Choose the number sentence that shows the distributive property of multiplication over addition. a. 3 × (4 + 5) = (3 × 4) + (3 × 5) b. 3 × (4 + 5) = (3 + 4) × (3 + 5) c. 3 × (4 + 5) = (3 × 4) + 5

we know that

distributive property of multiplication over addition:

now, we will verify each options

option-A:

3 × (4 + 5) = (3 × 4) + (3 × 5)

We can see that both sides match with property

so, this is TRUE

option-B:

3 × (4 + 5) = (3 + 4) × (3 + 5)

We can see that right side does not match with property

so, this is FALSE

option-C:

3 × (4 + 5) = (3 × 4) + 5

We can see that right side does not match with property

so, this is FALSE

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50