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3 years ago

What is the average rate of change for this quadratic function for the interval from x =3 to x = 5

Mathematics

1 answer:

Mrrafil [7]3 years ago

5 0

Answer:

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

here [ a, b [ = [ 3, 5 ]

From the table

f(b) = f(5) = - 26

f(a) = f(3) = - 10

Hence average rate of change

= $\frac{-26-(-10)}{5-3}$ = $\frac{-16}{2}$ = - 8 → A

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Step-by-step explanation:

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Find the equation of the line that passes through the given points

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3 years ago

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

2 years ago

If a student was randomly guessing while completing a 20 question multiple choice exam, what is the probability they would score

mario62 [17]

Answer:

you want 4 correct and 16 incorrect

there are 20 questions

each question has four answers, so

P(right answer) = 1/4

P(wrong answer) = 3/4

----

Since you want 4 correct of 20 we have a combination of 20C4

This is a binomial problem where p = 1/4, q = 3/4 and we get

(20 "choose" 4)*(probability correct)^(number correct)*(probability incorrect)^(number incorrect)

putting numbers in we get

(20c4)*(1/4)^4*(3/4)^16

This gives us

~ .189685

Step-by-step explanation:

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3 years ago