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4 years ago

Which is the best definition of an exterior angle of a triangle?

Mathematics

2 answers:

Lunna [17]4 years ago

8 0

An angle that forms a linear pair with one of the interior angles of the triangle.

vodomira [7]4 years ago

4 0

The interior angle of a triangle is the angle made by two sides of this triangle and what is the little angle made by these two sides

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If U = {x: X € N, 1 < × < 15)

Inessa05 [86]

Answer:

Step-by-step explanation:

Given:

U = {x: X € N, 1 < × < 15) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A = {2,4,6,8,10,12,14}

B = {3,6,9,12,15}

C = {5,10,15}

(a) Verify A(BnB)=(AUB)(AUB)

A U (B n B)

= {2,4,6,8,10,12,14} U ( {3,6,9,12,15} n {3,6,9,12,15} )

= {2,4,6,8,10,12,14} U {3,6,9,12,15}

= {2,3,4,6,8,9,10,12,14,15}

( A U B) n (A U B)

= {2,3,4,6,8,9,10,12,14,15} n {2,3,4,6,8,9,10,12,14,15}

= {2,3,4,6,8,9,10,12,14,15}

Therefore

A U (B n B) = ( A U B) n (A U B)

verifies

(b) Verify An(BUC)=(AnB)u(AnC)

A n ( B U C)

= {2,4,6,8,10,12,14} n ( {3,6,9,12,15} U {5,10,15} )

= {2,4,6,8,10,12,14} n {3,5,6,9,10,12,15}

= {6,10,12}

( A n B ) U ( A n C )

= ( {2,4,6,8,10,12,14} n {3,6,9,12,15} ) U ( {2,4,6,8,10,12,14} n {5,10,15} )

= {6,12} U {10}

= {6,10,12}

Therefore

A n ( B U C) = ( A n B ) U ( A n C )

verifies

AU(BUC)

= {2,4,6,8,10,12,14}U{3,6,9,12,15}U{5,10,15}

= {2,3,4,5,6,8,9,10,12,14,15}

(AUB)U(AUC)

= ({2,4,6,8,10,12,14}{3,6,9,12,15})U({2,4,6,8,10,12,14}U{5,10,15})

= {2,3,4,6,8,9,10,12,14,15}U{2,4,5,6,8,10,12,14,15}

= {2,3,4,5,6,8,9,10,12,14,15}

Therefore

AU(BUC)=(AUB)U(AUC)

verifies

5 0

3 years ago

A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues,

EleoNora [17]

Answer:

7,692 moose.

Explanation:

The table that shows the pattern for this question is:

Time (year) Population

0 40

1 62

2 96

3 149

4 231

A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.

Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.

Thus you must find both P₀ and r.

1) P₀ 

Using the first term of the sequence (0, 40) you get:

P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀

Then, P₀ = 40

2) r

Take two consecutive terms of the sequence:

P(0) = 40 r⁰ = 40

P(1) = 40 r¹ = 40r = 62

P(1) / P(0) = 40r / 40 = 62/40

r = 62/40 = 1.55

You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55

3) Model

Thus, your model is P(x) = 40(1.55)ˣ

 4) Population of moose after 12 years

P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.

7 0

3 years ago

Amelia pays $24 to rent a boat at the lake for up to six hours she constructs the inequality and number line below to represent

liubo4ka [24]

Money= how many hours
$4= 1h
$8=2h
$12=3h
$16=4h
$20=5h
$24=6h
l hope that helps :)

5 0

3 years ago

I am stuck at this question

Marrrta [24]

Answer:

Step-by-step explanation:

B(2,10); D(6,2)

Midpoint(x1+x2/2, y1+y2/2) = M ( 2+6/2, 10+2/2) = M(8/2, 12/2) = M(4,6)

Rhombus all sides are equal.

AB = BC = CD =AD

distance = √(x2-x1)² + (y2- y1)²

As A lies on x-axis, it y-co ordinate = 0; Let its x-co ordinate be x

A(X,0)

AB = AD

√(2-x)² + (10-0)² = √(6-x)² + (2-0)²

√(2-x)² + (10)² = √(6-x)² + (2)²

√x² -4x +4 + 100 = √x²-12x+36 + 4

√x² -4x + 104 = √x²-12x+40

square both sides,

x² -4x + 104 = x²-12x+40

x² -4x - x²+ 12x = 40 - 104

8x = -64

x = -64/8

x = -8

A(-8,0)

Let C(a,b)

M is AC midpoint

(-8+a/2, 0 + b/2) = M(4,6)

(-8+a/2, b/2) = M(4,6)

Comparing;

-8+a/2 = 4 ; b/2 = 6

-8+a = 4*2 ; b = 6*2

-8+a = 8 ; b = 12

a = 8 +8

a = 16

Hence, C(16,12)

6 0

3 years ago

The pythagorean theorem equation

nikklg [1K]

A^2+b^2=c^2
Is the Pythagorean theorem

6 0

3 years ago

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