Emily went to the movie theater for her birthday. A mix of adults and children attended, making a total of 22 people. Each adult
1 answer:
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Answer:
a)
b)
c)
Step-by-step explanation:
Given the curve
a) If the x-coordinate of P is , then the y-coordinate is
so point P has coordinates
If the x-coordinate of Q is , then the y-coordinate is
so point Q has coordinates
b) The gradient of the secant RQ is
c) If then the gradient
Answer:
The perimeter of the kite JKLM is 50 units ⇒ C
Step-by-step explanation:
The longest diagonal of the kite is its axis of symmetry which means the longest diagonal divides the kite into two congruent triangles
∵ JKLM is a kite
∵ KM is the longest diagonal
∴ KM is divides the kite into two congruent triangles
∴ Δ JKM is congruent to Δ LKM
∴ JK = LK
∴ JM = ML
∵ ML = 10 units
∴ JM = 10 units
∵ The diagonals of the kite are perpendicular
∴ KM ⊥ JL
∵ KM and JL intersected at N
∴ m∠JNK = 90°
∵ KM is the axis of symmetry of kite JKLM
∴ KM bisects JL at N
∴ JN = NL = JL
∵ JL = 18 units
∴ JN = (18)
∴ JN = 9 units
In Δ JNK
∵ m∠JNK = 90°
∵ JN = 9 units
∵ NK = 12 units
- By using Pythagoras Theorem
∵ (JK)² = (JN)² + (NK)²
∴ (JK)² = (9)² + (12)²
∴ (JK)² = 81 + 144
∴ (JK)² = 225
- Take √ for both sides
∴ JK = 15 units
∵ Jk = LK
∴ Lk = 15 units
∵ The perimeter of the kite is the sum of its 4 sides
∴ P = JK + KL + LM + MJ
∵ JK = LK = 15
∵ JM = ML = 10
∴ P = 15 + 15 + 10 + 10
∴ P = 50
The perimeter of the kite JKLM is 50 units
Answer: 22 kph
<u>Step-by-step explanation:</u>
distance (d) = rate (r) x time (t)
UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t
DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t
*x is the speed in still water and y is the current of the water.
Upstream equation: 5 = 2t(x - 2) -->
Downstream equation: 3 = t(x + 2) -->
Set the equations equal to each other to solve for x: