9 from Unit 2, Lesson 9 Noah orders an extra-large pizza. It costs $$ \$ 12.49 $$ for the pizza plus $$ \$ 1.50 $$ for each topping. He orders an extra-large pizza with $$ t $$ toppings that costs a total of $$ d $$ dollars. Select all of the equations that represent the relationship between the number of toppings $$ t $$ and total cost $$ d $$ of the pizza with $$ t $$ toppings. A. $$ 12.49+t=d $$ B. $$ 12.49+1.50 t=d $$ C. $$ 12.49+1.50 d=t $$ D. $$ 12.49=d+1.50 t $$ E. $$ t=\frac{d-12.49}{1.5} $$

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To find the correct equations that represent the relationship between the number of toppings $$ t $$ and the total cost $$ d $$ of the pizza, we can start by analyzing the cost structure given in the problem.

The cost of the pizza is $$ \$12.49 $$ and each topping costs $$ \$1.50 $$. Therefore, the total cost $$ d $$ can be expressed as:

$$
d = 12.49 + 1.50t
$$

Now, let's evaluate each of the provided options:

A. $$ 12.49 + t = d $$  
This is incorrect because it does not account for the cost of the toppings correctly.

B. $$ 12.49 + 1.50t = d $$  
This is correct as it matches the derived equation for total cost.

C. $$ 12.49 + 1.50d = t $$  
This is incorrect because it incorrectly relates $$ t $$ to $$ d $$.

D. $$ 12.49 = d + 1.50t $$  
This is incorrect because it rearranges the equation incorrectly.

E. $$ t = \frac{d - 12.49}{1.5} $$  
This is correct as it rearranges the original equation to solve for $$ t $$.

Thus, the correct equations that represent the relationship are:

- B. $$ 12.49 + 1.50t = d $$
- E. $$ t = \frac{d - 12.49}{1.5} $$
B. $$ 12.49 + 1.50t = d $$ E. $$ t = \frac{d - 12.49}{1.5} $$

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