Explanation:
We can rewrite the expression:
√8×√20
using the following rule for radicals:
√a⋅√b=√a⋅b
√8⋅√20⇒√8⋅20⇒√160
Now, we can use this rule for radicals to simplify the radical:
√a⋅b=√a⋅√b
√160⇒√16⋅10⇒√16⋅√10⇒4√10
Answer:
length of side = 10x + 3
Step-by-step explanation:
The area of a square = s² ( s is the length of the side )
given
A = 100x² + 60x + 9 ← perfect square in the form
(a + b)² = a² + 2ab + b²
100x² = (10x)² ⇒ a = 10x
9 = 3² ⇒ b = 3
and 2ab = 2 × 10x × 3 = 60x, hence
100x² + 60x + 9 = (10x + 3)²
s = 
= 10x + 3 ← length of side
Answer: the number of boats that are in the marina is 105.
Step-by-step explanation:
Let x represent the number of boats that are in the marina.
Two-thirds of the boats in the marina are white. It means that the number of white boats in the marina is
2/3 × x = 2x/3
The remaining number of boats will be
x - 2x/3 = x/3
4/7 of the remaining boats are blue. It means that the number of boats that are blue is
4/7 × x/3 = 4x/21
The number of boats left would be
x/3 - 4x/21 = 3x/21
If there are 15 red boats, it means that
3x/21 = 15
3x = 21 × 15 = 315
x = 315/3
x = 105
Answer:
Option (a).
Step-by-step explanation:
It is given that 3n is an odd number.
We need to find an even number from the given options.
Even numbers: Which are divisible by 2.
Odd numbers: Which are not divisible by 2.
We need know that the numbers are alternatively even and odd.
If we add or subtract 1 from an odd number, we always get an even number.
If we add or subtract 2 from an odd number, we always get an odd number.
3n is an odd number. So,
3n-1 is an odd number.
3n+2 is an even number.
3n+2 is an even number.
3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.
Therefore, the correct option is (a).
