Answer:
x = 3
Step-by-step explanation:
7(x + 1) + 2 = 5x + 15
~Simplify left side
7x + 7 + 2 = 5x + 15
~Combine like terms
7x + 9 = 5x + 15
~Subtract 9 to both sides
7x = 5x + 6
~Subtract 5x to both sides
2x = 6
~Divide 2 to both sides
x = 3
Best of Luck!
Answer:
Options (C)
Step-by-step explanation:
For the congruence of the triangles ΔADB and ΔADC,
Statements Reasons
1). AB ≅ AC 1). Given
2). AD ≅ AD 2). Reflexive property
3). ∠BAD ≅ ∠CAD 3). Given
4). ΔABD ≅ ΔCAD 4). SAS postulate
Therefore, Options (C) will be the correct option.
Answer:
y - (-7) = 4/5(x - 9)
y + 7 = 4/5 ( x - 9)
Step-by-step explanation:
those are
the answers
Assuming a d-heap means the order of the tree representing the heap is d.
Most of the computer applications use binary trees, so they are 2-heaps.
A heap is a complete tree where each level is filled (complete) except the last one (leaves) which may or may not be filled.
The height of the heap is the number of levels. Hence the height of a binary tree is Ceiling(log_2(n)), for example, for 48 elements, log_2(48)=5.58.
Ceiling(5.58)=6. Thus a binary tree of 6 levels contains from 2^5+1=33 to 2^6=64 elements, and 48 is one of the possibilities. So the height of a binary-heap with 48 elements is 6.
Similarly, for a d-heap, the height is ceiling(log_d(n)).
Answer:
m<N = 76°
Step-by-step explanation:
Given:
∆JKL and ∆MNL are isosceles ∆ (isosceles ∆ has 2 equal sides).
m<J = 64° (given)
Required:
m<N
SOLUTION:
m<K = m<J (base angles of an isosceles ∆ are equal)
m<K = 64° (Substitution)
m<K + m<J + m<JLK = 180° (sum of ∆)
64° + 64° + m<JLK = 180° (substitution)
128° + m<JLK = 180°
subtract 128 from each side
m<JLK = 180° - 128°
m<JLK = 52°
In isosceles ∆MNL, m<MLN and <M are base angles of the ∆. Therefore, they are of equal measure.
Thus:
m<MLN = m<JKL (vertical angles are congruent)
m<MLN = 52°
m<M = m<MLN (base angles of isosceles ∆MNL)
m<M = 52° (substitution)
m<N + m<M° + m<MLN = 180° (Sum of ∆)
m<N + 52° + 52° = 180° (Substitution)
m<N + 104° = 180°
subtract 104 from each side
m<N = 180° - 104°
m<N = 76°
