Coordinate of circumcenter of the given triangle = (3, 2)
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of circumcenter be (x , y)
Distance of Circumcenter from (4,2) =
[tex]\sqrt{(x - 4)^2 + (y-2)^2[/tex]
Distance of Circumcenter from (3, 3) =
[tex]\sqrt{(x - 3)^2 + (y-3)^2[/tex]
Distance of Circumcenter from (2,2) =
[tex]\sqrt{(x - 2)^2 + (y-2)^2[/tex]
By the problem,
[tex]\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\[/tex]..... (1)
Again,
[tex]\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\[/tex]...... (2)
Adding (1) and (2)
[tex]2x = 6\\x = \frac{6}{2}\\x = 3[/tex]
Putting the value of x in (1),
3 + y = 5
y = 5 - 3
y = 2
Coordinate of circumcenter = (3, 2)
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Plans for a new apartment building call for apartments directly across the hall from each other to be congruent. This computer printout shows Apartment D. If the vertices of Apartment E are located at (-2X1, Y1), (-2%2, Y/2), (-2X3, y3), and (-2%4, y4), will Apartment E be congruent to Apartment D?
Answer:
Step-by-step explanation:
no because (-2X1, Y1), and-2X3, y3), arent congruent so the whole problem is not congruent
write 75 (base 10) using 2 numerals
Answer:
Step-by-step explanation:
75 = 64 + 8 + 2 + 1 = 1*2^6 + 1*2^3 + 1*2^1 + 1*2^0
There is no power 5, 4, or 2 so zeros go in those slots.
75 = 1001011 (Base 2)
2) A cuboid has sides of length 10 cm, 6cm and 7 cm.
Find the total surface area of the cuboid.
6 cm
10 cm
7cm
The total surface are of cuboid is 304 cm square.
What is total surface area of cuboid?
The area of a cuboid refers to the surface area as the cuboid is a three dimensional solid. Thus, the area of cuboid can be calculated using the formula of area of rectangle, since the faces of a cuboid are in a rectangular shape.
The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:
Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units
The above formula gives the total surface area of a cuboid having all six faces.
Given, length = 10cm , width = 6 cm , height = 7cm
Total surface area = 2[10(6)+6(7)+10(7)]
=2(60+42+70)
=2(152)
=304.
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Please help me ASAP!!! Answer both questions for example: 1= C and 2= A
2. The equation is given as follows: x + 4x = 25.
3. The constrains are given as follows: 0 ≤ x ≤ 25, 0 ≤ y ≤ 75.
What is the equation in item 2?The time spent running is given by:
Running = 4x.
The time spent walking is one-fourth of the time spent walking, hence it is given by:
Walking = 4x/4 = x.
The total time is the sum of the times spent running and walking, hence the expression is presented as follows:
x + 4x = 25.
What are the constraints in item 3?The variables are given as follows:
x: number of out-of-state hires.y: number of in-state hires.You can accept at most 25 out-of-state hires, hence:
0 ≤ x ≤ 25
(as the number cannot be negative).
The company plans to have three times as many in-state hires, hence:
0 ≤ y ≤ 75.
As:
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I need help with this please
Answer:
Only the third one is incorrect. First 2 and last 1 are correct.
cybil and ronda are sisters. the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the cards. what is the probability that one letter is from each sister's name? express your answer as a common fraction.
Using the theories of probability, we got that 5/9 is the probability that one letter is from each sister's name if the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement.
We know very well that if we want to count number of ways by which r object can be chosen from n objects ,this can be done in [tex]^nC_r[/tex] ways which is equivalent to =(n!/(r!.(n-r)!)
Here are the same case, we have 10 cards, in each of the card there is letter written on it. So number of ways to choose two cards such that it contains any letter is can be done in [tex]^1^0C_2[/tex] ways which is equivalent to 45 ways.
Similarly, number of ways of choosing card which contains only Cybil`s name =[tex]^5C_2[/tex] ways=10 ways.
Similarly, number of ways of choosing card which contains only Ronda`s name =[tex]^5C_2[/tex] ways=10 ways.
So the number of ways containing one letter from each name = 45 - 10 - 10 = 25
So....the probability of choosing one of these sets = 25 / 45 = 5 / 9 =0.55
Hence, Cybil and Ronda are sisters. the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the cards. the probability that one letter is from each sister's name is = 5/9.
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(Complete question) is:
cybil and ronda are sisters. the 10 letters from their names are placed on 10 identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the 10 cards. what is the probability that one letter is from each sister's name? express your answer as a common fraction.
Why is the degree of the dilated function one more than the degree of the original function?
The degree of a function has no effect by the dilation of the function.
and the degree of the dilated function is same as the degree of the original function.
Dilation is defined as, when a function is multiplied by any number, the graph of the function retain a new shape, either by stretch or by compression in different directions.
Now, when a function is dilated it is either stretched or compressed in upward or downward direction.
It does not affect the degree of the function as the number of roots will be same as original function.
So, the degree of the dilated function is same as the degree of the original function.
Hence, the degree of the dilated function is same as the degree of the original function.
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£410 is divided between Gordon, Malachy & Paul so that Gordon gets twice as much as Malachy, and Malachy gets three times as much as Paul. How much does Malachy get?
The amount of money that Malachy get is £123 .
In the question ,
it is given that ,
£410 is divided between Gordon, Malachy and Paul .
also given that Malachy gets three times as much as Paul ,
let the amount that Paul get = x .
So , the amount that Malachy get = 3x
it is given that Gordon gets twice as much as Malachy ,
that means , the amount that Gordon get = 2(3x) = 6x
given the total amount is £410 ,
So, equation representing the total amount is
x + 3x + 6x = 410
4x + 6x = 410
10x = 410
x = 410/10
x = 41
So , the amount that Paul get = £41 ,
amount that Malachy get = 3(41) = £123
amount that Gordon get = 6(41) = £246
Therefore , The amount of money that Malachy get is £123 .
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Plumbing: If a 45 gallon hot water tank holds 360 lbs of water, what weight of water will a 55 gallon tank hold?
Weight of water will a 55 gallon tank hold 440 lbs.
How to find the weight of water will a 55 gallon tank hold ?If a 45 gallon hot water tank holds 360 lbs.
45 gal⇒ 360 lb
55 gal ⇒ x lb?
Ratio
45 : 360 = 55 : x
Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.
Here,
do the relation
[tex]\frac{45}{360} = \frac{55}{x}[/tex]
solve the x
[tex]x = \frac{55 * 360}{45} \\ = 440[/tex]
Hence weight of water will a 55 gallon tank hold 440 lbs.
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sin60° change to fraction
Answer:
[tex]\frac{\sqrt{2} }{3}[/tex]
Step-by-step explanation:
Explain how you would find 36×3/4 mentally
Answer:
= 27
Step-by-step explanation:
36×3/4
36 × 3
--
4
(cross multiplication)9 × 3
= 27
Evaluate: 3y - 5/4x=
when y = 2 and x = 4
Answer:
1
Step-by-step explanation:
3(2)-5/4(4)
6-20/4
6-5
1
Find the values of x and y. Write your answers in simplest form. Please show how the work so I can see and learn how to get the answer.
According to the area of triangle, the value of x is 8.6 and the value of y is 10.5
Area of triangle:
The area of the triangle is defined as the region enclosed by its perimeter or the three sides of the triangle.
Given,
Here we have the triangle with side values and height.
Now, we have to find the value of x and y in the triangle.
We know the formula of the triangle is,
A = 1/2 b x h
Here the value of b is x + 9 and the value of h = 6
So, the area of the triangle is,
=> [(x + 9) x 6]/2
=> 2 = 6x + 54
=> 6x = 52
=> x = 52/6
=> 8.6
Now, the value of y is calculated by using the Pythagoras theorem,
=> y² = (8.6)² + 6²
=> y² = 73.96 + 36
=> y² = 109.96
=> y = √109.96
=> y = 10.5
Therefore, the value of y is 10.5
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suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. a study was then done to see if the mean time has increased in the new century. a random sample of 27 first-time convicted burglars in a recent year was picked. the mean length of time in jail from the survey was four years with a standard deviation of 1.9 years. suppose that it is somehow known that the population standard deviation is 1.4. conduct a hypothesis test to determine if the mean length of jail time has increased. assume the distribution of the jail times is approximately normal. calculate the following. (enter exact numbers as integers, fractions, or decimals.) (a) x
Using Z- distribution it is found that the mean length of jail time has increased because the test statistics is greater than the critical value.
Z- distribution: It is a special normal distribution where the mean is 0 and standard deviation is 01.
z = (x -μ) / σ
At the Null hypothesis, it is tested if the mean length of jail time is still of 2.5 years.,
i.e., H₀ :μ = 2.5
Null hypothesis : It refers to a hypothesis that states that there is no relationship between two population parameters.
At the alternative hypothesis, it is tested if it has increased
i.e., H₁ :μ>2.5
Alternative Hypothesis: The alternative hypothesis states the research prediction of an effect or relationship.
we have the standard deviation for population thus the z- distribution is used. The test statistics is :
z= ⁻ₓ -μ /σ /√n
where, x is the sample mean
μ is the value tested at the null hypothesis.
σ is the standard deviation of sample.
n is the sample size.
For this problem the values of parameter are:
x= 5 ,σ =1.4 ,μ = 2.5 and n = 27
hence the value is :
z= ⁻ₓ -μ /σ /√n
= 5 - 2.5 / 1.4 ÷ √27
= 2.5 × √27 /1.4
= 9.27
The critical value for a right tailed test as we are testing if the mean is greater than a value with a significance level of 0.05 is of 2*= 1.645.
since, the test statistics is greater than the critical value, it can be concluded that the mean length of jail time has increased.
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Please help ASAP!! It's due tomorrow at 745am
Answer:
L = 22 W = 4
Step-by-step explanation:
It says that the length is 6 more than 4 times its width, this means
4W + 6 = L
Perimeter is 52, this means
2W + 2L = 52
and Area is 88, this means
W*L = 88
2W = 52 - 2L
W = 26 - L
4(26 - L) + 6 = L
104 - 4L + 6 = L
104 + 6 = L + 4L
110 = 5L
L = 22
W = 26 - 22
W = 4
7. Write an equation for the line in slope-
intercept form.
Ay
2
4-2 O
2
-4
2
4
X
Answer: y= -2/4x - 3
Step-by-step explanation:
b=y-intercept
Equation for slope-intercept form: y=mx+b
Locate the y-int/b: -3=b
Identify the slope/m: -2/4= 2 down, 4 to the right
Insert slope and y-int into slop-intercept form: y= -2/4x - 3
Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula a = p(1 + r)t, what is the approximate value of the account after 2. 5 years? $6,075 $6,118 $6,456 $6,778.
The approximate value of the account after 5 years will be $6778.
Given that,
Mario put $6,000 into a savings account that accrues interest at a rate of 5% per year.
The amount is given by,
A= p(1 + r)^t
P = 6000
R = 5%
T= 2.5 years
R = Rate of Interest
T= Time
P = Principal Amount
By substituting we get,
A= p(1 + r)^t
A = 6000(1 + 0.05)^2.5
A = 6000(1.05)^2.5
A = 6000 * 1.129
A = 6778.35
As a result, the account will roughly be worth $6778 after five years.
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given p(a) = 0.90, p(b) = 0.96, p(c) = 0.05 and that events a, b, and c are independent, what is p(a, b, and c).
The P(a, b and c) is 0.0432 when P(a) = 0.90, p(b) = 0.96, p(c) = 0.05.
From the given question, we know that
Probability of event 'a' occurring, P(a) = 0.90
Probability of event 'b' occurring, P(b) = 0.96
Probability of event 'c' occurring, P(c) = 0.05
We have been told that these three events are independent.
Thus, we can use the multiplication rule of probability, which states that the probability of three independent events a, b, and, c occurring is equal to the products of the probability of each individual event occurring.
p(a, b and c) = p(a) × p(b) × p(c)
= 0.90 × 0.96 × 0.05
= 0.0432
Hence, the probability(a, b, and c) is 0.0432.
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A trader old a writ watch for h.3150 after giving a 10% dicount.Find the marked price of the watch
The marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.
First, let us understand the percentage:
A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.
Let the marked price be x.
So,
According to the question;
x - x * 10% = 3150
x - x * 10/100 = 3150
100x - 10x / 100 = 3150
90x = 3150 * 100
x = 3150 * 100 / 90
x = 3500
So, the marked price is $3500.
Thus, the marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.
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Leo reads 11 pages in one third 1/3 hour. What is the unit rate for hours per pages?
Answer: 33 pages in 1 hour
Step-by-step explanation:
You could cross multiply
[tex]\frac{11}{1/3}[/tex] = [tex]\frac{x}{1}[/tex]
11=1/3x
x=33
Parker went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar. Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.
The number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.
Given,Parker went to the grocery store and bought bottles of soda and bottles of juice.
Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.
Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar.
we are asked to determine the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.
So, the total number of bottles:x+y=14
x=14-y ...eq(1)
As, Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.
50x+10y=300
Substituting the value of x from eq(1)
⇒ 50(14-y) + 10y = 300
⇒ 700 - 50y + 10y = 300
⇒ -40y = 300 - 700
⇒ -40y =-400
y = 400/40
y = 10
The number of juice bottles = 10.
Now, to get the number of bottle of soda by substituting the value of y in equation (1):
x = 14-y
x = 14 - 10
x = 4
The number of soda bottles = 4.
Therefore, the number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.
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Select the correct answer. What is the solution for x in the equation 5/3x + 4= 2/3x? A. B. C. D.
[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4=\dfrac{2}{3}x }}[/tex]
Subtract 2/3x on both sides.
[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4-\dfrac{2}{3}x=0 }}[/tex]
Combine 5/3x and -2/3x to get x.
[tex]\boldsymbol{\sf{x+4=0 }}[/tex]
Subtract 4 from both sides. Any value subtracted from zero results in its negative value.
[tex]\boldsymbol{\sf{x=-4 }}[/tex]
Answer:
x = - 4
Step-by-step explanation:
[tex]\frac{5}{3}[/tex] x + 4 = [tex]\frac{2}{3}[/tex] x ( multiply through by 3 to clear the fractions )
5x + 12 = 2x ( subtract 2x from both sides )
3x + 12 = 0 ( subtract 12 from both sides )
3x = - 12 ( divide both sides by 3 )
x = - 4
HELP MEEE PLEASE TYYYYYY
Answer:
45mi/h
Step-by-step explanation:
4 to 8 = 4 hours
v = space / time
v = 180/4 = 45 mi/h
Evaluate. 7^4 Responses 28 28 343 343 2401 2401 16,384
The exponential number 7⁴ we get expression as 2401.
Given that,
The exponential number is 7⁴.
We have to find the expression.
A number's exponent tells us how many times it has been multiplied by itself.
Exponent-related issues are resolved utilising exponentiation rules or exponentiation attributes.
How many times we must multiply the reciprocal of the base is indicated by a negative exponent is the exponential with negative symbol
A fractional exponent is one where the exponent of a number is a fraction.
Take the exponential number.
7⁴
7×7×7×7
2401
Therefore, The exponential number 7⁴ we get expression as 2401.
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Volume please help due today!
The new volume of the container will be 120 ft³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Given a container with dimensions 3ft by 4ft by 5ft
Its volume need to be twice.
Volume of container = length*width*height
Original volume = 3*4*5 = 60 ft³
After doubling = 60*2 = 120 ft³
New dimensions are = 4ft by 5ft by 6ft
Hence, The new volume of the container will be 120 ft³ and New dimensions are 4ft by 5ft by 6ft
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Factorize Completely
6xb + 2xy - 9mb - 6my
Answer:
(3b + 2y)(2x - 3m)
Step-by-step explanation:
6xb + 2xy - 9mb - 6my ( factor first/second and third/fourth terms )
= 2x(3b + y) - 3m(3b + 2y) ← factor out (3b + 2y) from each term
= (3b + 2y)(2x - 3m)
A triangle has two sides of length 4 and 6. What is the largest possible whole-number length for the third side?
Answer:
9
Step-by-step explanation:
given 2 sides of a triangle then the third side x lies within the limits
difference of 2 sides < x < sum of 2 sides , that is
6 - 4 < x < 6 + 4
2 < x < 10
then the largest possible length is 9
The straight line L passes through the points (4, -1) and (6, 4)
The straight line M is perpendicular to L and intersects the y-axis at the point (0, 8)
Find the coordinates of the point where M intersects the x-axis.
Answer:
Step-by-step explanation:
gradient of L:
4-(-1)/6-4
=5/2
Gradient of m=perpendicular gradient=m1xm2= -1
5/2m2=-1
5m2=-2
m2= 2/5
y intercept given=8
equation:
y= -2/5x+8
y will be0 when line crosses x-axis
input y as 0
0= -2/5x+8
2/5x=8
2=40x
x= 20
coordinate=(-20,0)
Please mark as brainliest
12x−x+8+3x= ______x + _______ Complete the equation so that it has infinitely many solutions.
Answer:
14x + 8 for the first column and the second one is i think its 2 (7x + 4)
Step-by-step explanation:
sorry if this is not what your looking for
1. Which ordered pair does NOT belong to any quadrant?
(-1,-3)
(1, 3)
(1, -3)
(0, 3)
The point(0,3) is not a part of any quadrant. option D is the correct answer
The points on the x-axis and the y-axis are not a part of any quadrant.
From the question, we have
The point(0,3) is not a part of any quadrant.
Cartesian Coordinate System:
A point in a plane can be found using the coordinate system by connecting two perpendicular lines. In two dimensions, points are represented as coordinates (x, y) with respect to the x- and y-axes. We will study the Cartesian Coordinate System in this article. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. A rectangular system's reference lines, the vertical and perpendicular axes, are used to measure distances.
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