The answer is A.

Ordered pairs that equate to a function would not have two separate points with the same x-value. In other words, every x-value must be associated with only one y-value.

5 0

3 years ago

Solve: In 2x + In 2 = 0<br> DONE

pychu [463]

Answer:

$x=\frac{1}{4}$

Step-by-step explanation:

We can use some logarithmic rules to solve this easily.

<em>Note: Ln means $Log_e$ </em>

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Now, lets start with the equation:

$ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)$

Writing left side with logarithmic base e, we have:

$Log_{e}(2x) = -ln(2)$

We can now use the property shown below to make this into exponential form:

$Log_{a}b=x\\means\\a^x=b$

So, we write:

$Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x$

We recognize another property of exponentials:

$a^{bc}=(a^{b})^{c}$

So, we write:

$e^{-ln(2)}=2x\\(e^{ln(2)})^{-1}=2x$

Also, another property of natural logarithms is:

$e^{(ln(a))}=a$

Now, we simplify:

$(e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}$

This is the answer.

7 0

3 years ago

What is the first term of the geometric sequence below?

Dominik [7]

C. 1/5

because you multiple it times 5 every time

5 0

3 years ago

Edge! 15 pts! PLEASE HURRY! Which is a diagonal through the interior of the cube?

aleksley [76]

Answer:

s√3

Step-by-step explanation:

Draw in the diagonal of the base, which is the line freom G to F. If the side length of this cube is s, then the length of this diagonal is

d = √(s² + s²) = (√2)s.

Now draw in the diagonal of the cube: draw a line segment from G to B. We have already found that the length of the diagonal GF is d = s√2. Apply the Pythagorean Theorem to the triangle whose sides are s√2 and s:

diagonal of cube = square root of the sum of the squares of s√2 and s:

= √(2s² + s²)= √(3s²) = s√3

7 0

2 years ago

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