Answer:
Step-by-step explanation:
At Home Depot, Johnny bought 3 rose bushes and 7 flats of petunias for a total of $114.75.
Let x = rose bushes
Let y = petunias
This means;
3x + 7y = 114.75 ..... (i)
Rosie bought 2 rose bushes and 6 flats of petunias for a total of $89.50.
2x + 6y = 89.50 ..... (ii)
How much does a rose bush cost? How much does a flat of petunias cost?
Multiply eqn (i) by 2 and eqn (ii) by 3.
This results too;
6x + 14y = 229.5 .... (iii)
6x + 18y = 268.5 .....(iv)
Subtract eqn (iii) from eqn (iv)
This results to;
4y = 39
y = 39 / 4 = $9.75
Subt the vale of y in eqn ii
2x = 89.50 - 6y
x = (89.50 - 6y) / 2
x = (89.50 - 6(39 / 4)) / 2
x = 31 / 2 = $15.5
Answer:
The function has at least 1 zero within the interval [-2,5].
Step-by-step explanation:
The intermediate value theorem states that, for a function continuous in a certain interval ![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
, then the function takes any value between 
and 
at some point within that interval.
This theorem has an important consequence:
If a function 
is continuous in an interval [a,b], and the sign of the function changes at the extreme points of the interval:
(or viceversa)
Then the function f(x) has at least one zero within the interval [a,b].
We can apply the theorem to this case. In fact, here we have a function f(x) continuous within the interval
[-2,5]
And we also know that the function changes sign at the extreme points of the interval:
Therefore, the function has at least 1 zero within the interval [-2,5], so there is at least one point x' within this interval such that
Answer:
m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ
Half-Life = 46.21 years.
Step-by-step explanation:
Radioactive reactions always follow a first order reaction dynamic
Let the initial mass of radioactive substance be m₀ and the mass at any time be m
(dm/dt) = -Km (Minus sign because it's a rate of reduction)
The question provides K = 0.015 from the given differential equation
(dm/dt) = -0.015m
(dm/m) = -0.015dt
∫ (dm/m) = -0.015 ∫ dt
Solving the two sides as definite integrals by integrating the left hand side from m₀ to m and the Right hand side from 0 to t.
We obtain
In (m/m₀) = -0.015t
(m/m₀) = (e^(-0.015t))
m = m₀ e^(-0.015t)) = m₀ e⁻⁰•⁰¹⁵ᵗ
m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ
At half life, m(t) = (m₀/2), t = T(1/2)
(m₀/2) = = m₀ e⁻⁰•⁰¹⁵ᵗ
e⁻⁰•⁰¹⁵ᵗ = (1/2)
In e⁻⁰•⁰¹⁵ᵗ = In (1/2)
-0.015t = - In 2
t = (In 2)/0.015
t = (0.693/0.015)
t = 46.21 years
Half life = T(1/2) = t = 46.21 years.
Hope this Helps!!!
2x-3yi=14+12i
=> 2x=14; -3yi=12i => x=7; y=-4
