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3 years ago

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Point GG is located at (-4,2)(−4,2) on the coordinate plane. Point GG is reflected over the xx-axis to create point G'G ′ . What

ordered pair describes the location of G'?G ′ ?

1 answer:

Taya2010 [7]3 years ago

7 0

Answer: (4,2)

Step-by-step explanation:

When a point is reflected over the x axis, only the x value changes to the opposite sign (positive or negative). The y value doesn’t change.

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My name is Ann [436]

$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
$\frac{1 - lnx}{x} = 0$
$lnx = 1, x = e$

(b) <em>Deduce:
</em> $e^{x} \geq x^{e}, x > 0$
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
$\frac{1}{e} \geq \frac{lnx}{x}$ , since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
$x \geq ln(x^{e})$

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.

3 0

3 years ago

A scalene triangle is an isosceles triangle. true false

Westkost [7]

False because they don't have the same length and shape you know they may be triangle but the their length are different.

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3 years ago

Use the Venn diagram to calculate probabilities. Circles A and B overlap. Circle A contains 15, circle B contains 10, and the in

grin007 [14]

Answer:

$(B) P(B)=\dfrac{16}{31}$

Step-by-step explanation:

From the Venn diagram, n(AUB)=31

The given probabilities in the option are calculated below:

$P(A)=\dfrac{21}{31}\\\\P(B)=\dfrac{16}{31}\\\\P(A|B)=\dfrac{P(A\cap B)}{P(B)}= \dfrac{6/31}{16/31} =\dfrac{6}{16}=\dfrac{3}{8} \\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{6/31}{21/31} =\dfrac{6}{21}=\dfrac{3}{7}$

The only correct option is the probability of B which is $\frac{16}{31}$

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3 years ago

|x - 1| > 4 is equivalent to which of the following?

Vsevolod [243]

Answer:

C. x > 5 or x < - 3

Step-by-step explanation:

|x - 1| > 4

Step 1:

x - 1 > 4

x > 4 + 1

x > 5

Step 2:

x - 1 < -4

x < -4 + 1

x < -3

HP: {x > 5 or x < -3} (c)

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2 years ago

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Luden [163]

Answer:

84

Step-by-step explanation:

Solve:

6*7= 42

42*2.00=84

Hope this helps!

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