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kupik [55]
3 years ago
12

-9 to the negative 1 power

Mathematics
1 answer:
Travka [436]3 years ago
8 0
Bear in mind that, (-9) and -9 are very different mammals, we're assuming, you meant (-9)⁻¹.


\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{  n}}}\implies \cfrac{1}{a^{-{{  n}}}}
\\\\
-------------------------------\\\\
(-9)^{-1}\implies \cfrac{1}{-9}\implies -\cfrac{1}{9}
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If f ( x ) f(x) is an exponential function where f ( − 3.5 ) = 25 f(−3.5)=25 and f ( 6 ) = 33 f(6)=33, then find the value of f
gavmur [86]

Given:

f(x) is an exponential function.

f(-3.5)=25, f(6)=33

To find:

The value of f(6.5).

Solution:

Let the exponential function is

f(x)=ab^x         ...(i)

Where, a is the initial value and b is the growth factor.

We have, f(-3.5)=25. So, put x=-3.5 and f(x)=25 in (i).

25=ab^{-3.5}         ...(ii)

We have, f(6)=33. So, put x=6 and f(x)=33 in (i).

33=ab^{6}         ...(iii)

On dividing (iii) by (ii), we get

\dfrac{33}{25}=\dfrac{ab^{6}}{ab^{-3.5}}

1.32=b^{9.5}

(1.32)^{\frac{1}{9.5}}=b

1.0296556=b

b\approx 1.03

Putting b=1.03 in (iii), we get

33=a(1.03)^{6}

33=a(1.194)

\dfrac{33}{1.194}=a

a\approx 27.63

Putting a=27.63 and b=1.03 in (i), we get

f(x)=27.63(1.03)^x

Therefore, the required exponential function is f(x)=27.63(1.03)^x.

4 0
2 years ago
Help plzzz!! Find the slope through these pairs of points
Colt1911 [192]
We can use the formula y2-y1/x2-x1 to find the slope.

1. 2-(-15)/12-5 gives us 17/7. The slope is 17/7.

2. -5-(-20)/6-(-18) gives us 15/24. We can simplify this to 5/8. The slope is 5/8.

3. -19-(-19)/-17-(-18) is 0/1. The slope is 0.

4. -17-3/-11-(-1) is -20/-10. The slope is 2.
8 0
2 years ago
What is the domain of the function y = square root x+6 -7?
salantis [7]

Answer:

  -6 ≤ x < ∞

Step-by-step explanation:

You want the domain of the function y = √(x+6) -7.

<h3>Domain</h3>

The domain of a function is the set of x-values for which the function is defined. On a graph, it is the horizontal extent of the graph.

The square root function is undefined for negative arguments, so that limits the domain of the given function:

  x+6 ≥ 0

  x ≥ -6 . . . . . domain of the given function

__

<em>Additional comment</em>

When the domain is written in interval notation, both the left and right ends of the interval must be specified.

  [-6, ∞)

The square bracket identifies -6 as being part of the domain. The parenthesis is used with ∞, because that number has no specific value.

8 0
2 years ago
In ^3/13, the 3 is called the:
JulijaS [17]

Answer:

Index

Step-by-step explanation:

The 3 is the index, the √ is the radical sign and the 13 is the radicand.

7 0
3 years ago
Write an equation of the line containing the point (2,1) and perpendicular to the line 5x – 2y = 3.
Ann [662]

So first, you want to isolate your Y. To do this, you must get it alone on ONE SIDE of the equation.

5x - 2y = 3

-5x         -5x

\frac{-2y}{-2} = \frac{3-5x}{-2}

 

ANSWER: y = \frac{3-5x}{-2}

6 0
3 years ago
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