<h3>
Answer: x = 1/2</h3>
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Explanation:
Recall that quadratic form is ax^2+bx+c.
So we need an x^2 term followed by an x term, then a constant at the end.
It may not look it, but the given equation is nearly in quadratic form.
Rewrite 9^(2x) as (9^x)^2
We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0
From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0
From here we can use the quadratic formula or factor. I'll factor.
w^2 - 2w - 3 = 0
(w - 3)(w + 1) = 0
w-3 = 0 or w+1 = 0
w = 3 or w = -1
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Now we use these values of w to find x
If w = 3, then,
w = 9^x
3 = 9^x
log(3) = log(9^x)
log(3) = x*log(9)
x = log(3)/log(9)
x = log(3)/log(3^2)
x = log(3)/(2*log(3))
x = 1/2
At the last step, we have the log(3) terms cancel.
Repeat for w = -1
w = 9^x
-1 = 9^x
log(-1) = log(9^x)
We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.
In short, w = -1 is extraneous so it doesn't lead to any x value solution.
So only w = 3 is useful.
Ultimately, the only solution is x = 1/2.
Answer:
g(4) = -3
Step-by-step explanation:
y = x - 7
y = 4 - 7 (substitute value for x)
y = -3 (solve)
2.709 is the answermmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
Respuesta: 70 pesos
Explicación paso a paso:
Dado que:
Sea la cantidad total poseída = t
Fracción gastada en alimentos = 1/3 t = t / 3
Fracción gastada en pasaje = 1/8 t = t / 8
Monto restante después del gasto total = 39 pesos
Fracción total gastada:
(t / 3 + t / 8)
= (8t + 3t) / 24
= 11t / 24
Fracción restante después del gasto total:
(t - 11t / 24)
= 13t / 24
Por lo tanto,
Fracción restante después del gasto total = Cantidad restante después del gasto total
13t / 24 = 39
13t = 936
t = 936/13
t = 72 pesos
Por lo tanto,
Monto total poseído = 72 pesos
Answer:
f ( 1 ) = 2 , f ( 0 ) = -1
Step-by-step explanation:
