Question 14 Find all $$ x $$ - and $$ y $$-intercepts. Answers in nondecimal, Change of Base, and round 3 decimals. $$ \begin{array}{l}y=7 \sqrt{x-5}-7 \ ext { Use the editor to format your answer }\end{array} $$ Und

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Question 14 Find all $$ x $$ - and $$ y $$-intercepts. Answers in nondecimal, Change of Base, and round 3 decimals. $$ \begin{array}{l}y=7 \sqrt{x-5}-7 \ 	ext { Use the editor to format your answer }\end{array} $$ Und

UpStudy AI · Accepted Answer

To find the $$ x $$- and $$ y $$-intercepts of the function $$ y = 7 \sqrt{x - 5} - 7 $$, we will follow these steps:

### Finding the $$ y $$-intercept:
The $$ y $$-intercept occurs when $$ x = 0 $$.

Substituting $$ x = 0 $$ into the equation:
$$
y = 7 \sqrt{0 - 5} - 7
$$
Since $$ \sqrt{-5} $$ is not a real number, there is no $$ y $$-intercept for this function.

### Finding the $$ x $$-intercept:
The $$ x $$-intercept occurs when $$ y = 0 $$.

Setting $$ y = 0 $$:
$$
0 = 7 \sqrt{x - 5} - 7
$$
Adding 7 to both sides:
$$
7 = 7 \sqrt{x - 5}
$$
Dividing both sides by 7:
$$
1 = \sqrt{x - 5}
$$
Squaring both sides:
$$
1^2 = x - 5
$$
$$
1 = x - 5
$$
Adding 5 to both sides:
$$
x = 6
$$

### Summary of Intercepts:
- **$$ y $$-intercept**: None (no real value)
- **$$ x $$-intercept**: $$ (6, 0) $$

### Final Answer:
- $$ y $$-intercept: None
- $$ x $$-intercept: $$ (6, 0) $$

In non-decimal form, the intercepts are:
- $$ y $$-intercept: None
- $$ x $$-intercept: $$ (6, 0) $$

In Change of Base (not applicable here since we are not dealing with logarithms), and rounding to three decimals is also not applicable since we have exact values.

Thus, the final answer remains:
- $$ y $$-intercept: None
- $$ x $$-intercept: $$ (6, 0) $$
y-intercept: None, x-intercept: (6, 0)

Question 14
Find all - and -intercepts. Answers in nondecimal, Change of Base, and round 3 decimals.

Und

Solución de inteligencia artificial de Upstudy

Responder

Solución

Finding the -intercept:

Finding the -intercept:

Summary of Intercepts:

Final Answer:

Mind Expander

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Latest Algebra Questions

Question 14 Find all - and -intercepts. Answers in nondecimal, Change of Base, and round 3 decimals. Und

Solución de inteligencia artificial de Upstudy

Responder

Solución

Finding the -intercept:

Finding the -intercept:

Summary of Intercepts:

Final Answer:

Mind Expander

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Question 14
Find all - and -intercepts. Answers in nondecimal, Change of Base, and round 3 decimals.

Und