To simplify the function, we need to know some basic identities involving exponents.
1. b^(ax)=(b^x)^a=(b^a)^x
2. b^(x/d) = (b^x)^(1/d) = ((b^(1/d)^x)
Now simplify f(x), where
f(x)=(1/3)*(81)^(3*x/4)
=(1/3)(3^4)^(3*x/4) [ 81=3^4 ]
=(1/3)(3^(4*3*x/4) [ rule 1 above ]
=(1/3) (3^(3*x)
=(1/3)(3^(3x)) [ or (1/3)(27^x), by rule 1 ]
(A) Initial value is the value of the function when x=0, i.e.
initial value
= f(0)
=(1/3)(3^(3x))
=(1/3)(3^(3*0))
=(1/3)(3^0)
=(1/3)(1)
=1/3
(B) the simplified base base is 3 (or 27 if the other form is used)
(C) The domain for an exponential function is all real values ( - ∞ , + ∞ ).
(D) The range of an exponential function with a positive coefficient and without vertical shift is ( 0, + ∞ ).
I only know how much does the fruit costs per pound is $4.82
Hi!
In one batch she uses 3/4 teaspoon of vanilla
therefore in 5 batch she uses 5*3/4=15/4 teaspoons of vanilla.
as it is given that 3 teaspoons=1 tablespoon
the amount of vanilla used for 5 batches =(15/4)/3=(15/4)*1/3=5/4==1.25 tablespoons.
All the best.
Answer:
Primul copil are 6 lei, al doilea are 12 lei, al treilea are 27 de lei.
Step-by-step explanation:
Lăsați suma primului copil să fie x.
Lăsați suma al doilea copil să fie y.
Lăsați suma al treilea copil să fie z.
Trei dintre ei au 45 de lei în total.
Aceasta înseamnă că:
x + y + z = 45 ________(1)
Al doilea are de două ori valoarea primului:
y = 2x
Al treilea are cu 15 lei mai mult decât al doilea:
z = 15 + y
=> z = 15 + 2x
Puneți valoarea y și z în (1):
x + 2x + 15 + 2x = 45
5x = 45 - 15 = 30
x = 30 / 5 = 6 lei
=> y = 2 * 6 = 12 lei
=> z = 15 + 12 = 27 lei
Primul copil are 6 lei, al doilea are 12 lei, al treilea are 27 de lei.
Answer:
-6 < x < 1
Step-by-step explanation:
-14 < 10 + 4x < 14
Subtract 10 from both sides
-24 < 4x < 4
Divide both sides by 4
-6 < x < 1
