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Diano4ka-milaya [45]
3 years ago
13

Consider the function f(x)=−5x−8 and find the following: a) The average rate of change between the points (−1,f(−1)) and (3,f(3)

) . b) The average rate of change between the points (a,f(a)) and (b,f(b)) . c) The average rate of change between the points (x,f(x)) and (x+h,f(x+h)) .
Mathematics
1 answer:
kipiarov [429]3 years ago
3 0

Answer:

a. -5

b.-5

c.-5

Step-by-step explanation:

In order to find the average rate of change of a function , we divide the change in the output value by the change in the input value.

Generally, the average rate of change (ARC) on an ecuatios  between two points (x1,f(x1)) and (x2,f(x2)) is

  • ARC = [f(x2)-f(x1)]/ (x2-x1)

<em>In case a)</em>

f(-1)= -5*(-1)-8=5-8= -3          f(3)= -5*3-8= -23

Then ARC= (-23-(-3))/(3-(-1))=-20/4=-5

<em>In case b)</em>

f(a)= (-5a-8)

f(b)= (-5b-8)

Then ARC= [(-5b-8)-(-5a-8)]/(b-a)= (-5b+5a)/(b-a)= -5(b-a)/(b-a)= -5

<em>In case c)</em>

f(x)= -5x-8

f(x+h)= -5(x+h)-8= -5x-5h-8

then ARC= [(-5x-5h-8)-(-5x-8)]/(x+h-x) =-5h/h= -5

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400*1.05=420

3 0
3 years ago
15. Divide the polynomial x^3 + x^2 - 2x + 3 by (x - 1).​
Stels [109]

Answer:

x² + 2x + [3\x - 1]

Step-by-step explanation:

Since the divisor is in the form of <em>x - c</em>, use what is called <em>Synthetic Division</em>. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

1| 1 1 -2 3

↓ 1 2 0

------------------

1 2 0 3 → x² + 2x + [3\x - 1]

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder, which in this case is a 3, so what you is set the divisor underneath the remainder of 3. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², 2 becomes <em>2x</em><em>,</em><em> </em>and the remainder of 3 is set over the divisor, giving you the other factor of <em>x² + 2x + [3\x - 1]</em>.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

5 0
3 years ago
2y greater than or equal to -12-4y OR 2y&gt;-14+6y
kirza4 [7]

Answer:

2y bigger or same -12-4y is correct

Step-by-step explanation:

Y=1

2=-12-4×1

2=-16

2 is bigger

Y=-2

-4=-12-4×(-2)

-4=-4 it's same

7 0
3 years ago
PLEASE HELP ASAP!! DUE!!!
Ipatiy [6.2K]

Answer:

s = (14 + 7 + 11)/2 = 32/2 =16

=> area = sqrt(16*(16-14)*(16-11)*(16-7)) = ~37.95

=> h = 2*Area/Base = 2*37.95/14 = 5.42

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3 years ago
Plz help ASAP HURRYYY UPPL PLZZZ
MrRa [10]
The answer is at least 6.
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3 years ago
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