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3 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(−1, 1) , B(5, 1) , and C(−1, −1) ?

1 answer:

7 0

Triangle ABC is a right triangle with vertex A containing the right angle.

You can tell because AB is a horizontal line since A and B have the same y-coordinate, and AC is a vertical line since A and C have the same x-coordinate.

A right triangle in a circumcircle is always in the semicircle, with the centre of the circle lying in the middle of the side opposite the right angle.

So, the circumcenter is the midpoint of BC.

The midpoint of BC is ((5-1)/2, (1-1)/2) = (2, 0)

You might be interested in

A dictionary contains the following 9 words: two, mice, three, squeaking, the, blind, deaf, birds, rabbits. What is the probabil

IgorC [24]

Answer:

The correct answer is B. 1/729

Step-by-step explanation:

1. Probability of any of the nine words would be randomly cited.

Using the Laplace Rule, we calculate that probability is 1/9

2. Now let's calculate the probability of any two - word phrase in specific order from those nine in the dictionary. We should remember that the probability of occurrence of two or more statistically independent events is equal to the product of their individual probabilities. So,

1/9 * 1/9 = 1/81

3. Using the same Multiplication Rule, we can calculate the probability of a random generation of the phrase "three blind mice", in that specific order. Because there are other phrases that could be generated with those three words, but in different order. The question was specific about the order.

1/9 * 1/9 * 1/9 = 1/729

The probability of randomly generating the phrase "three blind mice" is 1/729 or 0.137%

7 0

3 years ago

On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter

andrezito [222]

Answer:

1) The common ratio = 1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio = 1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0

3 years ago

What's the value of X?

elena-14-01-66 [18.8K]

Answer:

a) x=93

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

Y 45° 30° N 17 I need help pls

melisa1 [442]

Answer:

x=29.4

Step-by-step explanation:

To help find the sides of a triangle, I use SOHCAHTOA.

SOH - CAH - TOA

S=O/H ( $Sine=\frac{opposite}{hypotenuse}$ )

C=A/H ( $Cosine=\frac{adjacent}{hypotenuse}$ )

T=O/A ( $Tangent =\frac{opposite}{adjacent}$ )

Let's find x first. We know 2 parts of the triangle: the adjacent leg, and the angle that is opposite of that.

So it would be tangent (tan).

opposite = 17

adjacent = 30°

Plug these numbers into the calculator and you should get your answer.

$\frac{17}{tan(30)} = 29.44486372...$

x=29.4

Try to do y on your own and let me know if you have any questions!

Also correct me if I'm wrong on anything.

Hope this information helps!

4 0

3 years ago

PLEASE HELP! Answer quickly for points!! There are 5 times as many tomato plants as there are cucumber plants. The number of pep

miskamm [114]

Let x= cucumber plants
5x= tomato plants
6x+7= pepper plants
peppers = 19
therefore
6x+7=19
subtract 7 from both sides
6x= 12
divide both sides by 6
x=2
replace the x with 2

2= cucumber plants
10= tomato plants

hope this helps

3 0

3 years ago