Explanation

The greatest 3-digit number is 999, and the smallest 3-digit number is 100.

Their product: 999 × 100 = 99900.

Explanation

1 kilometer equals 10 hectometers. 

1 kilometer (km) = 1000 meters

1 hectometer (hm) = 100 meters

Therefore, 1 km = 1000 meters / 100 meters/hm = 10 hectometers

Explanation

Pie chart represents data using sectors of a circle, where each sector shows a proportion of the whole.

It is commonly used for percentage or proportional comparisons in statistics.

Explanation

Any nonzero number raised to the zero power is:

1

This is a fundamental property of exponents:

a⁰ = 1 (where a ≠ 0)

Explanation

To solve the equation:

75 - 9t = 5(-4 + 2t)

Expand the right-hand side:

75 - 9t = -20 + 10t

Add 9t to both sides:

75 = -20 + 19t

Add 20 to both sides:

95 = 19t

Divide by 19:

t = 95/19

t = 5

Explanation

To solve the system of equations:

x - y = 5 ... (1)

2x + y = 1 ... (2)

Multiply equation (1) by 1 and equation (2) by 1:

x - y = 5

2x + y = 1

Add both equations:

3x = 6

Divide by 3:

x = 2

Substitute x into equation (1):

2 - y = 5

Subtract 2 from both sides:

-y = 3

Multiply by -1:

y = -3

The solution is:

{(2, -3)}

Explanation

Since the point is on the x-axis, its coordinates are (x, 0).

To find the point equidistant from (0, 1) and (3, 1), set up the equation:

√((x - 0)² + (0 - 1)²) = √((x - 3)² + (0 - 1)²)

Simplify the equation:

√(x² + 1) = √((x - 3)² + 1)

Square both sides:

x² + 1 = (x - 3)² + 1

Expand and simplify:

x² = x² - 6x + 9

Subtract x² from both sides:

0 = -6x + 9

Add 6x to both sides:

6x = 9

Divide by 6:

x = 9/6

x = 1.5

So, the point on the x-axis is:

(1.5, 0)

Explanation

The incentre is the point where the internal angle bisectors of a triangle intersect.

It is the center of the incircle, which is the largest circle that fits inside the triangle.

Explanation

Convert minutes to decimal: 15' ÷ 60 = 0.25

Convert seconds to decimal: 36" ÷ 3600 = 0.01

Add to degrees: 8 + 0.25 + 0.01 = 8.26

Explanation

To find the remainder when 2x² + 1 is divided by x - 1:

Use the Remainder Theorem:

Remainder = f(a), where a is the root of the divisor (x - 1 = 0)

a = 1

Substitute a into the polynomial:

Remainder = f(1)

= 2(1)² + 1

= 2 + 1

= 3