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Snezhnost [94]
3 years ago
9

Let f(x)=x2−2x−4 . What is the average rate of change for the quadratic function from x=−1 to x = 4?

Mathematics
2 answers:
elena55 [62]3 years ago
7 0
The average rate of change <span>x=−1 to x = 4 is 

A= f(4) -f(-1) / 4- (-1)
f(4)=4²-2x4-4=16-12=4
f(-1)=1+2-4= -1
</span><span>f(4) -f(-1) / 4- (-1) = 4-(-1)/4-(-1)= 5/5=1
</span>the rate of change is A=1
goblinko [34]3 years ago
4 0

Answer:

The average rate of change for f(x) from x=−1 to x = 4 is, 1

Step-by-step explanation:

Average rate A(x) of change for a function f(x) over [a, b] is given by:

A(x) = \frac{f(b)-f(a)}{b-a}

As per the statement:

f(x) = x^2-2x-4

we have to find the average rate of change from x = -1 to x = 4

At x = -1

f(-1) = (-1)^2-2(-1)-4 = 1+2-4 = -1

and

at x = 4

f(4) = (4)^2-2(4)-4 = 16-8-4 = 4

Substitute these in [1] we have;

A(x) = \frac{f(4)-f(-1)}{4-(-1)}

⇒A(x) = \frac{4-(-1)}{4+1}

⇒A(x) = \frac{5}{5}

Simplify:

A(x) = 1

Therefore, the average rate of change for f(x) from x=−1 to x = 4 is, 1

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Eighteen boys joined a group of p students in the auditorium. If the ratio of boys to girls was then 5:4 write and algebraic exp
ycow [4]

Answer:  The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

  • <em>Number of boys added: 18 </em>
  • <em>Ratio of boys to girls: 5:4 </em>

So, the total number of boys is:

x + 18  

Number of girls = y

Number of boys / number of girls = 5/4

(x+18) /y = 5/4

Solving for "y"

4 (x +18) =5 y

4x +72 = 5y

(4x +72) /5 = y

The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5

8 0
3 years ago
Can anyone help me, i will give brainiest.
laila [671]

Answer: ∠DOB: 48°

Step-by-step explanation:

1. we need an equation first. the sum of all angles (108°, n°, 2n°) is equal to 180°. we can depict this with the equation: 108°+2n°+n°=180°

2. now we can solve for the missing variable, n.

108°+3n°=180° → subtract both sides by → 3n°=72° → divide both sides by 3 → n=24°

3. now that we know that n=24°, we can solve the value of ∠DOB. we can see that ∠DOB is 2n° which we just plug the number we got for n into the equation. 2*24=48° meaning ∠DOB is 48°

hope this heped! ♡

7 0
2 years ago
Read 2 more answers
Can somebody help me plz
dexar [7]

Answer:

Step-by-step explanation:

5 0
3 years ago
Finding Derivatives Implicity In Exercise, find dy/dx implicity.<br> 4x3 + ln y2 + 2y = 2x
lisov135 [29]

Answer:

\frac{dy}{dx}=\frac{y(1-6x^2)}{(1+y)}

Step-by-step explanation:

Given function : 4x³ + ln(y²) + 2y = 2x

on differentiating both sides with respect to 'x', we get

\frac{d(4x^3 + ln(y^2) + 2y)}{dx}= \frac{d(2x)}{dx}

or

12x^2+\frac{2}{y}(\frac{dy}{dx})+2(\frac{dy}{dx})=2

or

12x^2+(\frac{2}{y}+2)\frac{dy}{dx}=2

or

(\frac{2+2y}{y})\frac{dy}{dx}=2-12x^2

or

\frac{dy}{dx}=\frac{y(2-12x^2)}{2+2y}

or

\frac{dy}{dx}=\frac{2y(1-6x^2)}{2(1+y)}

or

\frac{dy}{dx}=\frac{y(1-6x^2)}{(1+y)}

3 0
3 years ago
How do I solve/ set up equation? Will give brainliest pls help
slamgirl [31]

Answer:

See below ~

Step-by-step explanation:

<u>Finding x</u>

  • 2x - 28 = x/2
  • 3/2x = 28
  • 3x = 56
  • x = 56/3 = 18.66666667

  1. The exact side length of the small square is <u>18.66666667 cm</u> and the exact side length of the big square is <u>37.3333334 cm</u>.
  2. The approximate side length of the small square is <u>18.7 cm</u> and the approximate side length of the big square is <u>37.3 cm</u>.
4 0
2 years ago
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