The answer is C. Y= x^2+7x+10
Answer:
9 hours
Step-by-step explanation:
According to Newton's laws of cooling
dT/dt = -k(T - A)
Let U = T - A
dU/dT = 1
dU = dT
dt/dt = -kU
dT = -kU(dt)
dU/U = -kdt
On integration
ln(U) = -kt + C
U = Ce^-kt
T - A = Ce^-kt
T(0) = 68
T(5) = 25
68 - 20 = Ce^-k(0)
C = 48
and
25 -20 = 48e^-k(5)
5 = 48e^-5k
e^-5k = 5/48
-5k = ln (5/48)
k = - ln(5/48) / 5
k = - 0.4524
T - 20 = 48e^-0.4524t
When T = 21
21 -20 = 48e^-0.4524t
1 = 48e^-0..4524t
e^-0.4524t = 1/48
-0.4524t = ln (1/48)
t = - ln(1/48) / 0.4524
t = 8.5570
t= 9 hours ( to the nearest hour)
Answer:
(3, - 25 )
Step-by-step explanation:
Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0
The the x- coordinate of the turning point is
x = - 
Given
y = (x + 2)(x - 8) ← expand factors using FOIL
= x² - 6x - 16 ← in standard form
with a = 1 and b = - 6, thus
x = - 
= 3
Substitute x = 3 into the equation for corresponding value of y
y = (3 + 2)(3 - 8) = 5(- 5) = - 25
turning point at (3, - 25 )
Answer:
A. 38
Step-by-step explanation:
Let d = number of dimes.
Let n = number of nickels.
First equation:
There are twice as many dimes as nickels. The number of dimes is 2 times the number of nickels. The first equation is:
<em>d = 2n</em>
Second equation:
The value of a dime is $0.10. The value of a nickel is $0.05. The value of d number of dimes is 0.1d. The value of n number of nickels is 0.05n. The total value of d dimes and n nickels is 0.1d + 0.05n. We are told the total value of her dimes and nickels is $4.75. That gives us the second equation:
<em>0.1d + 0.05n = 4.75</em>
We have two equations and two unknowns, so we can answer this question by solving a system of two equations in two unknowns.
d = 2n
0.1d + 0.05n = 4.75
We will use the substitution method.
Since d = 2n, replace d in the second equation with 2n.
0.1(2n) + 0.05n = 4.75
0.2n + 0.05n = 4.75
0.25n = 4.75
n = 4.75/0.25
n = 19
Now that we know the number of nickels, we use the equation d = 2n to find the number of dimes.
d = 2n
d = 2 * 19
d = 38
Answer: Debra had 38 dimes.
3.01 is the decimal notation for 3 1/100. You keep the three in the ones place. 1/100 is a decimal. If you use long division or a calculator, you can see that 1/100 is 0.01.
