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2 years ago

Which theorem explains why the circumcenter is equidistant from the vertices of a triangle

2 answers:

5 0

The circumcenter is the center of the circle which goes through the three vertices of the triangle. Recall that all radii of a circle are congruent, i.e. equal to one another. So this is why the circumcenter is equidistant from the vertices of the triangle.

Brut [27]2 years ago

3 0

Answer:

The proof is explained in step-by-step explaination.

Step-by-step explanation:

Circumcenter is the point at which the perpendicular bisector of sides of triangle intersects inside the circle.

This points lies inside the triangle as well as circle and the vertices of triangles lies on the circle. As a result the distance from circumcenter and vertices is called to be radius of the circle which is always equidistant from the center.

Hence, circumcenter is equidistant from the vertices of a triangle.

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Write the first 5 terms of the recursive sequence defined below. a1=0 an=2(an-1)²-1, for n>1

Aleksandr-060686 [28]

Answer:

0, -1, 1, 1, 1

Step-by-step explanation:

Given recursive formula

a₁ = 0
aₙ = 2(aₙ₋₁)² - 1, for n>1

The first 5 terms are:

a₁ = 0
a₂ = 2(0)² - 1 = 0 - 1 = -1
a₃ = 2(-1)² - 1 = 2 - 1 = 1
a₄ = 2(1)² - 1 = 2 - 1 = 1
a₅ = 2(1)² - 1 = 2 - 1 = 1

7 0

2 years ago

Plzz help!!!!!!! I 'll give brain liest

Basile [38]

Answer:

Step-by-step explanation:

1. 3x2 + 5x - 4 + 6x2 - x + 7

= combining like terms

= 9x2 + 4x + 3

2. 2y2 - 3y + 6 + y2 - 5y - 1 + (-4) + 2y2 - 2y

= 5y2 - 10y + 1

3. 2x2y - 3xy2 + x2y - 4x2y - 2xy2

= - x2y - 5xy2

4. x2 - y2 + 2x2 - 3xy + 4y2 + 3y2 - 5xy - x2

= 2x2 - 8xy + 6y2

7 0

2 years ago

Annie, Brianna & Carly are selling fruit boxes to raise money for their soccer team. All together the girls have sold 105 bo

GaryK [48]

Step-by-step explanation:

Annie = x

Brianna = y

Carly = z

Now,

x + y + z = 105 ...(1)

Carly has sold ten more than three times Brianna's sales.

z = 10 + 3y ...(2)

Brianna sold five more than Annie.

y = 5 + x ...(3)

Now,

z = 10 + 3y

z = 10 + 3(5 + x)

z = 10 + 15 + 3x

z = 25 + 3x

Now,

x + y + z = 105

x + (5 + x) + 25 + 3x = 105

5x + 30 = 105

5x = 105 - 30

5x = 75

5x/5 = 75/5

x = 15

So,

y = 5 + x

y = 5 + 15

y = 20

Now,

z = 25 + 3x

z = 25 + 3(15)

z = 25 + 45

z = 70

Thus,

Annie Sold 15 boxes

Brianna Sold 20 boxes

Carly Sold 70 boxes

6 0

1 year ago

The supplement of an angle is three times the measure of the angle.

stira [4]

Answer: The angle equals 45 ∘ and the supplement is 135 ∘

Explanation:

Since the supplement is three times the angle, we can say s = 3 a

Since we know the supplement is

180 − a , we can plug that in.

180 - a = 3a

180 = 4 a (add a to both sides)

45 = a (divide both sides by 4)

Since we know the angle now, all we have to do is multiply it times 3 to find the supplement.

45 × 3 = 135

4 0

2 years ago

Moshe has the container shown below on his desk to hold pencils and paper clips. 2 rectangular prisms. One has a length of 4 inc

iren2701 [21]

Answer:

2 inches by 3 inches by 6 inches and 2 inches by 2 inches by 4 inches

Step-by-step explanation:

7 0

2 years ago

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