Factorization of 8
= (2*2*2)
Answer:
{x,y} = {3,-2}
Step-by-step explanation:
// Solve equation [1] for the variable y
[1] y = 2x - 8
// Plug this in for variable y in equation [2]
[2] 3x - 2•(2x-8) = 13
[2] -x = -3
// Solve equation [2] for the variable x
[2] x = 3
// By now we know this much :
x = 3
y = 2x-8
// Use the x value to solve for y
y = 2(3)-8 = -2
Solution :
{x,y} = {3,-2}
Answer:
The pack of 12 pencils for 298 is better as it has a lower unit price.
Step-by-step explanation:
To be able to find the answer, you have to calculate the unit price for each brand by dividing the price of the pack by the number of pencils in the pack.
-298/12=24.83
-499/18=27.72
According to this, the answer is that the pack of 12 pencils for 298 is better as it has a lower unit price.
General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as
.
Comparing the function f(x)=ax^{2} +bx+c with the given function
, we get
,
and
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds
The maximum height is found by substituting
in the function as below:

Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts.