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2 years ago

9

Four married couples have bought 8 seats in the same row for a concert. in how many different ways can they be seated

1 answer:

Dimas [21]2 years ago

6 0

If no restrictions 40,320

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Which of the following numbers is a power of ten?

Vinil7 [7]

C.) 0.0001 is a power of ten

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3 years ago

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For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?

Klio2033 [76]

When b=0
f(x)=ax^2+c

test each
A. with x^2-1, A is false
B. with -x^2-1, B is false
C. cannot find contradiction
D. the axis is actually x=0, 0 is nithere positive nor negative, false

answer is C

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3 years ago

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I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

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2 years ago

If for a particular one-to-one function f(2) = 13, what are the corresponding input and output

maks197457 [2]

Answer:

$f^{-1}(13) = 2$ .

Step-by-step explanation:

For function $f$ , the notation $f(2) = 13$ means that when the input to the function is $2$ , the output would be $13$ .

The inverse function of a one-to-one function $f$ is commonly denoted as $\!f^{-1}$ .

The inverse function undoes the action of the original function. In this question, $f$ maps $2$ to $13$ . Thus, $f^{-1}$ would need to map $13\!$ back to $2\!$ . Therefore, $f^{-1}(13) = 2$ should be the corresponding input and output values.

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2 years ago

A bat and a ball cost a total of $1.10. If the bat costs a dollar more than the ball, how much does the ball cost?

Natalija [7]

10 cents hope this helps

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3 years ago

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