6. If M is replaced by one of the following numbers, the product $$ (M-10)(M+14) $$ becomes a perfect square. A. 0 B. 12 C. 14 D. 16 E. 18

Question

UpStudy AI · Accepted Answer

To determine which value of $$ M $$ makes the expression $$ (M-10)(M+14) $$ a perfect square, we will evaluate the expression for each option provided.

1. **Substituting $$ M = 0 $$**:
   $$
   (0 - 10)(0 + 14) = (-10)(14) = -140
   $$
   This is not a perfect square.

2. **Substituting $$ M = 12 $$**:
   $$
   (12 - 10)(12 + 14) = (2)(26) = 52
   $$
   This is not a perfect square.

3. **Substituting $$ M = 14 $$**:
   $$
   (14 - 10)(14 + 14) = (4)(28) = 112
   $$
   This is not a perfect square.

4. **Substituting $$ M = 16 $$**:
   $$
   (16 - 10)(16 + 14) = (6)(30) = 180
   $$
   This is not a perfect square.

5. **Substituting $$ M = 18 $$**:
   $$
   (18 - 10)(18 + 14) = (8)(32) = 256
   $$
   This is a perfect square since $$ 256 = 16^2 $$.

Thus, the value of $$ M $$ that makes $$ (M-10)(M+14) $$ a perfect square is $$ \boxed{18} $$.
$$ M = 18 $$ makes $$ (M-10)(M+14) $$ a perfect square.

6. If M is replaced by one of the following numbers, the product \( (M-10)(M+14) \) becomes a perfect square. A. 0 B. 12 C. 14 D. 16 E. 18

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions