Answer:
27
Step-by-step explanation:
If set A has 3 elements then number of elements in A*A*A is 27
x and x+4 are the numbers
3x=2(x+4)
3x=2x+8
3x-2x=8
x=8
x+4=12
Answer:
see explanation
Step-by-step explanation:
The perimeter is the sum of the 3 sides of the triangle.
Sum the sides and equate to 54, that is
3x + 4x + 5x = 54, that is
12x = 54 ( divide both sides by 12 )
x = 4.5
Thus
AB = 3x = 3 × 4.5 = 13.5 in
BC = 4x = 4 × 4.5 = 18 in
AC = 5x = 5 × 4.5 = 22.5 in
Answer:
Step-by-step explanation:
We are given that:
First term (a) = 5
common ratio (r) =
The nth term of a geometric sequence is given as:
Answer:
a). m∠AED = 70°
b). x = 10°
Step-by-step explanation:
a). Quadrilateral ABDE is a cyclic quadrilateral.
Therefore, by the theorem of cyclic quadrilateral,
Sum of either pair of opposite angle is 180°
m(∠AED) + m(∠ABD) = 180°
m(∠AED) = 180° - 110°
m(∠AED) = 70°
Since, ∠AED ≅ ∠EAD
Therefore, m∠AED = m∠EAD = 70°
b). By triangle sum theorem in ΔABD,
m∠ABD + m∠BDA + m∠DAB = 180°
110° + 40° + m∠DAB = 180°
m∠DAB = 180° - 150°
m∠DAB = 30°
m∠BAE = m∠EAD + m∠BAD
= 70° + 30° = 100°
By angle sum theorem in ΔACE,
m∠EAC + m∠AEC + m∠ACE = 180°
100° + 70° + x° = 180°
x = 180° - 170°
x = 10°
