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AysviL [449]
2 years ago
5

What kind of property is used in the following example?

Mathematics
1 answer:
aivan3 [116]2 years ago
7 0
Commutative Property
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Solve the system of two linear inequalities graphically.
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Step-by-step explanation:

Isolate y in the first inequality:

2x + 4y < -16\\4y < - 16 -2 x\\y < -4 -\frac{1}{2} x\\y < -\frac{x+8}{2} \\

Now, with both x and y inequalities found, graph it.

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A geometric sequence is defined by the general term tn = 75(5n), where n ∈N and n ≥ 1. What is the recursive formula of the sequ
andreyandreev [35.5K]
The correct answer is C) t₁ = 375, t_n=5t_{n-1}.

From the general form,
t_n=75(5)^n, we must work backward to find t₁.

The general form is derived from the explicit form, which is
t_n=t_1(r)^{n-1}.  We can see that r = 5; 5 has the exponent, so that is what is multiplied by every time. This gives us

t_n=t_1(5)^{n-1}

Using the products of exponents, we can "split up" the exponent:
t_n=t_1(5)^n(5)^{-1}

We know that 5⁻¹ = 1/5, so this gives us
t_n=t_1(\frac{1}{5})(5)^n&#10;\\&#10;\\=\frac{t_1}{5}(5)^n

Comparing this to our general form, we see that
\frac{t_1}{5}=75

Multiplying by 5 on both sides, we get that
t₁ = 75*5 = 375

The recursive formula for a geometric sequence is given by
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t_1=375; t_n=t_{n-1}(5)

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