#17. Given fx= 1 23−x2, what is the value of f(15)?
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can you write the anwser in actual symbols please?
i dont under the answer. can you example what are ther symbols because i need to copy this for my answer
18. Suppose you are a solving a quadratic equation using the quadratic formula and this is your work so far: 2x2+7x−15=0 x= −7 ±72−42−15 22 x= −7 ±??? 4👈 What number goes in place of ???
so what the answer
are you sure?
Answered by
GPT-4o
To find the value of \( f(15) \) for the given function \( f(x) = \frac{1}{2} \cdot 3^{-x^2} \):
1. Substitute \( x = 15 \) into the function:
\[
f(15) = \frac{1}{2} \cdot 3^{-15^2}
\]
2. Calculate \( 15^2 \):
\[
15^2 = 225
\]
3. Substitute \( 225 \) for \( x^2 \) in the exponent:
\[
f(15) = \frac{1}{2} \cdot 3^{-225}
\]
4. Simplify the expression:
\[
f(15) = \frac{1}{2} \cdot \frac{1}{3^{225}} = \frac{1}{2 \cdot 3^{225}}
\]
Therefore, the value of \( f(15) \) is:
\[
f(15) = \frac{1}{2 \cdot 3^{225}}
\]
1. Substitute \( x = 15 \) into the function:
\[
f(15) = \frac{1}{2} \cdot 3^{-15^2}
\]
2. Calculate \( 15^2 \):
\[
15^2 = 225
\]
3. Substitute \( 225 \) for \( x^2 \) in the exponent:
\[
f(15) = \frac{1}{2} \cdot 3^{-225}
\]
4. Simplify the expression:
\[
f(15) = \frac{1}{2} \cdot \frac{1}{3^{225}} = \frac{1}{2 \cdot 3^{225}}
\]
Therefore, the value of \( f(15) \) is:
\[
f(15) = \frac{1}{2 \cdot 3^{225}}
\]
Answered by
GPT-4o
Sure! The value of \( f(15) \) given the function \( f(x) = \frac{1}{2} \cdot 3^{-x^2} \) can be written as:
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Answered by
GPT-4o
Of course! Let's break it down step-by-step using the symbols to clarify:
Given the function:
\[ f(x) = \frac{1}{2} \cdot 3^{-x^2} \]
To find \( f(15) \), follow these steps:
1. **Substitute \( x = 15 \) into the function.**
\[ f(15) = \frac{1}{2} \cdot 3^{-15^2} \]
2. **Calculate \( 15^2 \):**
\[ 15^2 = 225 \]
3. **Substitute \( 225 \) into the exponent:**
\[ f(15) = \frac{1}{2} \cdot 3^{-225} \]
4. **Combine the terms:**
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
The answer in symbols is:
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Explanation of the symbols:
- \( \frac{1}{2} \) represents one half.
- \( 3^{-x^2} \) indicates 3 raised to the power of negative \( x^2 \).
- \( 15^2 \) means 15 squared, which equals 225.
- \( 3^{-225} \) means 3 raised to the power of negative 225.
- By multiplying \( \frac{1}{2} \) with \( 3^{-225} \), we get \( \frac{1}{2 \cdot 3^{225}} \).
This fraction is your final answer.
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Given the function:
\[ f(x) = \frac{1}{2} \cdot 3^{-x^2} \]
To find \( f(15) \), follow these steps:
1. **Substitute \( x = 15 \) into the function.**
\[ f(15) = \frac{1}{2} \cdot 3^{-15^2} \]
2. **Calculate \( 15^2 \):**
\[ 15^2 = 225 \]
3. **Substitute \( 225 \) into the exponent:**
\[ f(15) = \frac{1}{2} \cdot 3^{-225} \]
4. **Combine the terms:**
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
The answer in symbols is:
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Explanation of the symbols:
- \( \frac{1}{2} \) represents one half.
- \( 3^{-x^2} \) indicates 3 raised to the power of negative \( x^2 \).
- \( 15^2 \) means 15 squared, which equals 225.
- \( 3^{-225} \) means 3 raised to the power of negative 225.
- By multiplying \( \frac{1}{2} \) with \( 3^{-225} \), we get \( \frac{1}{2 \cdot 3^{225}} \).
This fraction is your final answer.
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Answered by
GPT-4o
To determine the number that goes in place of "???" in the given quadratic formula setup, we need to use the quadratic formula correctly.
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given the quadratic equation:
\[ 2x^2 + 7x - 15 = 0 \]
where \( a = 2 \), \( b = 7 \), and \( c = -15 \).
I'll show each step in detail:
1. **Identify \( a \), \( b \), and \( c \):**
- \( a = 2 \)
- \( b = 7 \)
- \( c = -15 \)
2. **Plug in the values into the quadratic formula:**
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
4. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
5. **Substitute back into the quadratic formula:**
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that goes in place of "???" is \( 13 \).
So the complete formula should look like this:
\[ x = \frac{-7 \pm 13}{4} \]
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given the quadratic equation:
\[ 2x^2 + 7x - 15 = 0 \]
where \( a = 2 \), \( b = 7 \), and \( c = -15 \).
I'll show each step in detail:
1. **Identify \( a \), \( b \), and \( c \):**
- \( a = 2 \)
- \( b = 7 \)
- \( c = -15 \)
2. **Plug in the values into the quadratic formula:**
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
4. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
5. **Substitute back into the quadratic formula:**
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that goes in place of "???" is \( 13 \).
So the complete formula should look like this:
\[ x = \frac{-7 \pm 13}{4} \]
Answered by
GPT-4o
The number that goes in place of "???" is \( 13 \).
So, completing your quadratic formula setup correctly gives:
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the missing number (indicated by "???") is:
\[ 13 \]
So, completing your quadratic formula setup correctly gives:
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the missing number (indicated by "???") is:
\[ 13 \]
Answered by
GPT-4o
Let's re-check the steps to be absolutely certain.
The quadratic equation given is:
\[ 2x^2 + 7x - 15 = 0 \]
Using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given values:
\[ a = 2 \]
\[ b = 7 \]
\[ c = -15 \]
1. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - 4 \cdot 2 \cdot (-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
2. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
So, substituting this back into the quadratic formula,
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that replaces "???" is indeed:
\[ 13 \]
Thus, the correct answer is:
\[ x = \frac{-7 \pm 13}{4} \]
The quadratic equation given is:
\[ 2x^2 + 7x - 15 = 0 \]
Using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given values:
\[ a = 2 \]
\[ b = 7 \]
\[ c = -15 \]
1. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - 4 \cdot 2 \cdot (-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
2. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
So, substituting this back into the quadratic formula,
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that replaces "???" is indeed:
\[ 13 \]
Thus, the correct answer is:
\[ x = \frac{-7 \pm 13}{4} \]
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