Answers
To begin with, the vertices of the triangle ABC are as follows;
\(\begin{gathered} A=(1,1) \\ B=(1,-3) \\ C=(7,-3) \end{gathered}\)We shall label the center of the triangle (that is the circum-radius) as point O.
That means
\(OA=OB=OC\)Note also that the distance between two points on a coordinate grid is given as follows;
\(d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)That means the distance from point OA equals OB and also equals OC.
Therefore;
\(\begin{gathered} OA=\sqrt[]{(x-1)^2+(y-1)^2} \\ OA^2=(\sqrt[]{(x-1)^2+(y-1)^2})^2 \\ OA^2=(x-1)^2+(y-1)^2 \\ OA^2=x^2-2x+1+y^2-2y+1 \end{gathered}\)Similarly, distance OB can be calculated as follows;
\(\begin{gathered} OB^2=(x-1)^2+(y-\lbrack-3\rbrack)^2 \\ OB^2=(x-1)^2+(y+3)^2 \\ OB^2=x^2-2x+1+y^2+6y+9 \end{gathered}\)Note that
\(\begin{gathered} OA=OB \\ \text{Also, } \\ OA^2=OB^2 \\ \text{Therefore;} \\ x^2-2x+1+y^2-2y+1=x^2-2x+1+y^2+6y+9 \\ \text{Collect like terms and we'll now have;} \\ x^2-x^2+y^2-y^2-2x+2x-2y-6y=9+1-1-1 \\ -8y=8 \\ \text{Divide both sides by -8} \\ -\frac{8y}{-8}=\frac{8}{-8} \\ y=-1 \end{gathered}\)We shall now calculate the distance between point OC, as follows;
\(\begin{gathered} OC=\sqrt[]{(x-7)^2+(y-\lbrack-3\rbrack)^2} \\ OC^2=(x-7)^2+(y+3)^2 \\ OC^2=x^2-14x+49+y^2+6y+9 \\ \end{gathered}\)Since;
\(\begin{gathered} OB=OC \\ \text{And} \\ OB^2=OC^2 \end{gathered}\)We would now have;
\(\begin{gathered} x^2-2x+1+y^2+6y+9=x^2-14x+49+y^2+6y+9 \\ \text{Collect all like terms and we'll now have;} \\ x^2-x^2+y^2-y^2-2x+14x+6y-6y=49+9-1-9 \\ 12x=48 \\ \text{Divide both sides by 12;} \\ \frac{12x}{12}=\frac{48}{12} \\ x=4 \end{gathered}\)Therefore, the circumcenter of this triangle with center labelled as point O would be found at the coordinates (4, -1)
ANSWER:
\(\text{Circumcenter}=(4,-1)\)Related Questions
25 feet equals how many inches
Answers
Directions: Solve the following. Show your solution.
1. Diane has clay in a can. Its radius is 6 cm while its height is 10 cm. She wanted to transfer some of her clay to her cone-shaped container. What is the volume of the cone to be filled up if it has the same radius and height with
Pls do it with a solution
Answers
the volume of the cone to be filled up if it has the same radius and height with is 376. 6 cm³
How to determine the volumeTo determine the volume, we need to know the formula for the volume of a cone.
The formula for the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters are expressed as;
V is the volume of the coner is the radius of the coneh is the height of the coneSubstitute the values, we have;
Volume = 3.14 × 6² × 10/3
Find the square value
Multiply the value, we have;
Volume = 1130. 4/3
Divide the values
Volume = 376. 6 cm³
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12. Use the diagram to determine the value of x
Answers
Answer:
127 degrees = x
Step-by-step explanation:
A six sided polygon has interior angles that sum to
(n-2)(180) = (6-2)(180 = 720
so all of the angles in the question add to 720
98 + 133 + x + x + 155 + 80 = 720
solve for x = 127 degrees
Answer:
x = 127
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 6 , then
sum = 180° × 4 = 720°
sum the interior angles and equate to 720
x + x + 155 + 80 + 98 + 133 = 720 , that is
2x + 466 = 720 ( subtract 466 from both sides )
2x = 254 ( divide both sides by 2 )
x = 127
If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles
Answers
Answer:
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
Step-by-step explanation:
The question is incomplete:
Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24 25–34 35–55 55 and over Total
Liked Crunchicles 4 9 3 23 39
Disliked Crunchicles 5 27 28 64 124
No Preference 7 27 10 93 137
Total 16 63 41 180 300
One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .
If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.
The number that likes Crunchicles and are 55 and over is 23.
If we calculate the probability as the relative frequency, we have:
\(P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278\)
L: Likes Crunchicles.
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
7th grade math problem please help !!
Answers
Answer:
136 units^2
Step-by-step explanation:
Hello, anyone to help me with this math problem please please
Answers
From the question;
given the figure PQR
This is an angle that is less than 90 degree and it is very close to 90 degree
By inspecting the other given angles,
angle 3 forms an angle that is concgruent to angle PQR
HENCE
The correct option is B
Easy simple problem i wanna ask just because 1+1=?
Answers
Answer:
2
Step-by-step explanation:
At their practices, the volleyball team ran a total of 10 miles in 14 days. The tennis team ran a total of 8 miles in 7 days. Which team ran more miles per day?
Answers
Answer:
tennis team
Step-by-step explanation:
because they ran 8 miles is 7 days to get equal amount of days you multiply by 2 on both 8 miles and 7 days so they ran 16 miles in 14 days thats y tennisbteam ran more miles
The probability of two candidates A and B passing an exam are 2/3 and 3/4 respectively find the probability only one will pass at least one will pass
Answers
Answer:
\(\rainbow{\rule{10000pt}{900000pt}}\)
1. Laura buys a pack of 24 blueberry muffins that has a total
of 1,536 calories. What is her calorie intake, if she ate 3
muffins for breakfast?
Answers
1536/24 = 64
64 x 3 = 192
Answer:
192
Step-by-step explanation:
you have divide 24 by 3 and once you get that you get 8 then you do the amount of calories divide by 8
plsss explain nd i’ll give brainliest answer
Answers
Answer: 118
Step-by-step explanation:
Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.
https://brainly.in/question/28196155#:~:text=Step%2Dby%2Dstep%20explanation%3A&text=1%20The%20corresponding%20angles%20are,alternate%20exterior%20angles%20are%20equal. See #5.
e) A student spent 50 minutes doing her homework. She spent m minutes doing Geography. 2m minutes doing Mathematics and the remaining (m + 7) minutes studying History. How many minutes did she spend doing Mathematics?
Answers
Answer: 22 minutes
Step-by-step explanation: m + 2m + m + 7 = 4m + 7
4m + 7 = 50
4m = 44
m = 11
2m = 11 x 2 = 22 minutes
Express the answers in simplest form. A list contains the names of six anthropology students, two sociology students, and four psychology professor's new study, find the probability that the chosen student (a) A psychology student (c) A psychology student or an anthropology (d) Not a sociology student.
Answers
a) P(psychology student) = 1/3. b) P(psychology or anthropology student) = 5/6. c) P(not sociology student)= 5/6
How to find the probability that the chosen student(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:
P(psychology student) = 4/(6+2+4) = 4/12 = 1/3
(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:
P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6
(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:
P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6
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An article claimed the state's typical price of a gallon of gasoline is $2.69. The prices from 5 gas stations surveyed were $2.79, $2.99, $2.69, $2.89, and $2.69.
According to this data, what is wrong with the article's statement?
Answers
The typical average price of gasoline should be $2.81 and not $2.69 because $2.69 is not the average of the sampled prices.
What is the mean of the sample?
We are given the prices of a gallon of gasoline from 5 gas stations surveyed as; $2.79, $2.99, $2.69, $2.89, and $2.69.
Thus, to calculate the mean, we will use the formula;
Mean = ∑x/n
Mean = (2.79 + 2.99 + 2.69 + 2.89 + 2.69)/5
Mean = 14.05/5
Mean = $2.81
Thus, the typical average price of gasoline should be $2.81 and not $2.69
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Please this is my last problem and all my points just solve this for im begging
Answers
Answer:
72.54
Step-by-step explanation:
Use formula for trapezoid: a+b/2 * h
HELP NEEDED! Thanks if you do!!
Answers
Answer:
We conclude that:
csc (U) = 26 / 24
Step-by-step explanation:
Given
The angle ∠U The opposite of the angle ∠U = 24The hypotenuse = 26To determine
csc (U) = ?
Using the trigonometric ration
sin Ф = opposite / hypotenuse
substituting Ф = U, opposite = 24, hypotenuse = 26
sin (U) = 24/26
We know that: csc (U) = [1 ] / [sin(U)]
Therefore,
csc (U) = [1 ] / [sin(U)]
= 26 / 24
Therefore, we conclude that:
csc (U) = 26 / 24
Michael borrowed $1000 on a 2 year loan. He is charged 5% simple interest per year.
How much interest is he charged for 2 year? What is the total amount he has to pay
back?
O $1000, $3000
O $10, $1010
O $50, $5000
O $100, $1100
Answers
Answer:
the last choice
Step-by-step explanation:
simple interest means there is only interest on the original principal (1000$)
so 2 years of 5% would be 10%, 10% of 1000 is 100.
total amount = interest+principal, so it is 100, 1100
John paid $50 for renting a cycle for 5 hours. Which graph shows the relationship between the cost of renting a cycle for different hours? (1 point)
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,10 and 2,20 and 3,30.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 50 and 2,50 and 3,50.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1, 5 and 2,10 and 3,15.
A graph is shown. The title of the graph is Cycle Renting. The horizontal axis label is Number of Hours. The horizontal axis values are 0, 1, 2, 3, 4, 5, 6. The vertical axis label is Cost in dollars. The vertical axis values are 0, 10, 20, 30, 40, 50, 60. Points are plotted on the ordered pairs 1,20 and 2,40 and 3,60.
Answers
Answer:
Graph A <==
Step-by-step explanation:
$ 50 for 5 hours......50/5 = 10...thats $ 10 per hr
so the equation would be : y = 10x...with x being the number of hrs and y being the total cost.
So ur x axis will be the hours and your y axis will be the total cost.
so ur answer is :the title of the graph is cycle renting. the x axis (the horizontal axis)...since it is the hours, will be labeled 0,1,2,3,4,5,6
the y axis (the vertical axis)...since it is the total cost, will be labeled
0,10,20,30,40,50,60. points are plotted on (1,10),(2,20), and (3,30)
Which of the following ordered pairs could Briggs add to the graph?
Answers
Answer: B
Step-by-step explanation:
The next point where the gap is would be B but you're looking for the point that comes after (8,4) it would be C
Gina might buy 10 oranges and _ apples
Answers
The number of apples that Gina can buy is 15 apples.
How to illustrate the information?From the information, it was stated that the ratio of orange to apples is 2:3.
In this case, let the number of apples be represented by x
Therefore, the number of will be:
2/3 = 10/x
Cross multiply
2x = 10 × 3
2x = 30
Divide
x = 30 / 2
x = 15
Therefore, the number of apples that Gina can buy is 15 apples.
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The ratio of orange to apples is 2:3. Gina might buy 10 oranges and _ apples
A triangle has vertices at A(-3, 2), B(-1, -5) and C(4, 5). The triangle is transformed using the rule ro,o . What are the coordinates of A", B', and C?
Answers
Answer:
I thinck letter c.
Step-by-step explanation:
Because C.
The sum of 14 and 3
divided by r
Answers
Answer:
?
Step-by-step explanation:
The sum of the 14 and 3 divided by r will be written as (17 / r).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the numbers 14 and 3 are added and then divided by r, The mathematical expression of the number will be written as,
E = ( 14 + 3 ) / r
E = 17 / r
Therefore, the sum of the 14 and 3 divided by r will be written as (17 / r).
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Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus five. A) Does not exist B) 0 C) 5 D) -5
Answers
Answer:
lim as x---->0 of (x²-5) = -5 which is D
which angle pairs in the diagram are supplementary angles? Check all that apply.
Answers
Answer: 1 & 4 4&5 6&7
Step-by-step explanation:
What is 75.4 in expanded form
Answers
Answer: 75.4 =
70
+ 5
+ 0.4
Step-by-step explanation:
Hope this helps :)
I NEED THIS NOW PLEASE!!!
Answers
Answer:
We can predict that the spinner will possible land on the green or blue 8 out of 12 times, or 66% of the time.
Step-by-step explanation:
First of all, we need to calculate the percentage of the spinner that is both green and blue.
There are a total of 12 sections on the spinner.
6 out of 12 of the sections are green. 6/12 = 0.5 or a 50% change
2 out of 12 of the secions are blue. 2/12 = 0.16 or a 16% change
3 out of 12 of the sections are pink. 3/12 = 0.25 or a 25% chance
1 out of 12 sections are yellow. 1/12 = 0.08 or a 8% chance
Athough I provided the percantages for each color, all we really need is the data for the green and blue.
0.5 + 0.16 = 0.66
12 x 0.66 = 7.92 or 8 when rounded to the nearest whole number
Therefore, we can predict that the spinner will possible land on the green or blue 8 out of 12 times, or 66% of the time.
Hope this helps! Have a blessed day! :)
Find the value of X.
WILL GIVE BRAINLIEST!
Answers
Answer:
36
Step-by-step explanation:
Angles in a triangle sum to 180 degrees.
The angle in the bottom left will equal 180 - (3x + 6) as angles along a staight line also sum to 180 degrees.
180 - ( 3x + 6)
180 - 3x - 6 [expand bracket]
174 - 3x
Now we can add up all the angles and equate them to 180 to solve for x.
24 + 2x + 18 + 174 - 3x = 180
216 - x = 180
216 = 180 + x
x = 36
What is the slope of the line that passes through the points ( 9 , 5 ) (9,5) and ( 21 , − 5 ) (21,−5)? Write your answer in simplest form.
Answers
Answer:
-5/6
Step-by-step explanation:
(9, 5) and (21, -5)
slope = m = (difference in y)/(difference in x)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Answer: -5/6
The slope of the line that passes through points (9,5) and (21,-5) is -5/6.
We can use the two-point formula to find the slope for the given line. The formula is as follows:
(y2 - y1) = m*(x2 - x1)
Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.
In the given case:
x1=9, x2=21
y1=5, y2=-5
Using these values in the two-point formula, we get:
(-5-5)=m*(21-9)
-10=m*12
m=-10/12
m=-5/6
Hence the slope of the line is -5/6.
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2. What is the conversion from cubic metres to litres?
Answers
Answer:
1 cubic meter equals 1000 liters
Step-by-step explanation:
i think this is right
A committee must be formed with 4 teachers and 7 students. If there are 9 teachers to choose from, and 8 students, how many different ways could the committee be made?
Answers
as compromises. One example of an adaptive con
bear's "thumb.' Modern pandas have five digits th
and a sixth digit that functions like a thumb. This
bone. Ancestral pandas with bigger wrist bones hac
ing and eating their food. Over time, this adaptati