The quadratic function y = -10x2 + 160x - 430 models a store's daily profit (y), in dollars, for selling T-shirts priced at x do

The general equation for exponential decay characterized by a half-life (T) is expressed as N(t) = N_0(1/2)^(t/T), where N(t) signifies the amount remaining at time t, N_0 stands for the initial amount (at t=0), and T denotes the half-life of the substance. The half-life of carbon-14 is about 5,730 years. When starting with 6 mg of carbon-14, the equation for the remaining amount after t years would be established.

Answer:

A) The total duration needed to paint the room is 50 minutes.

B) To paint 64% of the room takes 32 minutes.

Step-by-step explanation:

Given as:

After 18 minutes, 64% of the room still requires painting.

Therefore, within 18 minutes, (100% - 64% = 36%) of the room has been painted

Let T minutes be the total time required to paint the entire room.

Now, according to the question

A ) Using the unitary method

∵ In total, 36% of the room is covered in 18 minutes

Thus, in total time of minutes, 1% of the complete room is painted.Consequently, 100% of the room would be painted in × 100 minutes

i.e T =

Thus, T = 50 min

Therefore, the duration needed to paint the entire room = T = 50 minutes

Thus, the time required to finish painting the entire room is 50 minutes. Answer

B) Again

Time taken to paint 64% of the room = x minutes

∵ 36% of the room has been painted in a total of 18 minutes

Thus, 1% of the entire room gets painted in minutes

Consequently, painting 64% of the room will take × 64 minutes

i.e x =

Thus, x = 32 min

Therefore, the required time for painting 64% of the entire room = x = 32 minutes

Thus, the time required to paint 64% of the room amounts to 32 minutes. Answer

The question clearly seeks the highest values from both functions, meaning the vertices of each.

<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,

(h,k) = (1.5, 7.5)

Where (h,k) represents the vertex's location.

Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span> + 5x + 4<span>To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:

a = -2</span>
b = 5

Consequently,

x = - 5 ÷ - 4

x = 5 / 4




x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4
y = - 2(1.25)² + 5(1.25) + 4

y = - 3.125 + 6.25 + 4


y = 7.125


Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculations
Ed’s

<span>football attains a higher height.</span>

2(2w-5) + 2w = 50

4w - 10 + 2w = 50

6w - 10 = 50

6w = 60

w = 10

The length is calculated as 2(10) - 5 = 20 - 5 = 15

I hope this is useful!!