3 years ago

1. the moon is always half illuminated by....

Geography

1 answer:

miv72 [106K]3 years ago

5 0

1) sun
2)high in the sky
3)bigger

Explanation: I hope this is correct but if not sorry

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Match the definition in column 1 with the economic term in column 2.

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On a coordinate plane, 2 exponential functions are shown. f (x) = 5 Superscript x Baseline approaches y = 0 in quadrant 2 and in

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Answer:

$k = -7$

Explanation:

Given

$f(x) = 5^x$ through (0,1) and (1,5)

$g(x) = 5^x + k$ through (0,-6) and (1,-2)

Required

Determine the value of k if f(x) is translated vertically down

To get the value of k, we perform the following operations.

For (0,-6) --- Substitute 0 for x and -6 for g(x) in $g(x) = 5^x + k$

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$-6 = 5^0 + k$

$-6 = 1 + k$

$k + 1 = -6$

$k = -6 - 1$

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For (1,-2) --- Substitute 1 for x and -2 for g(x) in $g(x) = 5^x + k$

$g(x) = 5^x + k$

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$k = -7$

To further show that k = -7, we have the following:

$f(x) = 5^x$

When translated downward by 7 units, the function becomes

$g(x) = f(x) - 7$

Recall that: $g(x) = 5^x + k$ and $f(x) = 5^x$

So, we have:

$5^x + k = 5^x - 7$

Subtract $5^x$ from both sides

$5^x - 5^x + k = 5^x - 5^x + 7$

$k = -7$

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