12. $$ \frac{e}{f^{2}-2 f+1} $$, for $$ e=-6 $$ and $$ f=5 $$ 13. $$ \frac{17-u^{2}}{v^{2}-4 v} $$, for $$ u=-3 $$ and $$ v=2 $$ 14. $$ \frac{-50}{2 x^{2}-3 x+5} $$, for $$ x=-1 $$ 15. $$ \frac{y^{3}-4 y+6}{3} $$, for $$ y=-2 $$

Question

UpStudy AI · Accepted Answer

Sure, let's evaluate each of the given expressions by substituting the provided values step-by-step.

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### **Problem 12**
$$ \frac{e}{f^{2} - 2f + 1} $$
**Given:** $$ e = -6 $$, $$ f = 5 $$

**Step 1: Calculate the denominator**
$$
f^{2} - 2f + 1 = (5)^{2} - 2(5) + 1 = 25 - 10 + 1 = 16
$$

**Step 2: Substitute the values into the expression**
$$
\frac{e}{f^{2} - 2f + 1} = \frac{-6}{16} = -\frac{3}{8}
$$

**Answer:** $$-\frac{3}{8}$$

---

### **Problem 13**
$$ \frac{17 - u^{2}}{v^{2} - 4v} $$
**Given:** $$ u = -3 $$, $$ v = 2 $$

**Step 1: Calculate the numerator**
$$
17 - u^{2} = 17 - (-3)^{2} = 17 - 9 = 8
$$

**Step 2: Calculate the denominator**
$$
v^{2} - 4v = (2)^{2} - 4(2) = 4 - 8 = -4
$$

**Step 3: Substitute the values into the expression**
$$
\frac{17 - u^{2}}{v^{2} - 4v} = \frac{8}{-4} = -2
$$

**Answer:** $$-2$$

---

### **Problem 14**
$$ \frac{-50}{2x^{2} - 3x + 5} $$
**Given:** $$ x = -1 $$

**Step 1: Calculate the denominator**
$$
2x^{2} - 3x + 5 = 2(-1)^{2} - 3(-1) + 5 = 2(1) + 3 + 5 = 2 + 3 + 5 = 10
$$

**Step 2: Substitute the values into the expression**
$$
\frac{-50}{2x^{2} - 3x + 5} = \frac{-50}{10} = -5
$$

**Answer:** $$-5$$

---

### **Problem 15**
$$ \frac{y^{3} - 4y + 6}{3} $$
**Given:** $$ y = -2 $$

**Step 1: Calculate the numerator**
$$
y^{3} - 4y + 6 = (-2)^{3} - 4(-2) + 6 = -8 + 8 + 6 = 6
$$

**Step 2: Substitute the values into the expression**
$$
\frac{y^{3} - 4y + 6}{3} = \frac{6}{3} = 2
$$

**Answer:** $$2$$

---

### **Summary of Answers**
12. $$-\frac{3}{8}$$  
13. $$-2$$  
14. $$-5$$  
15. $$2$$
12. $$-\frac{3}{8}$$ 13. $$-2$$ 14. $$-5$$ 15. $$2$$

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