Explanation

Perimeter formula for a rectangle: 2 × (Length + Width)

2 × (210 + 118) = 2 × 328 = 656 cm

Explanation

To find the product of x^a and x^b:

x^a × x^b

Using the rule of exponents that states when multiplying two powers with the same base, add the exponents:

x^(a + b)

Explanation

Let's solve the equation x/2 - x/3 = 8.

To do this, find a common denominator for the fractions, which is 6.

This gives us (3x - 2x)/6 = 8, simplifying to x/6 = 8.

Multiplying both sides by 6 gives x = 48.

So, the solution is x = 48.

Explanation

To convert millimeters (mL) to liters (L), we divide by 1000 since 1 L = 1000 mL.

Quantity in liters = 1.7 mL / 1000

= 0.0017 L

Explanation

Given:

Area = 42 cm² (assuming the unit is consistent, but it's given as m² which seems incorrect given the base lengths are in cm. Let's proceed with cm² for calculation purposes)

Bases:

a = 5.6 cm

b = 2.9 cm

Formula:

Area = ((a + b) / 2) × height

42 = ((5.6 + 2.9) / 2) × height

42 = (8.5 / 2) × height

42 = 4.25 × height

height = 42 / 4.25

height = 9.88 cm

Explanation

L = length, W = width

Perimeter = 2(L + W) = 34 cm

If length increases by 2.5 cm:

New perimeter = 2(L + 2.5 + W)

= 2L + 5 + 2W

= 2(L + W) + 5

= 34 + 5

= 39 cm

Difference in perimeter = 39 - 34 = 5 cm

Explanation

A singleton set has only one element (e.g., {a}).

The only proper subset is the empty set (∅), so it has one proper subset.

Explanation

For the multiplication of two matrices A (size m x p) and B (size p x n), the resulting matrix AB will have dimensions m x n.

The number of rows of A and the number of columns of B determine the dimensions of the product matrix.

Explanation

A histogram is a type of vertical bar graph used to represent frequency distributions, where the bars touch each other to indicate continuous data.

Unlike bar graphs, histograms do not have space between the bars, reflecting intervals of data.

Explanation

10 is a multiple of itself because any number is a multiple of itself.