## Respuesta :

Given:

7x +2y +3z =42

I assumed that the format in the given choices is (x,y,z). So, I substituted each number to its corresponding variable.

A. (14,0,0) → 7(14) +2(0) +3(0) = 42 → 98 + 0 + 0 ≠ 42 NOT THE ANSWER

B. (7,0,0) → 7(7) +2(0) +3(0) = 42 → 49 + 0 + 0 ≠ 42 NOT THE ANSWER

C. (21,0,0) → 7(21) +2(0) +3(0) = 42 → 147 + 0 + 0 ≠ 42 NOT THE ANSWER

D. (6,0,0) → 7(6) +2(0) +3(0) = 42 → 42 + 0 + 0 = 42 CORRECT ANSWER.

The ordered triples indicated where the plane cuts the x-axis for this equation is D. (6,0,0).

**Answer:**

**Option D is correct.**

**Step-by-step explanation:**

Given Equation of plane is 7x + 2y + 3z = 42

We need to find ordered triplet where plane cuts the x-axis.

To find point of x-axis when plane cuts it. we put other coordinates equal to 0.

So, put y = 0 and z = 0 in equation plance to get x-coordinate of the required ordered triplet.

7x + 2 × 0 + 3 × 0 = 42

7x + 0 + 0 = 42

7x = 42

[tex]x=\frac{42}{7}[/tex]

x = 6

⇒ ordered triplet = ( 6 , 0 , 0 )

Therefore, **Option D is correct.**