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2 years ago

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply.

2 answers:

8 0

For this case we have a function of the form:
$y = A * (b) ^ x
$
Where,
A: initial amount
b: growth rate (for b> 1)
x: independent variable
y: dependent variable
We then have the following function:
$f (x) = 3 (2.5) ^ x
$
Using the definition, the following statements are correct:
1) The function is exponential
2) The function increases by a factor of 2.5 for each unit increase in x
3) The domain of the function is all real numbers

xz_007 [3.2K]2 years ago

6 0

Answer:

A,C,D

The function is exponential.

The function increases by a factor of 2.5 for each unit increase in x.

The domain of the function is all real numbers.

Step-by-step explanation:

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2 years ago

What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that ap

Bond [772]

So the right options are:

$y=-\frac{2}{5}x-1$

$2x+5y = -5$

$y-1=-\frac{2}{5}(x+5)$

Further explanation:

Given equation of line is:

2x+5y=10

We have to convert it into point-slope form

$2x+5y=10\\5y=-2x+10\\Dividing\ both\ sides\ by\ 5\\y=-\frac{2}{5}x+\frac{10}{5}\\y=-\frac{2}{5}x+2$

The co-efficient of x is the slope of the line

So,

$m= -\frac{2}{5}$

As the required line is parallel to given line, it will also have same slope.

Let m1 be the slope of required line

Then the line will be:

$y=m_1x+b$

Putting the value of slope

$y=\frac{2}{5}x+b$

Putting (-5,1) in the equation to find the value of b

$1=-\frac{2}{5}(-5)+b\\1=2+b\\b=1-2\\b=-1$

Putting the values of slope and b in equation

$y=-\frac{2}{5}x-1$

Multiplying the whole equation by 5 will give us:

5y = -2x-5

2x+5y = -5

Another form of equation of line is Point-slope form

$y-y_1=m(x-x_1)$

Putting the values of slope and point in the equation, we get

$y-1=-\frac{2}{5}(x+5)$

So the right options are:

$y=-\frac{2}{5}x-1$

$2x+5y = -5$

$y-1=-\frac{2}{5}(x+5)$

Keywords: Point-Slope form, Parallel lines

Learn more about point slope form at:

#LearnwithBrainly

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2 years ago

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