N; n+1; n+2 - 3 consecutive numbers
n(n + 1) = (n + 2)² - 19 |use a(b + c) = ab + ac and (a + b)² = a² + 2ab + b²
n² + n = n² + 4n + 4 - 19 |subtract n² from both sides
n = 4n - 15 |subtract 4n from both sides
-3n = -15 |divide both sides by (-3)
n = 5
n + 1 = 5 + 1 = 6
n + 2 = 5 + 2 = 7
Answer: 5; 6; 7.
Answer:
2 hours
Step-by-step explanation:
Train B's speed: 4/3 × 60 = 80
Combined speed = 80 + 60 = 120
Time = 240/120 = 2
Answer:
8
Step-by-step explanation:
10x-2x=8x
60+4=64
8x=64
x=8
Answer:
Step-by-step explanation:
In the given figure, PQRS is a rhombus and SRM is an equilateral triangle.
We are also given that SN⊥RM and that ∠PRS = 55°.
And we want to find the measure of ∠QSN.
Remember that since PQRS is a rhombus, the angles formed by its diagonals are right angles. Let the intersection point of the diagonals be K. Therefore:
Now, RKS is also a triangle. The interior angles of all triangles must be 180. Thus:
Substitute in known values:
Solve for ∠KSR:
Since SRM is an equilateral triangle, this means that:
Note that RNS is also a triangle. Therefore:
Substitute in known values:
So:
∠QSN is the addition of the two angles:
Therefore:
Answer:
5
Step-by-step explanation: