Mathematics High School

find the coordinates of the circumcenter of triangle ABC with vertices A(1,4) B(1,2) and C(6,2)
A. 5,2
B. 3,4
C. 2.5,1
D. 3.5,3

Answers

Answer 1
(3.5, 3) is the circumcenter of triangle ABC. The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors. Line segment AB: Slope (4-2)/(1-1) = 2/0 = infinity. This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3). So the equation for this perpendicular bisector is y = 3. Line segment BC (2-2)/(6-1) = 0/5 = 0 This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2) So the equation for this perpendicular bisector is x=3.5 So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC. Now let's do a cross check to make sure that's correct. Line segment AC Slope = (4-2)/(1-6) = 2/-5 = -2/5 The perpendicular will have slope 5/2 = 2.5. So the equation is of the form y = 2.5*x + b And will pass through the point ((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3) Plug in those coordinates and calculate b. y = 2.5x + b 3 = 2.5*3.5 + b 3 = 8.75 + b -5.75 = b So the equation for the 3rd bisector is y = 2.5x - 5.75 Now let's check if the intersection with this line against the other 2 works. Determining intersection between bisector of AC and AB y = 2.5x - 5.75 y = 3 3 = 2.5x - 5.75 8.75 = 2.5x 3.5 = x And we get the correct value. Now to check AC and BC y = 2.5x - 5.75 x = 3.5 y = 2.5*3.5 - 5.75 y = 8.75 - 5.75 y = 3 And we still get the correct intersection.
Answer 2

Answer:

D. (3.5, 3)

Step-by-step explanation:

Just something simple

Related Questions

Find the height of the pole if the shadow of a boy 6 ft. tall is 3 ft. and the shadow of the pole is 2 1/3 yards. 1 yards 4 feet 14 feet

Answers

Hi there! To solve this question, we can write and solve a proportion. We put shadow/height = shadow/x. We do this, because we're looking for the height of the pole and we already know the how big the shadow of the pole is. The yards need to be converted to feet. There are 3 feet in one yard and 3 * 7/3 is 21/3 or 7 in simplest form. The pole casts a shadow 7 feet tall. Plug in the numbers like this: 3/6 = 7/x. Cross multiply the values in order to get 3x = 42. now, you divide each side by 3 to isolate the "x". When you, you get x = 14. There. The height of the pole is 14 feet. The answer is C: 14 feet.

Answer:

14 feet

Step-by-step explanation:

he equation for the line of best fit is y = 0.39x + 15.89. Which of the following statements is true for the above graph?

Answers

The given equation is a slope intercept form of a line. In which,

y = mx + b

where: y = y coordinate
            x = x coordinate
            m = slope
            b = y-intercept

In the equation, y = 0.39x + 15.89. The y-intercept is 15.89 or approximately 16. Meaning at x = 0, there's already approximately 16 dogs visiting at the park.

Therefore, the answer is the last statement.

ANSWER: The y-intercept of the line is 15.89, meaning that on the day the dog park opened, there were about 16 dogs visiting the park.

Given ONL=MLN, O and M are right angles prove LM=NO

Answers

Final answer:

Using the properties of Isosceles triangles and right-angled triangles, it can be deduced that LM = NO given that angles ONL = MLN and O and M are right angles.

Explanation:

The given question is about proving equivalency of lines in a geometric figure. Given the figure has the angles ONL and MLN that are equal and O and M are right angles. Given these conditions, using the properties of triangles especially the Isosceles Triangle (where two sides are equal), we can conclude that LM = NO.

To prove this assumption, we incorporate the following facts: In an isosceles triangle, the angles opposite to equal sides are equal. Hence, if ONL = MLN, it implies that NO = LM. Additionally, if angles O and M are right angles, it signifies that the triangles formed are right angled triangles. Therefore, using the property of isosceles right angled triangles, the sides opposite to equal angles are equal.

Based on these facts and the properties of geometric concepts [Isosceles Triangle, Pythagorean theorem and right angled triangles], we can confidently conclude that LM = NO. This proves that given the conditions in the problem, the lines LM and NO are equal in length.

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Final answer:

Given that ONL=MLN and O and M are right angles, we can say that triangles ONL and MLN are congruent right-angled triangles. Therefore, according to the property of congruent triangles, the sides opposite the equal angles in these triangles (i.e., LM and NO) should also be equal to each other.

Explanation:

The question involves proving the equivalence of two lines in a geometric configuration, LM and NO, where two angles, ONL and MLN, are given as equal and O and M are right angles. This is quite a typical problem in Geometric Proof, an important topic in High School Mathematics.

To solve this, we need to apply the properties of triangles and the concept of congruent triangles. Since ONL and MLN are given as equal angles and O and M are right angles, we know that triangle ONL and MLN are right-angled triangles. In a right-angled triangle, if one angle is equal, then the other angles will be equal because the summing of angles in a triangle is 180 degrees.

Because we have now two right-angled triangles with their respective angles equal (ONL = MLN and NOM = LNM), they must be congruent triangles by the Angle-Angle (AA) criterion for congruency. This implies that the sides opposite the equal angles in these two triangles should also be equal. So, LM = NO in these triangles.

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Answer+explanation plz and thank you! :) these are quadratic equations.

Answers

equate both brackets to 0
3x+2=0
3x=-2
x=-2/3
and
x-5=0
x=5
the solution with a higher value is 5

CAN YOU PLEASE SOLVE THESE PROBLEMS!!! THANKS!!!!!
1) -3/4x=5
2) 0.6x= 0.48
3) -30=1.25x
4) -12 2/3= -1 1/9x
5) 12-3/5x = 27.
6) -17= 6x-5
7) 13= x/3 +4
8) -2/3x -4=10
9) 9x-14=2x
10) 2.5x -15=4x
11) 2x-31=-9x+24

Answers

Hello! Okay, so first things first, for these types of problems, you have to either divide if it's a whole number or multiply by the reciprocal (flipped over) if it's a fraction. Things you need to do is subtract the numbers with variables from the right side on both sides, then, subtract the whole number on the left to both sides, and then divide to get the answer. With that being said, here are the answers if you do them right.

1. -6 2/3
2. 0.8
3. -24
4. 11 2/5
5. -25
6. -2
7. 27
8. -21
9. 2
10. -10
11. 5

Note: I would've been able to explain to you better how you get these answers had there not been so many questions in one, but I tried my best.

Huilan is 15 years older than thomas. the sum of their ages is 55 . what is thomas's age?

Answers

55-15=40 Thomas is 35

50 pts.

Solve this algebraic equation.

-6x + 5 + 12x -6

Answers

−6x+5+12x−6                                                                                                                  =−6x+5+12x+−6

=−6x+5+12x+−6                                                                                                                             =(−6x+12x)+(5+−6)=6x+−1

6x−1 is your answer.
−6x+5+12x+−6

(−6x+12x)+(5+−6)

6x+−1

the answer is, 6x−1

CAN ANYONE HELP ME WITH THIS QUESTION!!!!!??? The length of a string in yards is a function f(n) of the length n in inches. Write a function rule for this situation.

A. f(n)=36n

B. f(n)=1/36 n

C. f(n)=12n

D. f(n)=n/12

Answers

Your answer would be B f(n)= 1/36 n

The hypotenuse of a right triangle is 6 inches and one of the legs is √ 6 inches, the exact value of the other leg is _______ inches.

A. 30
B. √ 15
C. 15
D. √ 30

Answers

the exact value is B

Jim has a membership to a comic book club. He pays $9.00 per month for membership and $2.50 for each comic book he purchases. What are the parameters in this scenario?

A.) The parameters are not defined.

B.) The slope is 9 and the y-intercept is 2.5

C.) The slope is 2.5 and the y-intercept is 9.

D.) x and f(x)

Answers

The answer is C) the slope is 2.50  and the y-intercept is 9, assuming the question refers to the parameters of his monthly cost.

His cost function could be described as y= 2.5x + 9, where x is the number of comic books he purchases. If he buys no comic books, he still has to pay the $9 membership fee. 

What is the point-slope form of the equation of a line that passes through the point (6, −8) and has a slope of −2? y+8=2(x-6) openstudy?

Answers

Point-slope form : y-y₁=m(x-x₁) ; Where m=slope

Passes through (6, -8) ; Slope is -2

Simply plug everything in :)

y - (-8) = -2(x - 6)

Simplify.

y + 8 = -2x + 12 → Answer

The answer from Openstudy is incorrect, because our slope is negative, not positive.

~Hope I helped!~

Which of the following is the inverse of the statement, "If it is an orange, then it is a citrus fruit"? A.If it is a citrus fruit, then it is not an orange. B.If it is a citrus fruit, then it is an orange. C.If it is not an orange, then it is not a citrus fruit. D.If it is not a citrus fruit, then it is not an orange.

Answers

Your answer would be D.If it is not a citrus fruit, then it is not an orange. The reason why is because there are multiple citrus fruit. A does not make sense because they just told you that an orange is a citrus fruit so that statement is invalid. B and C does not make sense because it's not always a true statement because of the multiple citrus fruit situation I explained earlier.
C is the answer i think.

C write function distance that calculates the distance between two points (x1, y1) and (x2, y2). all numbers and return values should be of type double.

Answers

Your question is unclear but here is my try.

Given (0, 5) and (5, 0), find the distance between the two points.

Let (0, 5) and (5, 0) be the two points.

Let d = distance

d = sqrt{(5 - 0)^2 + (0 - 5)^2}

d = sqrt{(5)^2 + (-5)^2}

d = sqrt{25 + 25}

d = sqrt{50}

d = sqrt{25}•sqrt{2}

d = 5•sqrt{2}

How do i do this problem?

(13z^9+6v)-11z^9

Answers

(13z^9+6v)-11z^9 =
13z^9 + 6v-11z^9 =
2z^9 + 6v

You want to buy a new TV. The diagonal measure of the screen is 42 inches, and the screen width is 36.6 inches. What is the screen height? Round your answer to the nearest hundredth.

Answers

you use pathogorian therom, the triangle thing, regardless your answer is 20.60
check the picture below.

How do you simplify -3.3+5.5

Answers

the answer is going to be 2 rounded

[tex]-3.3+5.5 =x[/tex]

Find the indicated real nth root(s) of a.

n=2, a=100

Answers

a=50 is the nth term for  a to equal 100

Find the mean of this data: 37, 36, 40, 36, 40, 36, 38. If necessary, round to the nearest tenth.

Answers

Add all the numbers together, and divide your total by the number of value there (in this case, 7). The nearest tenth is to one place after the decimal.
you add them all up to get 263 then you divide by how many number there are which is 7 so 263 dived by 7 = 37.571 then you round up (tenths)37.6

a baby elephant weighs 250 lb.

What is the elephants weight in TONS AND KILOGRAMS
(1kg=2.2lb)? round to the nearest thousandths place

Answers

2000 lb / 1 ton = 250 lb / x ton.  Cross multiply and solve for x.  2000x = 250.  x = 250/2000 = .125 ton

2000 lb / 907.185 kg = 250 lb / x kg.  2000x = 907.185(250).  x =  113.4 kg 

Answer:

250 lb⋅1 ton2000 lb=2502000 tons = 18 ton = 0.125 tons

250 lb⋅1 kg2.2 lb≈2502.2 kg ≈ 113.636 kg

What is the capacity of the cube in liters? Cube with length, width, and height labeled as 9 centimeters. 0.81 L 0.729 L 81 L 729 L

Answers

Take into account that 1 liter = 1 (dm)^3 and 1 dm = 10 cm

=> Conversión factor: 1 dm / 10 cm

=> 9 cm * 1 dm / 10 cm = 0.90 dm

Volume of cube with legth, width and height 0,9 dm = (0.90 dm)^3 = 0.729 dm^3 = 0.729 liter.

Answer: 0.729 L

Two fair dice are rolled. find the probability of a "double" given that the sum is 11.

Answers

Star with the statement: "Given that the sum is 11"
which may seem a bit odd considering its the last part of the problem

The "given" is important as it sets up the constraints of what we're dealing with. In this case, we know 100% (we can see or someone told us without lying) that the sum is 11. We don't know what the individual values are but we know they add to 11.

What are the ways to add to 11? Well they are...
5+6 = 11
6+5 = 11
so there are 2 ways to do it. As you can see, none of those ways involve a double. A double is where we have two of the same values (eg: snake eyes which is 1 and 1 giving 1+1 = 2 as the sum). It turns out that it's impossible to have doubles add to any odd number.

So if we know the sum is 11, and we're asking "what is the probability of rolling doubles", then the answer is 0. 
The 0 indicates "impossible" or "certainty of it never happening". 

There are 0 (zero) probability of a "double" given that the sum is 11.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

Two fair dice are rolled.

And, The probability of a "double" given that the sum is 11.

Now,

Since, The the probability of a "double" means;

''Two fair dice after rolled gives the same numbers.''

Since, The sum of two same number is always gives the even number.

So, We cannot get the sum 11.

Hence, There are 0 (zero) probability of a "double" given that the sum is 11.

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The product of two prime numbers is one less than 12 squared. What are they two prime numbers?

Answers

12 X 12 =144
144-1=143
143/11=13
So the answer would be 11 and 13.
Hope this helps!


1. ∠E and ∠F are vertical angles with m∠E=9x+12 and m∠F=3x+24
What is the value of x?

2. What is m∠KNL?

Answers

the value of x is 2 and KNL will be 102

What is 3x-9-5x=-7 if you solve for x

Answers

3x-9-5x = -7

combine like terms -9-2x = -7

add 9 to both sides

-2x = 2

divide both sides by -2

x - 2/-2 = -1

x = -1

What is the least common denominator (LCD) of 1/2 and 3/5 ?

Answers

Im pretty its 1 and 5

According to a survey, 75% of adults in the united states think the u. s. government system is broken. of these 75%, about 7 out of 10 think that the government can be fixed.
a.find the probability that a randomly selected adult thinks the u. s. government system is broken and thinks the government can be fixed.
b.given that a randomly selected adult thinks the u. s. government system is broken, find the probability that he or she thinks the government cannot be fixed.

Answers

1.       Probability that a randomly selected adult thinks the U.S. government system is broken and can be fixed:

P (A and B) = P (A) * P (B|A) = .75 * .7 = 0.525

2.       Probability that given that a randomly selected adult thinks the U.S. government system, he or she thinks the government cannot be fixed.

P (B|A) = (1 – P (B|A) = 3/10 = 0.3

To calculate the probability that an adult thinks the U.S. government is broken and can be fixed, multiply 75% by 70%, resulting in 52.5%. The probability that an adult thinks the government is broken but can't be fixed is found by subtracting 70% from 100%, yielding 30%.

The subject in question pertains to probability and statistics, which involves calculating the likelihood of certain outcomes based on given data and constructing confidence intervals to understand the population parameters.

Part A:

To find the probability that a randomly selected adult thinks the U.S. government system is broken and thinks the government can be fixed, we multiply the two given probabilities: 75% of adults think the system is broken and, of these, 70% think it can be fixed. Therefore:
0.75 (probability of thinking the system is broken) × 0.70 (probability of thinking it can be fixed given the system is broken) = 0.525 or 52.5%.

Part B:

Given that an adult thinks the government system is broken, to find the probability that they think it cannot be fixed, we subtract the probability that they think it can be fixed from 1:
1 - 0.70 = 0.30 or 30%.

In order to be elected to student council, Jeremy must have at least 50% of the current council members vote in his favor. If x represents the percent of favorable votes received, which inequality represents the percent of favorable votes that Jeremy needs for election to student council?

Answers

x = % of favorable votes received

x has to be at least 50% => 50% is the lower bound

=> x ≥ 50

Answer: x ≥ 50

Drag a statement or reason to each box to complete this proof.

If 3x−4=14, then x=6.

1. 3x−4=14 >>>> Given
2. 3x−4+4=14+4 >>>>?
3. Simplifying >>>>?
4. 3x3=183 >>>>?
5. >>>?

A. Simplifying
B. Division property of equality
C. Addition property of equality
D. x=6
E. 3x=18

Answers

The items below show the complete steps as to how this is being answered.

  1. 3x - 4 = 14 >>>> Given
   2. 3x - 4 + 4 = 14 + 4 >>>
      Step number 2 above is an addition property of equality. Both sides of the equation are added with 4. 
  3. Simplifying >>>
      3x = 18
   4. 3x/3 = 18/3 >>>> Division property of equality
   5. >>>> Simplifying,
        x = 6

Hence, the order of the choices as answers is C, E, B, A, D. 

Final answer:

In this proof, we use the Addition and Simplifying properties of equality to show that if 3x-4 equals 14, then x equals 6.

Explanation:

Given: 3x-4=14

3x-4=14 >> Given

3x-4+4=14+4 >> Addition property of equality

Simplifying >> Simplifying

3x=18 >> x=6

Answer: x=6

The sum of two numbers is $30$. the difference of twice the larger number and three times the smaller number is $5$. what is the positive difference between the two numbers?

Answers

The positive difference between the two numbers is 8, which is found by setting up a system of linear equations based on the sum of the numbers and the difference of twice the larger number and three times the smaller number.

To solve the system of equations given by the problem, we can set up two equations based on the information provided. Let x be the larger number and y be the smaller number. We are given:

The sum of two numbers is $30: x + y = 30.The difference of twice the larger number and three times the smaller number is $5: 2x - 3y = 5.

Solving this system of equations will allow us to find the values for x and y. From the first equation, we can express y in terms of x as y = 30 - x.

Substituting this into the second equation gives us 2x - 3(30 - x) = 5, which simplifies to 2x - 90 + 3x = 5 and further to 5x = 95.

Dividing both sides by 5, we find x = 19. Now we can determine y by plugging x back into the first equation, resulting in y = 30 - 19, so y = 11.

The positive difference between the larger and smaller number is 19 - 11 = 8.

If parallelogram rstu has all sides the same length then it would be true that rs = st

Answers

of course rs=st but it wouldn't be a parallelogram anymore but it would be a rhombus
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