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

Answer 1

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 2

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 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: \[ \boxed{y = 10(0.13)^x} \]