The circumcenter of the triangle that has vertices at (1, 10), (-5, 2), and (7, 2) is (1, 3.75)
What is the circumcenter of a triangle?The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the three sides of the triangle.
The distance from the circumcenter to each of the three vertices are congruent.
The coordinates of the circumcenter can found using the as follows;
Let (x, y), represent the coordinates of the circumcenter, we get;
The distance of the circumcenter from the vertices of the triangle is the same for the three vertices, therefore;
The specified vertices of the triangle are; (1, 10), (-5, 2), and (7, 2)
The distance of the circumcenter, (x, y), from (1, 10), is therefore;
D₁ = √[(x - 1)² + (y - 10)²]
The distance of the circumcenter, (x, y), from (-5, 2), is therefore;
D₂ = √[(x - (-5))² + (y - 2)²]
The distance of the circumcenter, (x, y), from (7, 2), is therefore;
D₃ = √[(x - 7)² + (y - 2)²]
The properties of the circumcenter indicates that we get;
D₁ = D₂ = D₃
D₁ = √[(x - 1)² + (y - 10)²] = D₂ = √[(x - (-5))² + (y - 2)²] = D₃ = √[(x - 7)² + (y - 2)²]
D₁ = D₂ indicates;
√[(x - 1)² + (y - 10)²] = √[(x - (-5))² + (y - 2)²]
(x - 1)² + (y - 10)² = (x - (-5))² + (y - 2)² = (x + 5)² + (y - 2)²
(x - 1)² + (y - 10)² = (x + 5)² + (y - 2)²
x² - 2·x + y² - 20·y + 101 = x² + 10·x + y² - 4·y + 29
According to the addition and subtraction properties of equality, we get;
x² - 2·x + y² - 20·y + 101 - (x² + 10·x + y² - 4·y + 29) = 0
12·x + 16·y - 72 = 0...(1)D₁ = D₃ indicates√[(x - 1)² + (y - 10)²] = √[(x - 7)² + (y - 2)²]
(x - 1)² + (y - 10)² = (x - 7)² + (y - 2)²
x² - 2·x + y² - 20·y + 101 = x² - 14·x + y² - 4·y + 53
x² - 2·x + y² - 20·y + 101 - (x² - 14·x + y² - 4·y + 53) = 0
12·x - 16·y + 48 = 0...(2)Equation (1) and (2) indicates;
12·x + 16·y - 72 = 12·x - 16·y + 48
12·x - 12·x + 16·y - (-16·y) = 48 - (-72) = 48 + 72 = 120
16·y - (-16·y) = 16·y + 16·y = 32·y = 120
y = 120 ÷ 32 = 3.75
y = 3.75
12·x - 16·y + 48 = 0...(2)
12·x - 16 × 3.75 + 48 = 0
12·x - 12 = 0
12·x = 12
x = 12/12 = 1
x = 1
The coordinates of the circumcenter is; (1, 3.75)Learn more about the circumcenter of a triangle here:
https://brainly.com/question/7894175
#SPJ1
to what is 9% increased to get 79.57
Please help :(
Answer:
Step-by-step explanation:
6.57
0.7 divided by 33.3
round answer to 2 decimal places
Answer:
0.02
Step-by-step explanation:
Joann and Phyllis each improved their flower gardens by
planting daisies and carnations. Joann bought 10 daisies and 4
carnations and paid $52.66. Phyllis bought 3 daisies and 6
carnations and paid $43.11. How much is each daisy? How
much is each carnation?
2.99 for each daisy and 5.69 for each carnation.
What is carnation?
carnation is a flowering devotion.
Sol- Let x represent the cost of each daisy.
Let y represent the cost of each carnation.
Given that as per question,
Joann brought 3 Daisy and 4 carnation and paid $52.66.-------eq(1)
10x+4y =52.66
Phyllis bought 3 daisies and 6 carnation and paid $043.11---------eq(2)
Multiplying the EQ 1 by 3
30x +12y= 157.98------eq (3)
Multiplying the equation (2) by -2
-6x -12y= -86.22-------eq(4)
On equation (3) and (4)
X=2.99
Substitute the value of x into the equation 2 we get
Y= 5.69
Thus each daisy costs
2.99 and each carnation cost 5.69.
To know more about carnation click-
https://brainly.com/question/29005519
#SPJ13
suppose that for a given least-squares regression, the sum of squares for error is 100 and the sum of squares for regression is 105. find the coefficient of determination.
51.21% is the coefficient of determination.
What does coefficient of determination mean?
A statistical model's ability to predict a result is indicated by the coefficient of determination (R2), a value between 0 and 1. The proportion of variation in the dependent variable that the statistical model predicts can be understood as the R2 value.SST = SSE + SSR
Here, SSE = 100 and SSR = 105
SST = 100+105 = 205
Coefficient of determination , R^2 = 105/205 = 51.21%
Learn more about coefficient of determination
brainly.com/question/16258940
#SPJ4
Johnson electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The variable production cost is $5 per catalog. Data indicate that, on average, each printed catalog generates a profit of $35 from sales (i. E. , $40 revenue). What is the optimal service level for the catalogs printing decision?.
Johnson electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The variable production cost is $5 per catalog. Data indicate that, on average, each printed catalog generates a profit of $35 from sales.
The optimal order quantity will be 11450.
Let’s use the news vendor model here.
The profit means that if we print less we will incur a certain opportunity loss. This is also known as cost of understocking (Cu) = 35
The production cost is $5 and if the product is not sold, we will incur a cost of (Co) = 5. The fixed cost is incurred either way in a year. As a result we need to consider the critical fractile value
C.F. = Cu/(Cu + Co) = 35/(40) = 0.875
The value of z at 0.875 is 1.15. This means that the optimal order/production will be 8000 + 1.15*3000 = 11450
Hence the answer is, the optimal order quantity will be 11450.
To learn more about decisions click here https://brainly.com/question/26869005
#SPJ4
help pls if ur good with money
Answer:Top right answer (You had extra money at the end of the month
Step-by-step explanation:
Do a first then Do b by the way OMG this is urgent
Answer:
The answer for questions A is 2 over 8
Step-by-step explanation:
The robot can complete 7 tasks is one 2 over 5 hour so you multipy 7 by 2 over 5 because then you get 2 over 8
the slope of the curve y= 3x²-8/5-2x at the point (2,4).
pls answer this
Answer: y=3x2
Step-by-step explanation:
a random sample of 25 was drawn from a normal distribution with a standard deviation of 5. the sample mean is 80. determine the 95% confidence interval estimate of the population mean.
Answer:
For A, the confidence interval formula above cannot be applied because n is less than 30, so we use the t-score confidence interval value
C.I = Mean ± t score × Standard deviation/√n
Mean = 80
Standard deviation = 5
n = 25
Degree of freedom = 25 - 1 = 24
Hence, 95% confidence interval degree of freedom t score = 2.064
Hence, Confidence Interval =
80 ± 2.064 × 5/√25
80 ± 2.064 × 1
80 ± 2.064
Confidence Interval =
80 - 2.064
= 77.936
80 + 2.064
= 82.064
Confidence Interval: (77.936, 82.064)
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (1 −1), and Monique's desk is located at (−4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk? square root of 7 feet square root of 14 feet square root of 85 feet square root of 61 feet
The distance from Maria's desk to Monique's desk is √61 feet.
According to the question,
We have the following information:
Maria's desk is located at (1 −1), and Monique's desk is located at (−4, 5). And each unit represents 1 foot.
Now, we know that the following formula is used to find distance between two points:
Distance = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]
In this case, we have x1 = 1, y1 = -1, x2 = -4 and y2 = 5.
D = [tex]\sqrt{(5+1)^{2} +(-4-1)^{2} }[/tex]
(We have converted -1 of y1 directly to 1 because the multiplication of two negative integers give positive results.)
D = [tex]\sqrt{(6)^{2} +(5)^{2} }[/tex]
D = [tex]\sqrt{36+25}[/tex]
D = [tex]\sqrt{61}[/tex] feet
Hence, the correct option is D (the last one).
To know more about distance here
https://brainly.com/question/24485622
#SPJ1
Answer:
The solution to this question is (D) - Square root of (61) feet
Step-by-step explanation:
George baked a cake to share with his family. Jenny ate 15 of the cake and Brett ate 13 of the cake. How much of the cake did Jenny and Brett eat in all? Responses 215 of the cake 2 over 15 of the cake 28 of the cake 2 eighths of the cake 815 of the cake 8 over 15 of the cake 85 of the cake 8 fifths of the cake
The fraction of the cake that Jenny and Brett eat in all is C. 8 over 15 of the cake.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Jenny ate 1/5
Brett ate 1/3.
The fraction that they eat will be:
= Jenny + Brett
= 1/5 + 1/3
= 3/15 + 5/15
= 8/15
Therefore, the correct option is C.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
On Monday, the drama club starts a bake sale to earn money for supplies. The equation 3 = -3x + 24 represents that there are 3 remaining treats after a number of days since Monday.
How many complete days have passed when the club has 3 remaining treats?
The complete days have passed when the club has 3 remaining treats will be 7.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation 3 = -3x + 24 represents that there are 3 remaining treats after a number of days since Monday.
If the club has 3 remaining treats, we have to find complete days that have passed, which is x in the given equation,
3 = -3x + 24
-3x= 3 -24
-3x= -21
x=21/3
x=7
Thus, the complete days that have passed when the club has 3 remaining treats will be 7.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ1
Fiona is x years old.
Thomas is 3 years older than Fiona.
Cara is twice as old as Fiona.
Solve the equation and work out Fiona`s,Thoma`s and Cara`sage
Fiona's age will be 'x' years, age of the Thomas is 'x+3' years whereas Cara is '2x' years old.
What is a system of linear equations in three variables?
A three-variable system of three equations can be solved using a series of steps that force one variable to be eliminated. The steps include rearranging equations, multiplying both sides of an equation by a nonzero constant, and adding a nonzero multiple of one equation to another.
If age of Fiona is 'x', the age of Thomas is 'y' and the age of Cara is 'z' years old.
Then by the given conditions, we can write
y = x + 3
z = 2x
Hence, if Fiona's age will be 'x' years, age of the Thomas is 'x+3' years whereas Cara is '2x' years old.
To learn more about the system of linear equations, visit:
https://brainly.com/question/24085666
#SPJ1
exercise statement: the initial pressures for bicycle tires when first filled are normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. a random sample of 15 tires is drawn from this population. what is the probability that the mean tire pressure of the sample is less than 69 psi? use minitab how-to
Answer:
Below
Step-by-step explanation:
70 - 69 = 1
1/1.2 is .83 S.D. below the mean for a z-score = -.83
from a z-score table this corresponds to .2033 or 20.33%
How does the solution to a system of equations compare to the solution of a system of inequalities?.
A collection of equations with the same variables is known as a system of equations. The only difference is that you're working with inequalities rather than equations in a system of inequalities.
What are inequalities?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
A system of equations has one solution for each variable, whereas a system of inequalities has a range of possible values for each variable.
Set up the equations as follows:
ax + by = c
dx +ey = f
Let the inequitable system exist:
ax + by <c
dx +ey > f
The same technique, such as graphing, substitution, and elimination, can be used to solve both systems.
But there's a difference because:
A system of equations can only have one solution for each variable, whereas a system of inequalities can have any number of solutions for each variable.
Learn more about inequalities and systems of equations:
https://brainly.com/question/28230245
#SPJ4
find the value of the expression of -1/3 - (-5/12)
Answer:
to subtract fractions, find the LCD and then combined
The answer is 1/12.
Stanley deposits $1,000 into a savings account that pays 1% interest per year. At the end of the first year, he's earned $10 in interest and there is $1,010 in the account. If the account has simple interest, the 1% interest for year two would be based off ____________. If the account has compounding interest, the 1% interest for year two would be based off ________________. (note: the first choice goes in the first blank, the second choice goes in the second blank).
If the account has simple interest, the 1% interest for year two would be based off simple interest. If the account has compounding interest, the 1% interest for year two would be based off Compound interest.
Interest on Interest
In performing a straightforward interest calculation, $1,000 that earned 1% interest in one year would yield $1,010 (or .01 x 1,000) at the end of the year. However, that calculation is based on simple interest, paid only on the principal or the deposited funds.
In savings accounts, interest can be compounded, either daily, monthly, or quarterly, and you earn interest on the interest earned up to that point.
The more frequently interest is added to your balance, the faster your savings will grow. Using our $1,000 example earlier and applying daily compounding every day, the amount that earns interest grows by another 1/365th of 1%. At the end of the year, the deposit has grown to $1,010.05 versus $1,010 via simple interest.
Hence the answer is If the account has simple interest, the 1% interest for year two would be based off simple interest. If the account has compounding interest, the 1% interest for year two would be based off Compound interest.
To learn more about simple and compound interest click here https://brainly.com/question/3575751
#SPJ4
Which equation represents a line passing through the point (8, 9)(8, 9) with a slope of 3?.
The equation represent a line passing through the point (8,9) with a slope of 3 is y= 3x-15.
Linear EquationTo make a linear equation, there is several methods depending on what known:
Given 2 pointsIf you know 2 points, for example point A(x1, y1) and B(x2, y2). Then the formula that can be used is:
[tex]\frac{y-y_{1} }{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given 1 point and slopeIf one point is known, for example point A(x1,y1) and slope m. Then the formula that can be used is:
[tex]y-y_{1}=m(x-x_1)[/tex]
Given 1 point and other related linear equationsIf there are other linear equations that have certain properties (parallel or perpendicular) to the linear equation to be searched for, then we can first find out the slope of the linear equation. If the gradient of another linear equation is m1 and the gradient of the linear equation to look for is m2
If the two lines are parallel
[tex]m_{2}=m_1[/tex]
If the two lines are perpendicular
[tex]m_2=\frac{-1}{m_1}[/tex]
In the problem, it is known 1 point and slope. Then the formula that can be used is:
[tex]y-y_{1}=m(x-x_1)[/tex]
1 known point is (8,9) and the slope of m is 3. Then substitute it into the formula:
[tex]y-9=3(x-8)\\y-9=3x-24\\y=3x-24+9\\y=3x-15[/tex]
Learn more about linear equation here: https://brainly.com/question/13738061
#SPJ4
If a car rental company charges $7 a day and 9 a mile to rent one of its cars, then the cost z, in dollars, to rent a
car for 2 days and drive y miles can be found from the equation
z = 7x + 0.09y
a. How much does it cost to rent a car for 4 days and drive it for 280 miles under these conditions? It costs $__
b. A second company charges $10 a day and 7¢ a mile for the same car. Write an equation that gives the cost z,
in dollars, to rent a car from this company for a days and drive it y miles.
Z=___
c. A car is rented from each of the companies for 2 days. To find the mileage at which the cost of renting the
cars from each of the two companies will be equal, solve the following system for y:
z= 7x + 0.09y
Z= 102 +0.07y
H= 2
y=____ miles
Answers for a) $53.2, b) z = 10x+0.07y and c) y =300
What is an equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a car rental company charges $7 a day and 9 a mile to rent one of its cars, then the cost z, in dollars, to rent a car for 2 days and drive y miles can be found from the equation
z = 7x + 0.09y
a) x = 4, y = 280
z = 7*4 + 280*0.09
z = 53.2
Therefore, the cost to rent a car for 4 days and drive it for 280 miles is $53.2
b) The equation that gives the cost z
z = 10x+0.07y
c) When the costs are equal, then,
10*2+0.07y = 7*2+0.09y
20+0.07y = 14+0.09y
0.02y = 6
y = 300
Therefore, the cost of renting the cars from each of the two companies will be equal when y = 300 miles.
Hence, Answers for a) $53.2, b) z = 10x+0.07y and c) y =300
For more references on equations, click;
https://brainly.com/question/10413253
#SPJ1
(Factoring Algebraic Expressions MC) (Also If I use ^ that means its the power of a number)
Rewrite x^4y^2 − 2x^3y^3 using a common factor.
A: x^2y(xy − 2xy^2)
B: x^2y^2(x^2 − 2xy)
C: 2xy^2(x^2 − x^2y)
D: 2xy(x^3y − x^2y)
Rewritten equation using a common factor is (B) [tex]x^{2} y^{2}(x^{2} -2xy)[/tex].
Given equation,
[tex]x^{4}y^{2}-2x^{3}y^{3}[/tex]
Taking [tex]x^{2} y^{2}[/tex] common,
[tex]x^{2} y^{2}(x^{2} -2xy)[/tex]
Hence, the equation.
To learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
what is the simplified fraction form of 75 over 100
Answer:
75/100
3/4
there it is
Divide £24 in the ratio 3:2
Answer:16
Step-by-step explanation:
can someone help me really quick
(Please Explain how you know this is correct.)
The rate of calories burned by bike riding is 4 calories per minute
First we have to choose points from the graph
The coordinates of the first point = (10, 40)
The coordinates of the second point = (20, 80)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line = (80-40) / (20-10)
= 40/10
= 4 calories per minute
Hence, the rate of calories burned by bike riding is 4 calories per minute
Learn more about slope of the line here
brainly.com/question/16180119
#SPJ1
PLSSS HELPP MEEE I RLLY NEED ITTT ASAP
Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°. 250.4° 63.2° 70.4° 19.6°
Answer:
70.4*
Step-by-step explanation:
Supplementary angles add up to 180*. This means that we must take 109.6 and try to find a number to add up to 180. We do the equation
180-109.6=70.4 therefore, the answer is 70.4*
Answer: 70.4
Step-by-step explanation: i took the test and got it right
solve by completing the square 3x^2+4x-6=0
Answer:
36.5x-53=543
Step-by-step explanation:
I need help with this as soon as possible
Answer: 763*42 = 32,046
32,046/82 = 390.8048
Do You KNOW HOW?
Solve each literal equation for the given variable.
5. y = x + 12; x
The given equation is y = x + 12 and in terms of x is x = y - 12
Define Linear equation
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
The given expression is ,
y = x + 12
Now, we have to solve for 'x'
so, for that just take constant term right side
y - 12 = x
Next, swap the sides like this
x = y - 12
Hence, the equation in terms of x is x = y - 12.
To read more about Linear equation.
https://brainly.com/question/26310043
#SPJ13
Verify that each equation is an identity.
tan+1/sec = sin+ cos
[tex]\cfrac{tan(\theta )+1}{sec(\theta )}~~ = ~~sin(\theta )+cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{tan(\theta )+1}{sec(\theta )}\implies \cfrac{~~ \frac{ sin(\theta )}{cos(\theta ) } +1~~}{\frac{1}{cos(\theta )}}\implies \cfrac{~~ \frac{ sin(\theta )+cos(\theta )}{cos(\theta ) } ~~}{\frac{1}{cos(\theta )}}[/tex]
[tex]\cfrac{ sin(\theta )+cos(\theta )}{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \cdot \cfrac{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\implies sin(\theta )+cos(\theta )[/tex]
pls send the correct answer
Answer:
z=53 y=37 and x=90
Step-by-step explanation:
Since there's a transversal, x is 90 because of alternate angles. Also alternate exterior angles are z so z=53 degrees. 180-(90+53)=37 degrees is y.
