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

Multiply the constants: 3 × 4 = 12.

Add the exponents of x: x² × x³ = x⁵, so the product is 12x⁵.

Explanation

Solve the equation: 2x + 3 = 9 → 2x = 6 → x = 3.

The value of x = 3 satisfies the equation.

Explanation

Given 2x - 6 = 0:

2x = 6

x = 6/2 = 3

Explanation

Given x³ = 64:

x = ∛64 = 4 (since 4³ = 64)

The question seems to be asking for the value of x.

The correct answer is 4.

Explanation

To evaluate the expression 3x + 6y + 4x, we need to combine like terms:

3x + 6y + 4x = (3x + 4x) + 6y

= 7x + 6y

So, the correct result is 7x + 6y.

Explanation

Given log(x) - 2log(y):

Using logarithmic properties:

log(x) - 2log(y) = log(x) - log(y^2) = log(x/y^2)

Explanation

Let's check each equation by plugging in a = -5:

(3/5)a + 19 = 16

→ (3/5)(-5) + 19 = -3 + 19 = 16 → True

So, the equation (3/5)a + 19 = 16 has a solution of a = -5

Explanation

Given the matrix:

[4 -9]

[-1 2]

The determinant is calculated as:

(4 * 2) - (-9 * -1)

= 8 - 9

= -1

Explanation

A binomial expression contains exactly two terms, and x² + y² fits that definition.

x²y² is a monomial (single term).

x + y + 1 is a trinomial (three terms).