All categories

2 years ago

Fill in the blank

Mathematics

1 answer:

Gnom [1K]2 years ago

4 0

Answer:

<u>multiply</u> the base and <u>add </u>the exponents

You might be interested in

1. What is the growth/ decay rate for this exponential function?

Firdavs [7]

Answer:

1. The growth rate is 2

2. The sample is losing half its mass, so the decay factor is 1/2 or 0.5

Step-by-step explanation:

The growth and decay factor in an exponential function is the number that is being multiplied to the power of x

It is a growth rate when that number is greater than 1
It is a decay rate when the number is less than 1
If it's 1 then it's not growing or decaying
If it's 0 you will have an answer of 0

8 0

2 years ago

Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s

Nataliya [291]

Answer:

$f(x)=\frac{1}{2}x^2-4x+5$

Step-by-step explanation:

A parabola is written in the form

$f(x)=a((x-h)^2+k)$ (1)

where:

$h$ is the x-coordinate of the vertex of the parabola

$ak$ is the y-coordinate of the vertex of the parabola

$a$ is a scale factor

For the parabola in the problem, we know that the vertex has coordinates (4,-3), so we have:

$h=4$ (2)

$ak=-3$

From this last equation, we get that $a=\frac{-3}{k}$ (3)

Substituting (2) and (3) into (1) we get the new expression:

$f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3$ (4)

We also know that the parabola contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

$-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6$

So we also get:

$a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}$

So the equation of the parabola is:

$f(x)=\frac{1}{2}((x-4)^2 -6)$ (5)

Now we want to rewrite it in the standard form, i.e. in the form

$f(x)=ax^2+bx+c$

To do that, we simply rewrite (5) expliciting the various terms, we find:

$f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5$

6 0

3 years ago

If you borrow 421$ for nine years at an interest rate of 4% how much will you pay

satela [25.4K]

Interest = (Principal X rate X time)/100
Interest =421*9*4/100
Interest = 151.56 dollars

5 0

3 years ago

Can someone plz explain to me when to use an open and closed dot

balandron [24]

closed dot is if the number is part of the solution so if it is equal to

and

use open if it is not part of solution as in if it is greater than or less than

so for your picture x greater or equal to -2 it would be a closed dot

5 0

3 years ago

Find the Missing demension of each triangle described:

Ganezh [65]

4 and then we will have a good day to sleep at church and ok then I just woke you up I love wieieuueueiewiowowo ohhh

7 0

3 years ago