Explanation

"3x" usually represents 3 rectangles (each representing x).

"+2" typically means 2 small unit squares (each representing 1).

So, a model showing 3 long bars and 2 small squares matches 3x + 2.

Explanation

Explanation

Given the area of the rectangle:

x² - 5x + 6

Let's factorize the quadratic expression:

x² - 5x + 6 = x² - 3x - 2x + 6

= x(x - 3) - 2(x - 3)

= (x - 3)(x - 2)

Explanation

x² - xy + y²

= (-2)² - (-2)(2) + (2)²

= 4 + 4 + 4

= 12

Explanation

We know that 1/7 of x is 4:

(1/7)x = 4

To find x, multiply both sides by 7:

x = 4 × 7

x = 28

Now, find 1/4 of x:

(1/4)x = (1/4) × 28

= 7

Explanation

Thus, nth term = a+(n−1)

d=(p+q−1)+(n−1)×(−1)

d =(p+q−n)

Explanation

Given xy = 1 and x > 0:

y = 1/x

We want to minimize x + y = x + 1/x.

Let's find the minimum value:

Let f(x) = x + 1/x

f'(x) = 1 - 1/x² = 0 for minimum

x² = 1

x = 1 (since x > 0)

f(1) = 1 + 1/1 = 2

The minimum value of x + y is 2.

Explanation

Let the two consecutive odd numbers be x and x + 2.

Given x² + (x + 2)² = 394:

x² + x² + 4x + 4 = 394

2x² + 4x - 390 = 0

x² + 2x - 195 = 0

(x + 15)(x - 13) = 0

x = -15 or x = 13

For x = 13, the numbers are 13 and 15.

13² + 15² = 169 + 225 = 394

The sum of the numbers is 13 + 15 = 28.

Explanation

The absolute value | -12 | represents the distance of -12 from zero, which is always positive.

Therefore, | -12 | = 12.

Explanation

The orthocenter is the point where the three altitudes of a triangle intersect.

An altitude is a perpendicular line from a vertex to the opposite side (or its extension).