Explanation

Total work = 16 men × 10 days = 160 man-days
Time for 8 men = $frac{160}{8}$ = 20 days

Explanation

1 carton = 10 boxes × 12 cubes = 120 cubes
Total cartons needed = $\frac{\mathrm{<font\; color="\#ff0000">960</font>}}{\mathrm{<font\; color="\#ff0000">120</font>}}<font\; color="\#ff0000">=</font>\mathrm{<font\; color="\#ff0000">8</font><span\; style="font-family:\; Overpass,\; sans-serif;\; font-size:\; 0.875rem;"><br></span>}$

Explanation

Let income be $x$.
10% of $x$ = 1500
10/10​0×x=1500
$x=\frac{1500\times 100}{10}<br>$

​=15000

Explanation

To find the quotient, perform polynomial long division:

Divide 6n² + 5n + 12 by 2n + 3:

6n² + 5n + 12 | 2n + 3

First, divide 6n² by 2n:

3n

Multiply 2n + 3 by 3n:

6n² + 9n

Subtract this from the original polynomial:

-4n + 12

Now, divide -4n by 2n:

-2

Multiply 2n + 3 by -2:

-4n - 6

Subtract this from -4n + 12:

18

Since 18 is a constant and cannot be divided by 2n + 3, the remainder is 18.

The quotient is:

3n - 2

Explanation

To find the value of a² + b²:

Use the identity:

a² + b² = (a - b)² + 2ab

Given a - b = 3 and ab = 5:

a² + b² = (3)² + 2(5)

= 9 + 10

= 19

Explanation

Explanation

Explanation

When multiplying matrices, the order of the resulting matrix is determined by the rows of the first matrix (A) and columns of the second matrix (B).

Since A is 2×3 and B is 3×1, the resulting matrix AB will be of order 2×1.

Explanation

Altitude is the shortest perpendicular distance from the base to the opposite vertex in a geometric figure (such as a triangle).

Median, on the other hand, is a line segment joining a vertex to the midpoint of the opposite side.

Explanation