Teresa be1ro 5/16123 What Is the Title of This Picture ? Solve ... - Free Printable

Let’s solve each quadratic equation by factoring (as the objective says: “solve quadratic equations by factoring”) and match the solution set to the letter in the answer bank. Then we’ll decode the coded title.

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Equation 1:

a² + 7a + 10 = 0
Factor: (a + 5)(a + 2) = 0 → a = -5, -2
→ Solution set: {-5, -2} → Matches I

✔ So, #1 → I

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Equation 2:

n² - 8n + 12 = 0
Factor: (n - 6)(n - 2) = 0 → n = 6, 2
→ Solution set: {6, 2} → Matches D

✔ #2 → D

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Equation 3:

y² - 49 = 0
Difference of squares: (y - 7)(y + 7) = 0 → y = 7, -7
→ Solution set: {7, -7} → Matches O

✔ #3 → O

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Equation 4:

x² + 5x - 6 = 0
Factor: (x + 6)(x - 1) = 0 → x = -6, 1
→ Solution set: {-6, 1} → Matches Y

✔ #4 → Y

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Equation 5:

u² - 7u - 18 = 0
Factor: (u - 9)(u + 2) = 0 → u = 9, -2
→ Solution set: {-2, 9} → Matches L

✔ #5 → L

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Equation 6:

m² - 5m = 0
Factor: m(m - 5) = 0 → m = 0, 5
→ Solution set: {0, 5} → Matches S

✔ #6 → S

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Equation 7:

2t² + 5t - 3 = 0
Multiply 2*(-3) = -6; find factors of -6 that add to 5 → 6 and -1
Split middle term: 2t² + 6t - t - 3 = 0
→ 2t(t + 3) -1(t + 3) = 0 → (2t - 1)(t + 3) = 0
→ t = 1/2, -3
→ Solution set: {1/2, -3} → Matches J

✔ #7 → J

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Equation 8:

3w² - 8w + 4 = 0
Multiply 3*4=12; factors of 12 that add to -8 → -6 and -2
Split: 3w² - 6w - 2w + 4 = 0
→ 3w(w - 2) -2(w - 2) = 0 → (3w - 2)(w - 2) = 0
→ w = 2/3, 2
→ Solution set: {2/3, 2} → Matches R

✔ #8 → R

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Equation 9:

2x² - 3x - 5 = 0
Multiply 2*(-5) = -10; factors of -10 adding to -3 → -5 and 2
Split: 2x² - 5x + 2x - 5 = 0
→ x(2x - 5) + 1(2x - 5) = 0 → (x + 1)(2x - 5) = 0
→ x = -1, 5/2
→ Solution set: {5/2, -1} → Matches B

✔ #9 → B

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Equation 10:

5v² + 29v + 20 = 0
Multiply 5*20=100; factors of 100 adding to 29 → 25 and 4
Split: 5v² + 25v + 4v + 20 = 0
→ 5v(v + 5) + 4(v + 5) = 0 → (5v + 4)(v + 5) = 0
→ v = -4/5, -5
→ Solution set: {-4/5, -5} → Matches F

✔ #10 → F

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Equation 11:

6n² - 19n + 15 = 0
Multiply 6*15=90; factors of 90 adding to -19 → -10 and -9
Split: 6n² - 10n - 9n + 15 = 0
→ 2n(3n - 5) -3(3n - 5) = 0 → (2n - 3)(3n - 5) = 0
→ n = 3/2, 5/3
→ Solution set: {3/2, 5/3} → Matches A

✔ #11 → A

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Equation 12:

2k² + 7k = 0
Factor: k(2k + 7) = 0 → k = 0, -7/2
→ Solution set: {0, -7/2} → Matches E

✔ #12 → E

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Equation 13:

3b² + b - 10 = 0
Multiply 3*(-10) = -30; factors of -30 adding to 1 → 6 and -5
Split: 3b² + 6b - 5b - 10 = 0
→ 3b(b + 2) -5(b + 2) = 0 → (3b - 5)(b + 2) = 0
→ b = 5/3, -2
→ Solution set: {5/3, -2} → Matches N

✔ #13 → N

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Equation 14:

4y² - 25 = 0
Difference of squares: (2y - 5)(2y + 5) = 0 → y = 5/2, -5/2
→ Solution set: {5/2, -5/2} → Matches T

✔ #14 → T

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## Now, let’s decode the “Coded Title”:

The coded title is given as:

> 14 12 13 13 1 6 9 11 5 5
> ( _ _ _ _ _ _ _ _ _ _ )

We replace each number with its corresponding letter:

- 14 → T
- 12 → E
- 13 → N
- 13 → N
- 1 → I
- 6 → S
- 9 → B
- 11 → A
- 5 → L
- 5 → L

So the decoded title is:
> T E N N I S B A L L

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## ✔ Final Answer:
TENNIS BALL

*(That matches the image — it’s a cube with curved lines resembling a tennis ball!)*