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luda_lava [24]
3 years ago
10

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

Mathematics
2 answers:
Neporo4naja [7]3 years ago
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]3 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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CD is perpendicular to AB and passes through point C5, 12).
Aleksandr-060686 [28]

Answer:

x intercept of CD = 17

Step-by-step explanation:

We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD mCD = -\frac{1}{mAB}

Hence we start from determining slope of AB

slope is given as

m= \frac{y_2-y_1}{x_2-x_1}

m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1

Hence mAB=1

There fore mCD=-1

(∵  Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

m=\frac{y-y_1}{x-x_1}

-1=\frac{y-12}{x-5}

-x+5=y-12

y=-x+17

Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x

0=-x+17

x=17

Hence the x intercept is 17

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