracting 5 from both sides we have:
[tex]x = -5[/tex]
Thus, the first solution of the equation is:
[tex]x_ {1} = - 5[/tex]
On the other hand we have:
[tex]x-3 = 0[/tex]
Adding 3 to both sides:
[tex]x = 3[/tex]
Thus, the second solution of the equation is:
[tex]x_ {2} = 3[/tex]
Answer:
The solutions of the equation are:
[tex]x_ {1} = - 5\\x_ {2} = 3[/tex]
How many tons are in 448,000 ounces?
Answer: 14
Step-by-step explanation: hope this helps u :)
Answer:
14 tons
Step-by-step explanation:
divide the mass value by 32000
448,000 divided by 32000 = 14 tons
PLS HELP EMERGENCY Select the BEST classification for the square root of 27 . A) irrational B) rational C) imaginary D) complex E) natural
Answer:
A) Irrational
Step-by-step explanation:
The square root of 27 is an irrational number since it's not a rational number. We identify rational numbers because they can be expressed as fractions
If we take the value of [tex]\sqrt{27}[/tex] we get
5.1961524227066318805823390245176...
There is no way to transform that number into a fraction because
* It has no decimal limit
* It has no decimal pattern (or period)
Examples of rationals are
5.44444...
[tex]0.\overline{32}[/tex]
2.375
The last one has limited decimals, the first two have repetitive patterns or a period.
use characteristics to describe the following matrix
Answer:
[tex]A_{21} = 6[/tex]
Step-by-step explanation:
We are given that
[tex]A = \left [\begin{array}{cccc}10&4&11&12\\6&3&2&8\end{array}\right][/tex] and we have to find the value of [tex]A_{21}[/tex]
Now, the general term [tex]A_{mn}[/tex] denotes the term in the matrix whose position is mth row and nth column.
So, [tex]A_{21}[/tex] denotes the term in matrix A whose position is 2nd row and 1st column.
Hence, the term is 6.
So, [tex]A_{21} = 6[/tex] (Answer)
In rectangle abcd, diagonal ac, which is 20 inches in length
The question is incomplete. The complete question is attached below.
Answer:
(a). AB = 16.4 in
(b) BC = 11.5 in
Step-by-step explanation:
From the rectangle ABCD shown below,
AB is the base of rectangle and CB is the altitude of the rectangle.
Given:
AC = 20 in
(a)
From triangle ABC,
Applying cosine ratio for angle 35°, we get:
[tex]\cos(35)=\frac{AB}{AC}\\AB=AC\times \cos(35)\\AB=20\times \cos(35)=16.38\approx 16.4\ in[/tex]
Therefore, AB = 16.4 in
(b)
Applying sine ratio for angle 35°, we get:
[tex]\sin(35)=\frac{CB}{AC}\\CB=AC\times \sin(35)\\AB=20\times \sin(35)=11.47\approx 11.5\ in[/tex]
Therefore, CB = 11.5 in
Final answer:
Using the cosine function, the base AB of the rectangle is approximately 16.4 inches. Using the sine function, the altitude CB is approximately 11.5 inches, both rounded to the nearest tenth of an inch.
Explanation:
To find the base AB and the altitude CB of rectangle ABCD with a given diagonal AC of 20 inches and an angle of 35° with base AB, we can use trigonometric ratios.
First, we will use the cosine function, which relates the base of a right-angled triangle to the hypotenuse:
cos(35°) = AB / ACcos(35°) = AB / 20AB = 20 * cos(35°)AB \approx 16.4 inches (to the nearest tenth)Next, we use the sine function, which relates the altitude to the hypotenuse:
sin(35°) = CB / ACsin(35°) = CB / 20CB = 20 * sin(35°)CB \approx 11.5 inches (to the nearest tenth)Type the correct answer in each box. Use numerals instead of words. What are the x-intercept and vertex of this quadratic function? g(x)=-5(x-3)^2
Answer:
The x-intercept is (3,0).
The vertex of the function is (3,0).
Step-by-step explanation:
Given : Function [tex]g(x)=-5(x-3)^2[/tex]
To find : What are the x-intercept and vertex of this quadratic function?
Solution :
Function [tex]g(x)=-5(x-3)^2[/tex]
The x-intercept is when g(x)=0.
i.e. [tex]-5(x-3)^2=0[/tex]
Divide by -5 both side,
[tex](x-3)^2=0[/tex]
Taking root both side,
[tex]x-3=0[/tex]
Add 3 both side,
[tex]x=3[/tex]
The x-intercept is (3,0).
The general vertex form of the quadratic function is [tex]y=a(x-h)^2+k[/tex]
where, (h,k) is the vertex
Compare the given function [tex]g(x)=-5(x-3)^2[/tex]
a=-5 , h=3 and k=0
The vertex of the function is (3,0).
The x-intercept and the vertex of the quadratic function g(x) = -5(x - 3)² are both (3, 0).
Step-by-Step Solution
Finding the x-intercept:
The x-intercept occurs where the function equals zero: g(x) = 0.Set the function equal to zero: 0 = -5(x - 3)².Divide both sides by -5: 0 = (x - 3)².Take the square root of both sides: 0 = x - 3.Solve for x: x = 3.Therefore, the x-intercept is (3, 0).
Finding the Vertex:
The given function is in vertex form: g(x) = a(x - h)² + k, where (h, k) is the vertex. Here, a = -5, h = 3, and k = 0.Therefore, the vertex is (3, 0).
The ratio of the length of a chameleon's tongue to the length of its body is 2:1. If a chameleon is 6 inches long, how many inches long is its tongue?
Answer:
4 inches long
Step-by-step explanation:
2+1=3
6÷3=2
2×2=4
The length of a chameleon's tongue is 4 inches
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
We have been given that the ratio of the length of a chameleon's tongue to the length of its body is 2:1
Let the length of a chameleon's tongue is 2x and the length of its body is x
⇒ 2x + 1x = 3x
We have been given that a chameleon is 6 inches long
⇒ 3x = 6
⇒ x = 6/3
⇒ x = 2
Therefore, the length of a chameleon's tongue = 2(2) = 4 inches
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ6
Whats the square root of 12356
Answer:
111.15754585272 or 2√3089
Step-by-step explanation:
Here I will show you two methods that you can use to simplify the square root of 12356. In other words, I will show you how to find the square root of 12356 in its simplest radical form using two different methods.
To be more specific, I have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.
√12356 = A√B
Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12356 to simplify the square root of 12356. This is how to calculate A and B using this method:
A = Calculate the square root of the greatest perfect square from the list of all factors of 12356. The factors of 12356 are 1, 2, 4, 3089, 6178, and 12356. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.
B = Calculate 12356 divided by the greatest perfect square from the list of all factors of 12356. We determined above that the greatest perfect square from the list of all factors of 12356 is 4. Furthermore, 12356 divided by 4 is 3089, therefore B equals 3089.
Now we have A and B and can get our answer to 12356 in its simplest radical form as follows:
√12356 = A√B
√12356 = 2√3089
Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12356 to simplify the square root of 12356 to its simplest form possible. This is how to calculate A and B using this method:
A = Multiply all the double prime factors (pairs) of 12356 and then take the square root of that product. The prime factors that multiply together to make 12356 are 2 x 2 x 3089. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.
B = Divide 12356 by the number (A) squared. 2 squared is 4 and 12356 divided by 4 is 3089. Therefore, B equals 3089.
Once again we have A and B and can get our answer to 12356 in its simplest radical form as follows:
√12356 = A√B
√12356 = 2√3089
How is the equation of this circle written in standard form?
x2 + y2 - 6x + 14y = 142
Answer:
[tex]\large\boxed{(x-3)^2+(y+7)^2=200\to(x-3)^2+(y+7)^2=(10\sqrt2)^2}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2+y^2-6x+14y=142[/tex]
We must use
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]x^2-6x+y^2+14y=142\\\\x^2-2(x)(3)+y^2+2(y)(7)=142\qquad\text{add}\ 3^2\ \text{and}\ 7^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(3)+3^2}_{(a-b)^2=a^2-2ab+b^2}+\underbrace{y^2+2(y)(7)+7^2}_{(a+b)^2=a^2+2ab+b^2}=142+3^2+7^2\\\\(x-3)^2+(y+7)^2=142+9+49\\\\(x-3)^2+(y+7)^2=200\\\\(x-3)^2+(y+7)^2=(\sqrt{200})^2\\\\(x-3)^2+(y+7)^2=(\sqrt{100\cdot2})^2\\\\(x-3)^2+(y+7)^2=(10\sqrt2)^2[/tex]
[tex]center:(3,\ -7)\\radius:10\sqrt2[/tex]