When will the dependent variable in the equation Y=[(sqrt)(x+4-3)] equal or exceed 4?
• x ≥ –0.17
• x ≥ 45
• x ≥ 48
• x ≥ 53
Show how.
I suppose you mean
Y(x)=sqrt(x+4)-3
in which case you can evaluate the function for the various given values and see which one, if any, gives Y(x)=0.
I think this is the right way????
When will the dependent variable in the equation y= sqrt [x+4-3] equal or exceed 4
• x ≥ –0.17
• x ≥ 45
• x ≥ 48
• x ≥ 53
Not sure what your choice is, and also if the actual question should read:
Y(x)=sqrt(x+4)-3
or
Y(x)=sqrt(x+4-3) [as you had it]
Can you check if there is a typo?
To determine when the dependent variable (Y) in the equation Y = sqrt(x + 4 - 3) will equal or exceed 4, we need to solve the inequality.
Here's the step-by-step process:
1. Start with the given equation: Y = sqrt(x + 4 - 3).
2. Set Y ≥ 4 for the dependent variable to be equal to or exceed 4.
3. Write the inequality: sqrt(x + 4 - 3) ≥ 4.
4. Square both sides of the inequality to eliminate the square root: (sqrt(x + 4 - 3))^2 ≥ 4^2.
Simplifying, we get x + 4 - 3 ≥ 16.
5. Combine like terms: x + 1 ≥ 16.
6. Subtract 1 from both sides to isolate x: x ≥ 16 - 1.
7. Simplify: x ≥ 15.
Therefore, the solution to the inequality, x ≥ 15, indicates that the dependent variable (Y) in the equation will equal or exceed 4 when x is greater than or equal to 15.
Now, let's compare the given options to identify which one satisfies the inequality:
• x ≥ –0.17: This option does not satisfy the inequality x ≥ 15.
• x ≥ 45: This option satisfies the inequality x ≥ 15 since 45 is greater than 15.
• x ≥ 48: This option satisfies the inequality x ≥ 15 since 48 is greater than 15.
• x ≥ 53: This option satisfies the inequality x ≥ 15 since 53 is greater than 15.
Therefore, the correct answer is: x ≥ 15.