Determine the center and radius of the following circle equation:
x2 + y2 – 12x – 18y + 108 = 0
Center:
Radius:
Pls help :)
Answers
Answer:
(6, 9 ) and r = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 12x - 18y + 108 = 0
Rearrange the x- terms and the y- terms together and subtract 108 from both sides, that is
x² - 12x + y² - 18y = - 108
To obtain standard form use the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 9)y + 81 = - 108 + 36 + 81
(x - 6)² + (y - 9)² = 9 ← in standard form
with centre = (6, 9 ) and r = [tex]\sqrt{9}[/tex] = 3
Related Questions
I need help
5x^2 +60x+180=0
Answers
Answer:
x
Step-by-step explanation:
x
Answer:
-6
Step-by-step explanation:
khan academy
Select the correct answer. Amelia lost her credit card one day while on vacation. She reported the loss to the credit card company the next day. However, someone had used her card to make purchases worth $1,600 at different shopping outlets. What is the maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card? A. $0 B. $50 C. $800 D. $1,600
Answers
Answer:a
Step-by-step explanation:
The maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card is $50.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
According to the Fair Credit Billing Act (FCBA) in the United States, a consumer's liability for unauthorized charges on a credit card is limited to $50.
Amelia will be responsible for paying the first $50 of the fraudulent charges, but she will not be held responsible for any charges above that amount.
However, most credit card companies have a zero liability policy, which means that the consumer will not be responsible for any unauthorized charges made on their credit card.
Hence, the maximum amount that Amelia may have to pay back for the fraudulent charges of $1,600 made on her card is $50.
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Please answer quickly I am running out of time
Answers
The value of [tex]g(-4)=\frac{-4}{3}, \ g(-2)=3 \ \text{and} \ g(2)=\frac{8}{3}[/tex] .
Solution:
Given function:
[tex]g(x)=\left\{\begin{array}{ll}-\frac{1}{3} x^{2}+4 & \text { if } x \neq-2 \\3 & \text { if } x=-2\end{array}\right.[/tex]
Substitute x = –4 in g(x), we get
[tex]$g(-4) =- \frac{1}{3}(-4)^2+4[/tex]
[tex]$=- \frac{16}{3}+4[/tex]
To make the denominator same, multiply and divide the 2nd term by 3.
[tex]$=- \frac{16}{3}+\frac{12}{3}[/tex]
[tex]$g(-4)=- \frac{4}{3}[/tex]
It is given that, if x = –2, then g(x) = 3
Therefore g(–2) = 3
Substitute x = 2 in g(x), we get
[tex]$g(2) =- \frac{1}{3}(2)^2+4[/tex]
[tex]$=- \frac{4}{3}+4[/tex]
To make the denominator same, multiply and divide the 2nd term by 3.
[tex]$=- \frac{4}{3}+\frac{12}{3}[/tex]
[tex]$g(-2)= \frac{8}{3}[/tex]
The value of [tex]g(-4)=\frac{-4}{3}, \ g(-2)=3 \ \text{and} \ g(2)=\frac{8}{3}[/tex] .
plz help me i need work plz
Answers
For the given figure;
Perimeter = 41 cm and
Area = 49.5 cm².
Step-by-step explanation:
Step 1; The given figure consists of a rectangle and a triangle. The rectangle's length is 6 cm and the rectangle's width is 7 cm. The triangle's base is 6 cm long while its height is 2.5 cm and the third side measures 6.5 cm.
Step 2; The figure's area = The rectangle's area + The triangle's area.
The rectangle's area is given by multiplying the rectangle's length with the rectangle's width. The area of the rectangle = 7 × 6 = 42 cm².
The area of a triangle is given by multiplying [tex]\frac{1}{2}[/tex] with the product of the triangle's base and height. The area of the rectangle = [tex]\frac{1}{2}[/tex] × 6 × 2.5 = 7.5 cm².
The figure's area = 42 + 7.5 = 49.5 cm².
Step 3; The figure's perimeter = The perimeter of the rectangle + the perimeter of the triangle.
The rectangle's perimeter is 2 times the sum of the length and width. The perimeter of the rectangle = 2 × (6 + 7) = 2 × 13 = 26 cm.
The perimeter of a triangle is the sum of all the three side lengths.
The area of the triangle = 6 + 2.5 + 6.5 = 15 cm.
The perimeter of the figure = 26 + 15 = 41 cm.
Part B: Set up an equation and solve for x. In your answer, include the equation, your calculations and the value of x.
Part C: Use your equation from Part A and the value of x from Part B to prove your equation to be true for the adjacent angles in the diagram.
Answers
The adjacent angles in the diagram are 112° and 68°.
Step-by-step explanation:
The measure of angle in a straight line is 180°.
Therefore, the sum of the two angles is equal to 180°.
⇒ 2x + 68 = 180
The equation formed to solve for x value is 2x+68 = 180
⇒ 2x = 180 - 68
⇒ 2x = 112
⇒ x = 112/2
⇒ x = 56
∴ The adjacent angles in the diagram are 2x=2(56)= 112° and 68°
4. What is the measure of each interior angle of a regular 28-gon?
Answers
Step-by-step explanation:
Measure of each interior angle of 28 sided polygon
[tex] \frac{(28 - 2) \times 180 \degree}{28} \\ \\ = \frac{26 \times 180 \degree }{28} \\ \\ = \frac{4680 \degree }{28} \\ \\ = 167.14\degree \\ [/tex]
The measure of each interior angle of a regular 28-gon is 167.14 degrees.
The measure of each interior angle of a regular 28-gon can be calculated using the formula:
Interior Angle = (n-2) * 180 / n
Substitute n = 28 into the formula:
Interior Angle = (28 - 2) * 180 / 28 = 24 * 180 / 28 = 167.14 degrees
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts? A. 2/9 pie B. 4/9 pie C. 1 1/4 pies D. 2 1/4 pies
Answers
Answer:
D. 2 1/2
Step-by-step explanation:
9/4 = 2.50 = 2 1/2
Answer:
D. 2¼
Step-by-step explanation:
9/4
(8+1)/4
8/4 + 1/4
2¼
What is the GCF of 12m + 3mx?
Answers
Answer:
3m
Step-by-step explanation:
You can check
3m(4+x)
12m+3mx
see
and its gcf because inside () has no common factors
Answer:
3m(4+x)
Step-by-step explanation:
Morgan’s mom wants to borrow $720 to buy a new computer. The store will charge her 8% simple interest for one year. How much will she have to pay back if she pays the full amount in one year?
Answers
Answer:
$770.60
Step-by-step explanation:
Simple interest is the same amount every year.
So first you work out 10%, then 5%, and then 1% which then you x3 to get 3%
10% = 72
5% = 36
1% = 7.2
3% = 14. 6
you then add together the 5% and the 3% to get the simple interest, which is
50.6
then you add the simple interest and the money she borrowed and that is your answer
720 + 50.6 = 770.60
Answer:
$900
Step-by-step explanation:
The Highly Improbable Foods Company makes vegetarian versions of burgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of one burger, three hot dogs, and $5$ chicken wings, which costs $\$16.$ Platter B consists of two burgers, one hot dog, and $8$ chicken wings, which costs $\$20.$
A picnic organizer requires $80$ hamburgers, $95$ hot dogs, and $380$ chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?
Answers
Answer:
$1020
Step-by-step explanation:
Let x and y represent the numbers of Platter A and Platter B the organizer needs to purchase, respectively. The given conditions can be summarized as ...
x + 2y ≥ 80 . . . . . . 80 or more hamburgers are required
3x + y ≥ 95 . . . . . . 95 or more hot dogs are required
5x +8y ≥ 380 . . . . 380 or more chicken wings are required
16x +20y = c . . . . . c must be minimized
__
It is useful to graph these inequalities, and look for the vertex of the feasible region that is closest to the origin. That vertex is (x, y) = (20, 35). The other vertex that is close to the origin is (60, 10). The cost of that order would be $1310.
The value of an order of 20 Platter A and 35 Platter B is ...
20×$16 +35×$20 = $320 +700 = $1020
The minimum cost of the picnic food is $1020.
The temperature at 6:00 a.m. was ‐3.5°C. From 6:00 to 7:00, the temperature increased 2.5°C. From 7:00 to 8:00, it decreased by 0.25°C, and from 8:00 to 11:00, the temperature dropped 3.25°C. Which expression shows the temperature in °C at 11:00 a.m.?
Answers
The expression that shows the temperature in °C is [tex]-3.5+2.5+(-0.25)+(-3.25)[/tex].
Step-by-step explanation:
Step 1:
The initial temperature at 6.00 am was [tex]-3.5[/tex] °C.
Step 2:
From 6.00 to 7.00 am, the temperature increased by another 2.5°C, so the temperature at 7.00 am was [tex](-3.5 + 2.5)[/tex] °C.
Step 3:
From 7.00 to 8.00 a.m, the temperature decreased by another 0.25°C, so the temperature at 8.00 am was [tex](-3.5+2.5+(-0.25))[/tex] °C.
Step 4:
From 8.00 to 11.00 a.m, the temperature dropped by another 3.25 °C, so the temperature at 11.00 am was [tex](-3.5+2.5+(-0.25)+-(3.25))[/tex] °C which is represented by the fourth option.
Answer:
A i did did question on think through math think it is the answer
Step-by-step explanation:
Simplify. 10/27 divided by 5/9
Answers
Answer:
2/3 or 0.6
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
According to the question,10/27÷5/9
So we will have to be careful when solving this kind of question
So let's solve
10/27÷5/9
To solve we will have to convert the division to multiplication and during this process the 5/9 will actually change to 9/5
10/27×9/5
If you calculate it well,you will get
2/3
Which means that the final answer is 2/3 since it cannot be solved further
So 10/27÷5/9 gives 2/3
Big Ben a famous clock tower London , England . The diameter of the clock face 23 feet . Find the circumference of the clock face . Round to the nearest tenth .
Answers
Answer:
23pi, or approx. 72.27
Step-by-step explanation:
circumference = 2(pi)r, or 2d
pi = approx. 3.14, r = radius, and d = diameter
You are given diameter, so all you have to do is multiply 23 feet by pi.
The circumference of the clock face of is 72.1 feet or 23π.
Given that the diameter of the clock face is 23 feet.
To calculate the circumference of the clock face, use the the following formula:
The value of π is approximately 3.14159.
Circumference = 2πr
In the formula r is the radius.
Since, the diameter is 23 and the radius is half of the diameter.
Thus, the radius r is 11.5.
Further, calculate the circumference:
Circumference = 2 × 3.14159 × 11.5
Circumference ≈ 72.08357
Circumference ≈ 72.1 feet
Therefore, the circumference of the clock face is 72.1 feet.
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A coin is flipped 3 times If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?
Answers
Answer:
12.50
Step-by-step explanation:
The expected amount is $12.50.
What is the probability?The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
There are 8 possibilities, if coin is flipped three times.
HHH, HHT, HTH, TTH, HTT, THT and TTH,
where H is possibility of head and T is tail.
Now the probabilities,
0 tails: 1 way out of 8 total: P(0) = 1/8
1 tails: 3 ways out of 8 total: P(1) = 3/8
2 tails: 3 ways out of 8 total: P(2) = 3/8
3 tails: 1 way out of 8 total: P(3) = 1/8
The expected amount;
(1/8)X 0 + (3/8)X 5 +(3/8)X15 +(1/8)X40
= 15/8 + 45/8 + 40/8
= 100/8
= 12.50
Therefore, the expected amount is $12.50.
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This graph shows the temperature in Diego's house between noon and midnight one day.
temperature (degrees F)
R
3
TO
1
2
3 4 5 6 7 8 9
time (hours after noon)
10
11
12
Which of the statements below are true statements? Correct the statements that are false to make them
true.
Example:
The highest temperature happened at 9:00. This statement is false. The correct statement is: The
highest temperature happened at 4:00.
A. Time is a function of temperature.
B. The lowest temperature occurred between 4:00 and 5:00.
C. The temperature was increasing between 9:00 and 10:00
D. The temperature was 74 degrees twice, during the 12-hour period.
E. There was a four-hour period during which the temperature did not change.
REMEMBER TO CORRECT WRONG STATEMENTS. YOU GET 1 POINT FOR EACH LETTER, 1 FOR
CORRECT, 1 FOR CORRECTING FALSE STATEMENTS.
Answers
The first three statements are false because they are opposite from the data shown in the graph, while the two last statements are true.
To determine whether a statement is true or false, you need to:
Carefully analyze the information of the graph.Read and understand the statement.Compare the information of the statement to the one of the graph.Now, let's analyze each statement:Time is a function of temperature:This statement is false, this is because time does not change with temperature, and therefore time is an independent variable. The corrected statement would be Temperature is a function of time.
The lowest temperature occurred between 4:00 and 5:00:In the graph, you can see the lowest temperature was 67° and this occurred between 11 and 12 p.m. Therefore, the lowest temperature occurred between 11:00 and 12:00.
The temperature was increasing between 9:00 and 10:00:Based on the graph from 9 to 10 p-m the temperature went from 70° to almost 65°. Therefore the temperature was decreasing between 9:00 and 10:00.
The temperature was 74 degrees twice, during the 12-hour period:This statement is true, this temperature occurred at 3:00 and 4:00.
There was a four-hour period during which the temperature did not change:This statement is true, the temperature is the same between 5:00 and 9:00.
Note: This question is incomplete because the graph is missing, here is the graph.
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Six is one hundred times ???????????
Answers
Answer:
0.06
Step-by-step explanation:
6 is 6.0 and 0.06 times 100 is 6.
Answer:
0.06
Step-by-step explanation:
if you times 0.06 by 10 it is 0.6
if you times it by 100 it is 6
Which image shows a reflection of triangle ABC over the x-axis?
CLEAR CHECK
Math item response image
Math item response image
Math item response image
Answers
Answer:
Please add images.
Step-by-step explanation:
Which statement is true regarding the functions on the
graph?
Of(-3) = g(4)
Of(-4) = 9(-3)
f(-3) = g(-3)
Of 4) = g(4)
Answers
Answer:
f(-3) = g(-3)
Step-by-step explanation:
Remember points on the graph get their location from the x-axis (horizontal) and y-axis (vertical).
In function notation, "f(x)" means when "x" is the value in the brackets, what the value of "y" will be.
First option for example: f(-3) = g(4)
Value of "y" for f(x) when x = -3:
On the blue line, when x = -3, y = -4.
Value of "y" for g(x) when x = 4:
On the red line, when x = 4, y = -3.
Therefore:
f(-3) = g(4)
-4 = -3 <= This is false.
In the third option: f(-3) = g(-3)
On f(x) blue, when x = -3: y = -4
On g(x) red, when x = -3: y = -4
Therefore:
f(-3) = g(-3)
-4 = -4 <= This is true.
Answer:C
Step-by-step explanation:
5d2-50d+125 =
Fully factor each expression
Answers
5d^2 - 50d + 125
We can divide all the numbers by 5 in order to simplify it:
5(d^2 - 10d + 25)
Now all we need to do is factor.
Since -5*-5 = 25 and -5 - 5 = -10, we can use this to factor:
5(d - 5)(d - 5)
Or
5(d - 5)^2
Tickets for the school play cost $4 for students and $7 for adults. For one performance, 146 tickets were sold for $779. How many tickets were for adults and how many were for students?
a 65 students and 81 adults
b 80 students and 66 adults
c 70 students and 77 adults
d 81 students and 65 adults
Answers
Answer: D
Step-by-step explanation:
Total tickets sold is $779
Calculate the options to get the right answer.
Option D is correct at
81 students at $4 = 324
65 adults at $7= 455
Total is $ 779
URGENT!!!!!!!!
I need the answer to both parts in this screenshot.
Answers
Answer:
a) $10
b) 0.1 hours
Step-by-step explanation:
The total amount earned by Cary,E after working h hours is calculated using:
[tex]E=10h[/tex]
The dollars Cary earns per hour is the unit rate, which is $10
If Cary earns $10 per hour, then she earns
$1 in
[tex] \frac{1}{10} hours = 6mins[/tex]
Carry has to work for 0.1 hours to earn $1
What is the area of the figure?
Enter your answer in the box.
❏in²
Answers
Answer:32
Step-by-step explanation:
add 10 + 10 + 6 + 6 = 32
(4, 1) and (6,7)what is the slope
Answers
Answer:
3
Step-by-step explanation:
[tex]m = \frac{y}{x} = \frac{7 - 1}{6 - 4} = \frac{6}{2} = 3[/tex]
Solve the system of linear equations by graphing. Y=-5/2x-7 X+2y=4
Answers
Answer:
They intersect at (-4.5, 4.25)
Assuming you can graph them, just put the equations in your calculator or graphing software and find the intersection, next time.
what is the equation for this line
Answers
The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
Solution:
The points on the line are (–6, –3) and (4, –5).
[tex]x_{1}=-6, y_{1}=-3, x_{2}=4, y_{2}=-5[/tex]
Slope of the line:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]$m=\frac{-5-(-3)}{4-(-6)}[/tex]
[tex]$m=\frac{-5+3}{4+6}[/tex]
[tex]$m=\frac{-2}{10}[/tex]
[tex]$m=\frac{-1}{5}[/tex]
Point-slope formula:
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]$y-(-3)=\frac{-1}{5}(x-(-6))[/tex]
[tex]$y+3=\frac{-1}{5}(x+6)[/tex]
[tex]$y+3=\frac{-1}{5} x-\frac{6}{5}[/tex]
Subtract 3 from both sides of the equation.
[tex]$y=\frac{-1}{5} x-\frac{21}{5}[/tex]
The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
Answer the following question
Answers
The formula for the area of triangles is lwh × 1/2.
Multiply the length by the width, height, and then by 1/2.
1.1 × 3.8 × 0.5 = 2.09
Since both triangles are equal, both triangles area will be the same, 2.09.
Now multiply the are by 2.
2.09 × 2 = 4.18
The area of the shaded areas equals 4.18in.
42
97
-----
[tex]42 \times 97[/tex]
Answers
Answer:
4074
Step-by-step explanation:
there are 800 students at weaver middle school. to determine which mascot name is preferred by the students at the school, each of the 30 teachers surveyed their two top-scoring students. would this be an appropriate sampling technique for the school to use?
Answers
Answer:
This would not be an appropriate sampling technique because it is biased and it would not be fair for 60 students to choose a mascot for a school with 800 students.
Step-by-step explanation:
I need a word problem for 4x + 5 = 37
Answers
Alexa has 5 grapes. She went to the store and bought 4 times a number. When she counted the grapes, she had 37 grapes in total.
When you make a word problem with this, you will get 4x+5=37
what is 1 and 1/8 plus 1 and 1/4
Answers
Answer:2.375
Step-by-step explanation:
1 and 1/8 =(1×8+1)/8=9/8
1 and 1/4 =(1×4+1)/4=5/4
9/8+5/4=9/8+10/8=19/8=2.375
Answer: 2.375