Explanation

Let's denote the son's current age as x. Then the father's current age is 13x.

After 4 years:

Son's age = x + 4

Father's age = 13x + 4

According to the problem, after 4 years, the father's age will be 5 times the son's age:

13x + 4 = 5(x + 4)

13x + 4 = 5x + 20

8x = 16

x = 2

So, the father's current age is 13x = 13 * 2 = 26.

Explanation

0 is called additive identity because a + 0 = a for any number 'a'.

It does not change the value of a number when added.

Explanation

To convert (10101)₂ to decimal: = 1×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰

= 16 + 0 + 4 + 0 + 1

= 21

Explanation

(n - 2)180° formula calculates the sum of all internal angles of an n-sided polygon.

It works because any polygon can be divided into (n - 2) triangles.

Explanation

Given A = [a b; b a] and A² = [l m; ...], let's calculate A²:

A² = [a b; b a] * [a b; b a]

= [a² + b² 2ab; 2ab a² + b²]

Comparing A² = [l m; ...] with our calculation:

l = a² + b²

m = 2ab

The correct answer is l = a² + b², m = 2ab.

Explanation

Let's simplify the expression:

log6 25 − 2 log6 5 + log6 a

Since 25 = 5^2:

log6 25 = log6 (5^2) = 2 log6 5

So, the expression becomes:

2 log6 5 - 2 log6 5 + log6 a

= log6 a

If this expression equals 0 (assuming that's the goal):

log6 a = 0

This implies:

a = 6^0

a = 1

Explanation

To find the distance traveled by the rider, we need to calculate the arc length:

Given:

Radius (r) = 49 meters

Angle (θ) = 150°

First, convert the angle to radians:

θ = 150° * (π / 180)

= 150 * π / 180

= 5π/6 radians

Now, calculate the arc length (s):

s = r * θ

= 49 * (5π/6)

= 49 * 5 * 3.14159 / 6

≈ 128.33 meters

Explanation

Given:

Z1 = 2 - i

Z2 = 3 + i

Product of Z1 and Z2:

Z1 * Z2 = (2 - i) * (3 + i)

= 6 + 2i - 3i - i²

Since i² = -1,

= 6 - i + 1

= 7 - i

Explanation

A sphere is a 3D (three-dimensional) shape because it has depth, along with height and width.

Circle, rectangle, and triangle are 2D (two-dimensional) shapes as they have only length and width.

Explanation

A chord is a line segment that connects two points on a circle.

If the chord passes through the center, it is called the diameter.