Answer:X=-15
Step-by-step explanation:
-4x/5=12
5x-4x/5=5x12
-4x=5x12
-4x=60
-4x/-4=60/-4
x=-15
Answer:
The constant of proportionality is 2.50
Step-by-step explanation:
For a weight of 1 lb, the price is $2.50, so the price in dollars is related to the weight in pounds by the constant 2.50.
The constant of proportionality is 2.50 (dollars per pound).
Y = - 10x has a negative slope, m = -10, and a y-intercept of (0, 0).
The graph includes the following points:
{(-2, 20), (-1, 10), (0, 0), (1, -10), (2, -20)}.
Attached is a screenshot of the graph, where it includes the y-intercept crossing along the point of origin, (0, 0).
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Answer:
x = 8
Step-by-step explanation:
180 = 78 + 94 + x
180 =172 + x
-172 -172
18 = x
Answer:
% Remaining![= [1-(1/2)^{\frac{t}{2.6}}]x100](https://tex.z-dn.net/?f=%20%3D%20%5B1-%281%2F2%29%5E%7B%5Cfrac%7Bt%7D%7B2.6%7D%7D%5Dx100%20)
And replacing the value t =5.5 hours we got:
% Remaining![= [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%](https://tex.z-dn.net/?f=%20%3D%20%5B1-%281%2F2%29%5E%7B%5Cfrac%7B5.5%7D%7B2.6%7D%7D%5Dx100%20%3D76.922%5C%25)
Step-by-step explanation:
Previous concepts
The half-life is defined "as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not".
Solution to the problem
The half life model is given by the following expression:

Where A(t) represent the amount after t hours.
represent the initial amount
t the number of hours
h=2.6 hours the half life
And we want to estimate the % after 5.5 hours. On this case we can begin finding the amount after 5.5 hours like this:

Now in order to find the percentage relative to the initial amount w can use the definition of relative change like this:
% Remaining = 
We can take common factor
and we got:
% Remaining![= [1-(1/2)^{\frac{t}{2.6}}]x100](https://tex.z-dn.net/?f=%20%3D%20%5B1-%281%2F2%29%5E%7B%5Cfrac%7Bt%7D%7B2.6%7D%7D%5Dx100%20)
And replacing the value t =5.5 hours we got:
% Remaining ![= [1-(1/2)^{\frac{5.5}{2.6}}]x100 =76.922\%](https://tex.z-dn.net/?f=%3D%20%5B1-%281%2F2%29%5E%7B%5Cfrac%7B5.5%7D%7B2.6%7D%7D%5Dx100%20%3D76.922%5C%25)