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babunello [35]
3 years ago
9

Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 2^2x

Mathematics
1 answer:
Nookie1986 [14]3 years ago
3 0

Answer:

a) This is not an exponential function because the variable is in the exponent position.

c) The base is 4 not 2.

Step-by-step explanation:

The given function is f(x) = (2)^{2x} = 4^{x} ........... (1)

a) This is not an exponential function because the variable is in the exponent position.

c) The base is 4 not 2.

The general form of an exponential function is given by f(x) = A(B)^{x}, where A is the initial value of the function and B is the base. (Answer)

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Which is an equation of the line that contains the points (0,2) (4,0)
alekssr [168]

Answer:

Y= -1/2x+2

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m=

0 - 2

4 - 0

or...

m=

-2

4

or...

m=-1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(4,0). When x of the line is 4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-1/2x+b. b is what we want, the -1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=-1/2 × 0+b, or solving for b: b=2-(-1/2)(0). b=2.

(4,0). y=mx+b or 0=-1/2 × 4+b, or solving for b: b=0-(-1/2)(4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (4,0)

is

y=-1/2x+2

4 0
3 years ago
What is the value of the 1 in the following number. 2043.61
kompoz [17]
The answer for this is hundredth because it is .01 (two values behind decimal means hundredths)
4 0
3 years ago
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Let A = (1, 0, 3) and B = (−3, 2, 1).
Romashka-Z-Leto [24]

Answer:

a) (-\frac{\sqrt{24}}{6} ,\frac{\sqrt{24}}{12} ,-\frac{\sqrt{24}}{12})

b) (-1,1,2)

c) -2x+y-z=1

Step-by-step explanation:

a)

AB, OB, OA are vectors.

AB = OB - OA = (-3, 2, 1) - (1, 0, 3) = (-4, 2, -2)\\||AB|| = \sqrt{(-4)^2+2^2+(-2)^2}=\sqrt{24}\\

Normalizing AB: \frac{AB}{||AB||} = (\frac{-4}{\sqrt{24}},\frac{2}{\sqrt{24}}, \frac{-2}{\sqrt{24}})=(-\frac{\sqrt{24}}{6} ,\frac{\sqrt{24}}{12} ,-\frac{\sqrt{24}}{12})

b)

OM, OA, OB are vectors.

OM = \frac{1}{2}OA+\frac{1}{2}OB=(\frac{-3+1}{2} ,\frac{2+0}{2}, \frac{1+3}{2} )=(-1,1,2)

So, M = (-1,1,2)

c)

-4x+2y-2z=(-4)(-1)+(2)(1)+(-2)(2)=4+2-4=2

Hence,

-2x+y-z=1

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3 years ago
F(x) = x2 +1<br> g(x) = 5-X<br> (f+g)(x) =
Darina [25.2K]

Answer:

8762

Step-by-step explanation:

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2 years ago
Can anyone help me to solve c no.?​
taurus [48]

Answer:

I Think It Is Side Side Side

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3 years ago
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