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4 years ago

When 27x^2z/-3x^2z^6 is completely simplified, the exponent on the variable z is _____.

1 answer:

7 0

<span>The expression given (27x^2)z/(-3x^2)(z^6), can be simplify as below:

By properties of powers, if you have the same base, you can substract the exponents. Then:

=(</span>27x^2)z/(-3x^2)(z^6)
=-9z/z^6 (As you can see: x^2-2= x^0=1)
=-9/z^5 (Then, z^6-1=z^5)
<span>
Therefore, the answer is: The exponent on the variable z is 5.</span>

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3 years ago

Need help with this question.

solniwko [45]

We have this equation:

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First, combine both logarithms using the multiplication property and simplify the expression.

$\log[x(x + 99)] = 2$

$\log[ {x}^{2} + 99x ] = 2$

Now, use the definition of logarithm to transform the equation.

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Finally, use the quadratic formula to solve the equation.

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2 years ago

How to determine if a fraction is repeating or terminating?

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3 years ago

Jerald jumped from a bungee tower. If the equation that models his height, in feet, is h = –16t2 + 729, where t is the time in s

Snezhnost [94]

Answer. First option: t > 6.25

Solution:

Height (in feet): h=-16t^2+729

For which interval of time is h less than 104 feet above the ground?

h < 104

Replacing h for -16t^2+729

-16t^2+729 < 104

Solving for h: Subtracting 729 both sides of the inequality:

-16t^2+729-729 < 104-729

-16t^2 < -625

Multiplying the inequality by -1:

(-1)(-16t^2 < -625)

16t^2 > 625

Dividing both sides of the inequality by 16:

16t^2/16 > 625/16

t^2 > 39.0625

Replacing t^2 by [ Absolute value (t) ]^2:

[ Absolute value (t) ]^2 > 39.0625

Square root both sides of the inequality:

sqrt { [ Absolute value (t) ]^2 } > sqrt (39.0625)

Absolute value (t) > 6.25

t < -6.25 or t > 6.25, but t can not be negative, then the solution is:

t > 6.25

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4 years ago

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