A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation

H (t) = - 16t ^ 2 + 16t + 480
To address this, we first set the polynomial to zero to find its roots.
So we have:
0 = -16t ^ 2 + 16t + 480
This leads us to the roots of the polynomial:
t1 = -5
t2 = 6
We disregard the negative root since time cannot be less than zero.
Final answer:
Rose takes about
t = 6 seconds

Imagine having a pile of pennies and you want to determine if the count is odd or even without tallying them one by one. You can separate them into pairs by placing one coin in the left pile and one in the right.

If no coin is left unmatched, then the total number is even; if there is one coin remaining unpaired, the number is odd.

 

Part A

The weight of a wire piece correlates directly to its length

⇒ Weight of wire (W) is proportional to Length of wire (L)

⇒ W = k × L

With L = 25 cm, then W = 6 gms

⇒ = k

⇒ k =

To find weight for 30 cm wire, substitute k and W into W = k × L

⇒ W = × 30

⇒ W = 7.2 gms

Part B

p is inversely proportional to m

⇒ p = k × m

If p=48 when m=9

k =

⇒ k =  

Now to deduce p when m = 12, replace m and k in p = k × m

p = × 12

⇒ p = 64

Part A:

Please refer to the attached image to view the graph illustrating the inequalities.

There are two distinct lines shown, one with a steeper negative slope than the other. The shaded region in between indicates the solution set.

The green line corresponds to 2x+y≤8, while the blue line represents x+y≥4

Part B:

To determine if (8, 10) is included, substitute x = 8 and y = 10 into both inequalities. If it fails to satisfy either inequality, then it won't be part of the solution area.

2(8) + 10 ≤ 8

16 + 10 ≤ 8

26 ≤ 8... 26 is NOT less than or equal to 8

Hence, (8, 10) cannot be a solution because the inequality does not hold.

Part C:

I will select a random point from the graph, such as (2, 3). For your answer, any point within the shaded region where both x and y are positive would suffice.

The point (2, 3) indicates that Sarah can purchase 2 cupcakes and 3 pieces of fudge, ensuring that she acquires at least 4 pastries for her siblings while adhering to her 8 dollar budget.

Please let me know if you need any further clarification. Happy studying!

Since there is no accompanying figure, we assume points L, M, and N lie on the same line, with point L between M and N.

The total length of segment MN equals the sum of segments LN and LM, expressed as:
             LN + LM = MN

Substituting the given lengths:
             MN = 54 + 31
             MN = 85

ANSWER: MN = 85