Question

which expression is equivalent to (3a+7) (2a-5)

Answer 1

Which equation represents exponential decay?

y=1/100(31)^x

y=1/10(3.1)^x

y=10(0.13)^x

y=100(1.03)^x

Answer 2

To find the expression equivalent to \((3a + 7)(2a - 5)\), we can use the distributive property (also known as the FOIL method for binomials).

1. **First**: Multiply the first terms in each binomial.
\[
3a \times 2a = 6a^2
\]

2. **Outer**: Multiply the outer terms.
\[
3a \times -5 = -15a
\]

3. **Inner**: Multiply the inner terms.
\[
7 \times 2a = 14a
\]

4. **Last**: Multiply the last terms.
\[
7 \times -5 = -35
\]

Now, combine all these results:
\[
6a^2 - 15a + 14a - 35
\]

Combine the like terms \(-15a\) and \(14a\):
\[
6a^2 - 15a + 14a = 6a^2 - a
\]

So, the expression simplifies to:
\[
\boxed{6a^2 - a - 35}
\]

Answer 3

In exponential functions, exponential decay occurs when the base of the exponent is between 0 and 1.

Let's analyze each of the equations you provided:

1. **\(y = \frac{1}{100}(31)^x\)**: The base is 31, which is greater than 1. This represents exponential growth.

2. **\(y = \frac{1}{10}(3.1)^x\)**: The base is 3.1, which is also greater than 1. This represents exponential growth as well.

3. **\(y = 10(0.13)^x\)**: The base is 0.13, which is between 0 and 1. This represents exponential decay.

4. **\(y = 100(1.03)^x\)**: The base is 1.03, which is greater than 1. This represents exponential growth.

Thus, the equation that represents exponential decay is:
\[
\boxed{y = 10(0.13)^x}
\]