Answers
The circumcenter of a triangle is the center of a circumference where the three vertex are included. So basically we must find the circumference that passes through points O, V and W. The equation of a circumference of a radius r and a central point (a,b) is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]We have three points which give us three pairs of (x,y) values that we can use to build three equations for a, b and r. Using point O=(6,5) we get:
[tex](6-a)^2+(5-b)^2=r^2[/tex]Using V=(0,13) we get:
[tex](0-a)^2+(13-b)^2=r^2[/tex]And using W=(-3,0) we get:
[tex](-3-a)^2+(0-b)^2=r^2[/tex]So we have a system of three equations and we must find three variables: a, b and r. All equations have r^2 at their right side. This means that we can take the left sides and equalize them. Let's do this with the second and third equation:
[tex]\begin{gathered} (0-a)^2+(13-b)^2=(-3-a)^2+(0-b)^2 \\ a^2+(13-b)^2=(-3-a)^2+b^2 \end{gathered}[/tex]If we develop the squared terms:
[tex]a^2+b^2-26b+169=a^2+6a+9+b^2[/tex]Then we substract a^2 and b^2 from both sides:
[tex]\begin{gathered} a^2+b^2-26b+169-a^2-b^2=a^2+6a+9+b^2-a^2-b^2 \\ -26b+169=6a+9 \end{gathered}[/tex]We substract 9 from both sides:
[tex]\begin{gathered} -26b+169-9=6a+9-9 \\ -26b+160=6a \end{gathered}[/tex]And we divide by 6:
[tex]\begin{gathered} \frac{-26b+160}{6}=\frac{6a}{6} \\ a=-\frac{13}{3}b+\frac{80}{3} \end{gathered}[/tex]Now we can replace a with this expression in the first equation:
[tex]\begin{gathered} (6-a)^2+(5-b)^2=r^2 \\ (6-(-\frac{13}{3}b+\frac{80}{3}))^2+(5-b)^2=r^2 \\ (\frac{13}{3}b-\frac{62}{3})^2+(5-b)^2=r^2 \end{gathered}[/tex]We develop the squares:
[tex]\begin{gathered} (\frac{13}{3}b-\frac{62}{3})^2+(5-b)^2=r^2 \\ \frac{169}{9}b^2-\frac{1612}{9}b+\frac{3844}{9}+b^2-10b+25=r^2 \\ \frac{178}{9}b^2-\frac{1702}{9}b+\frac{4069}{9}=r^2 \end{gathered}[/tex]So this expression is equal to r^2. This means that is equal
Related Questions
Is y = 8 a solution to the inequality below?
Answers
Answer:
Yes
Step-by-step explanation:
136/8 = 17
17 +3 = 20
20 is less than or equal to 123 so 8 does work as a solution
Three times a number decreased by 1 is 10 Three times the difference of a number is 1 is 10One less than three times a number is 10The quotient of a number and 3 is 10
Answers
Three times a number decreased by 1 is 10:
X is the number.
3x = three times a number.
3x - 1 = 10 (Three times a number decreased by 1 is 10)
3x = 10 + 1
3x = 11
x = 11/3
Need help asap please and thank you
Answers
Answer:
y=[tex]\frac{1}{2}[/tex]x+1
Step-by-step explanation:
y=mx+b
m is the slope of the line, which you find by counting the rise over run between two points. In this case its up one, and right two, or [tex]\frac{1}{2}[/tex].
b is the y intercept, or where the line crosses the y axis
reduce to lowest term.5p+5q/4p+4q
Answers
Explanation
[tex]\frac{5p+5q}{4p+4q}[/tex]Step 1
factorize
[tex]\begin{gathered} 5p+5q\rightarrow5\text{ is a common factor, so}\rightarrow5(p+q) \\ 4p+4q\rightarrow4\text{ is a common factor, so}\rightarrow4(p+q) \end{gathered}[/tex]hence, the expression would be
[tex]\begin{gathered} \frac{5p+5q}{4p+4q}=\frac{5(p+q)}{4(p+q)} \\ \frac{5(p+q)}{4(p+q)} \end{gathered}[/tex]Step 2
now, we can see there is the same factor in numerator and denominator (p+q), so it can be eliminated.
[tex]\begin{gathered} \frac{5(p+q)}{4(p+q)}=\frac{5}{4} \\ \frac{5}{4} \end{gathered}[/tex]therefore, the answer is
[tex]\frac{5}{4}[/tex]I hope this helps you
The length of time (T) in seconds it takes the pendulum of a clock to swing through one compete cycle is givenby the formulaT= 2T✔️L/32 Where L is the length, in feet, of the pendulum, and is pie approximately 22/7. How long must the pendulum be of one complete cycle takes 2 seconds? Answer as a fraction or round to at least 2 decimal places.The pendulum must be__ feet.
Answers
we have the formula
[tex]T=2\pi\sqrt{\frac{L}{32}}[/tex]For T=2 seconds
substitute in the given formula
[tex]\begin{gathered} 2=2\pi\sqrt{\frac{L}{32}} \\ \\ 1=\frac{22}{7}\sqrt{\frac{L}{32}} \\ \\ squared\text{ both sides} \\ \\ (\frac{7}{22})^2=\frac{L}{32} \\ \\ L=\frac{7^2*32}{22^2} \\ \\ L=3.24\text{ ft} \end{gathered}[/tex]Please someone can help me please #1
Answers
Complete the following Division
Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively
What is Division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
1) 96
Divisor = 8
96 / 8
= 12
Quotient = 12
2) 55
Divisor = 5
55 / 5
= 11
Quotient = 11
3) 84
Divisor = 6
84 / 6
= 14
Quotient = 14
4) 63
Divisor = 3
63 / 3
= 21
Quotient = 21
Hence , Quotient of 96, 55, 84 and 63 is 12, 11, 14 and 21 respectively
To learn more about Division click on the link
https://brainly.com/question/25289437
#SPJ13
the following table shows student test scores on the first two tests in into three chemistry class. If a student scored a 74 on his first test, make a prediction for his score on the second test . Assume the regression equation is appropriate for prediction. Round your answer to two decimal places if necessary
Answers
68.29
ExplanationIf we locate each point (x, y) on the plane we will obtain the following graph:
We can approximate the resulting figure to a straight line:
In order to discover the equation of this line we use a linear regression calculator and enter the values as follows:
The calculator gives as the following equation as an approximation:
ŷ = 0.82X + 7.61
Using this equation we can predict the score of the second test of the exam using the score of the first test.
On this case, we want to make a prediction for a score on the second test if a student scored a 74 on his first test.
This means, we want to find ŷ when X=74. Let's replace it on the equation:
[tex]\begin{gathered} ŷ=0.82X+7.61 \\ \downarrow \\ ŷ=0.82\cdot74+7.61 \\ ŷ=68.29 \end{gathered}[/tex]That is why we can say that the student will have 68.29 as his score on the second test.
Solve the equation 7-(5t-13)=-25-15b+21+5b=-19
Answers
Let's solve the following expressions:
a.) 7 - (5t - 13) = -25
[tex]\text{ 7 - (5t - 13) = -25}[/tex][tex]\text{ 7 - 5t + 13 = -25}[/tex][tex]\text{ 20 - 5t = -25}[/tex][tex]\text{-5t = -25 - 20}[/tex][tex]\text{-5t = -4}5[/tex][tex]\frac{\text{-5t}}{-5}\text{ = }\frac{\text{-4}5}{-5}[/tex][tex]\text{ t = 9}[/tex]Therefore, t = 9
b.) -15b + 21 + 5b = -19
[tex]-15b+21+5b=-19[/tex][tex]-10b+21=-19[/tex][tex]-10b=-19\text{ - 21}[/tex][tex]-10b=-40[/tex][tex]\frac{-10b}{-10}=\frac{-40}{-10}[/tex][tex]\text{ b = 4}[/tex]Therefore, b = 4
Use the Distributive Property to solve the equation 2/3 (9a + 6) = 23.8
Answers
Distributive property tell us how to solve expressions in the form a(b+c), it says:
a(b+c)=ab+ac
Then,
[tex]\begin{gathered} \frac{2}{3}(9a+6)=23.8 \\ \frac{18a}{3}+\frac{12}{3}=23.8 \\ 6a+4=23.8 \\ 6a=23.8-4 \\ a=\frac{19.8}{6}=3.3 \end{gathered}[/tex]What two variables can you define to write an equation to match this scenario?x = number of minutes for fruit cans and y = number of minutes for vegetable cansx = total number of minutes and y = total number of cansx = number of minutes for fruit and y = total number of cansx = total number of minutes and y = number of minutes for vegetables
Answers
An equation to correctly match this scenario would have to include both separate products. The current order which is 384 cans of food, includes both fruits and vegetables, and therefore any expression that does not include them both would give a wrong answer and the order would not be properly met.
The correct scenario is;
[tex]\begin{gathered} x=Number\text{ of minutes for fruit cans} \\ y=\text{Number of minutes for vegetable cans} \end{gathered}[/tex]This way you can produce both at a maximum without overproducing one and underproducing the other.
Amanda y Pedro realizaron queques iguales, Lurdes se comió 2/4 partes, Amanda 2/3 y Pedro 3/4, quien comió menos?
Answers
An analyst notices that a CEO has consistently achieved 25% growth in profits from one year to the next. The CEO's company currently has annual profits of $870,000. If the trend continues, what will the annual profits be in 6 years?
Answers
The currennt annual profit of the company is $ 870,000.
The growth percentage is 25%.
The annual profit of the company in the 6 years can be determined,
[tex]\begin{gathered} \text{Annual Profit=870000(1+}\frac{25}{100})^6 \\ =870000(\frac{5}{4})^6 \\ =3318786.62 \end{gathered}[/tex]Thus, the aanyal profits after 6 years will be $ 3318786.62
Will give brainliest thank you..!
Answers
Answer:
4
Step-by-step explanation:
4
4
4
4
A straight line is 180 degrees. Find the value of X.
Answers
Given a straight line angle = 180
So, the angles (9x-100) and (40-x) are supplementary angles
So,
[tex](9x-100)+(40-x)=180[/tex]Solve for x:
[tex]\begin{gathered} (9x-x)+(40-100)=180 \\ 8x-60=180 \\ 8x=180+60 \\ 8x=240 \\ x=\frac{240}{8}=30 \end{gathered}[/tex]So, the answer will be x = 30
Using the GCF you found in Part B, rewrite 72 + 81 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work.
Answers
The factors of 72 and 81 are
[tex]\begin{gathered} 72=2^3\cdot3^2 \\ 81=3^4 \end{gathered}[/tex]Therefore, their GCF is equal to 3^2=9
Then,
[tex]72+81=9\cdot8+9\cdot9=9(8+9)[/tex]The answer is 9(8+9).
The factors of 8 and 9 are
[tex]\begin{gathered} 8\to2,4,8 \\ 9\to3,9 \end{gathered}[/tex]Can you help me solve the domain of this math word problem?
Answers
the domain refers to all possible values of x in the function.
since a negative time does not make sense, the smallest value of the domain is zero
on the other hand, the problem indicates that the model is considered accurate up to 100,000 years, therefore that would be the largest value of t
in conclusion, the domain of the function A(t) is
[tex]\lbrack0,100000\rbrack[/tex][ 0 , 100,000 ]
in chess, the knight (the piece shaped like a horse) moves in an L pattern.
Answers
Answer:
That is true but still remember that playing the knight at the start can be very useful.
solve the equation for x. x/16=10
Answers
To solve further cross multiply both sides
so that
[tex]x\text{ }\times1\text{ = 16 }\times10[/tex]x = 160
Which of the following statements follows from (x - 3)2 = 7? ox2 +9=7 Ox-3=1 / OX-3 = +49 NEXT QUESTION O ASK FOR HELP
Answers
So, given the equation:
We could take the square root to both sides of the equation to obtain that:
So the correct option is B.
use the angle shown to determine if the line are parallel
Answers
If the lines were parallel then
angle H would be corresponding to angle L and then
[tex]\measuredangle H\cong\measuredangle Z.[/tex]Since angles H and Z are a linear pair then if the lines were parallel angle H, Z and L would have to be right angles. Since the problem never states that those angles are right angles, then the lines are not necessarily parallel.
Answer: No.
P(A) = 1/4 P(A n B) = 1/12 P(AUB) = 13/24 Find P(B) c 21/24 5/24 O O O 3/8 11/24
Answers
Okay, here we have this:
Considering that P(AUB)=P(A)+P(B)-P(AintersectionB), we obtain that:
P(B)=P(AUB)-P(A)+P(AnB)
P(B)=(13/24)-(1/4)+(1/12)
P(B)=3/8
Finally we obtain that P(B) is equal to 3/8.
Tiffany works at a lawnmower store.Part AA portion of Tiffany's monthly salary is based on commission. She earns 21% of everything she sells. This month she sold $27,000 worth of lawnmowers. Howmuch was her sales commission this month?Part BThe store purchased one riding lawn mower for $1,500 and sold it for $2025. What percentage was the markup for the mower?PartTiffany earns $15 per hour. The store offers her a raise-a 2% increase per hour. After the raise, how much will Tiffany make per hour?
Answers
1) Gathering the data
Part A
Tiffany's Commission: 21%
Sales Revenue: 27,000
2) In this case, we can figure out how much has she earned by doing this:
[tex]27,000\text{ }\times0.21=5,670[/tex]Part B)
$1,500
$ 2,025
We can solve it in 2 steps. Firstly let's find the equivalence of 2025 in percentage.
1500-------100%
2025- ----x
1500x = 202500
x=202500/1500
x =135%
Now we need to subtract from 100%. 135%-100%= 35%
So the percentage (markup) was 35%. That lawnmower was sold 35% above the price.
Part C)
$15 per hour
2% per hour (0.02)
In this, case we need a simple calculation multiplying that 15 by (1 +0.02)
15 x ( 1 +0.02)
15 x (1.02)
15.3
After the raise, Tiffany earns $15.30 per hour
If the ratio of KL to JK is 2.7. and JL = 162, find JK
Answers
KL / JK = 2:7
JL = 162
JK = ?
JL = KL + JK = 162 KL = 2 JK = 7
KL / JK = 2.7
KL = 162 - JK
Substitution
(162 - JK) / JK = 2.7
Solve for JK
162 - JK = 2.7 JK
162 = 2.7 JK + JK
162 = 3.7 JK
JK = 162 / 3.7
JK = 43.8
Margie uses 36 inches of lace to make one pillow. She makes 24 pillows for the school fair. How many total inches of lace does Margie use on the pillows?
Answers
Margie used a total of 264 inches of lace for the 24 pillows
How to calculate the total inches of lace used ?
Margie used 36 inches of lace for one pillow
She needs to make 24 pillows
The total inches of lace that was used for the 24 pillows can be calculated as follows
= 36 × 24
= 864
Hence Margie used 864 inches of lace for 24 pillows
Read more on inches here
https://brainly.com/question/20562937
#SPJ1
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 64 m wide. Find the area of the training field. Use the value 3.14 for n, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
To find:
The area of the training field.
Solution:
The training field is made of two semicircles and a rectangle.
The length and width of the rectangle is 96 m and 64 m. So, the area of the rectangle is:
[tex]\begin{gathered} A=l\times w \\ =96\times64 \\ =6144\text{ m}^2 \end{gathered}[/tex]The diameter of the semicircle is 64 m. SO, the radius of the semicircle is 32 m.
The area of two semicircles is:
[tex]\begin{gathered} A=2\times\frac{1}{2}\pi r^2 \\ =3.14\times(32)^2 \\ =3.14\times1024 \\ =3215.36 \end{gathered}[/tex]So, the area of the training field is:
[tex]\begin{gathered} A=6144+3215.36 \\ =9359.36 \end{gathered}[/tex]Thus, the area of the training field is 9359.36 m^2.
Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,529.6 miles. The next time he fills up his Jeep, he pays for 10 gallons of gasoline he notes his odometer reading is 23,640.6 miles. How many miles per gallon did he get? (Round the answer to the nearest 10th if necessary.)
Answers
Answer:
11.1 miles per gallon
Explanation:
Given;
Odometer reading when the jeep is filled up with gasoline = 23,529.6 miles
Odometer reading when the jeep is filled up with 10 gallons of gasoline =23,640.6 miles
We can now go ahead and determine how many miles per gallon Harry got as seen below;
[tex]\begin{gathered} \frac{(Reading\text{ when j}eep\text{ is filled with 10 gallons }-Reading\text{ when j}eep\text{ is filled up)}}{\text{Gallo of gasoline}} \\ =\frac{23640.6-23529.6}{10}=\frac{111}{10}=11.1\text{miles per gallon} \end{gathered}[/tex]So Harry got 11.1 miles per gallon
Factor the expression using the GCF. 11. 24 - 9 12. 14x + 63
Answers
Recall that the GCF of two ( or more numbers) is the highest number that divides exactly the two numbers.
11.- Notice that:
[tex]\begin{gathered} 24=3\cdot8, \\ 9=3\cdot3. \end{gathered}[/tex]Therefore:
[tex]9-24=3(8-3)\text{.}[/tex]12.- Notice that.
[tex]\begin{gathered} 14x=7\cdot2x, \\ 63=7\cdot9. \end{gathered}[/tex]Therefore:
[tex]14x+63=7(2x+9)\text{.}[/tex]Answer:
11.-
[tex]3(8-3)\text{.}[/tex]
12.-
[tex]7(2x+9)\text{.}[/tex]
What Is the inverse of.. (ignore pencil writing) -matrices- (there may be more than one answer
Answers
To find the inverse of the matrix, first let's find the determinant:
[tex]\begin{gathered} |A|\text{ = 3(2) - 5(1)} \\ |A|\text{ = 6 - 5} \\ |A|\text{ = 1} \end{gathered}[/tex]Then, we'll find the Adjunct of the matrix:
[tex]\begin{gathered} \begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}\text{ : interchange }3\text{ and 2. negate 1 and 5} \\ \text{Adjunct = }\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} In\text{verse of the matrix = }\frac{1}{|A|}\times\text{ adjunct} \\ A^{-1}\text{ = }\frac{1}{1}(\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}) \\ A^{-1}\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)} \\ \end{gathered}[/tex]Can someone help me with this geometry question?A.Triangular prismB.Hexagonal prismC.Triangular pyramidD.Hexagonal pyramid
Answers
B. Hexagonal Prism
1) One prism is defined, in terms of naming it by the base.
2) Counting the edges of the base in this net surface, we can tell that this is a Hexagonal Prism for the base is a hexagon.
hi, can you please explain mistake made on one side the other side the correct work with the answer thanks
Answers
Notice that:
[tex]3x-3x\ne x,[/tex]therefore the mistake is the last step.
Now, all the work of the student is correct up to:
[tex]undefined[/tex]