Find the average rate of change for the interval [-4, 0] for the function below
Answer Choices
A. 3/4
B. -4/3
C. 4/3
D. -3/4

Find The Average Rate Of Change For The Interval [-4, 0] For The Function Below Answer Choices A. 3/4

Answers

Answer 1

Answer:

The average rate of change of the function for the interval [-4, 0] is  [tex]\frac{3}{4}[/tex] ⇒ A

Step-by-step explanation:

The average rate of change of the function is the slope of the line that represents the function, m = Δy/Δx, where

Δx = (x2 - x1)Δy = (y2 - y1)

From the given figure

→ The values of x in the interval [-4, 0] are -4 and 0

∵ The point (-4, 0) and (0, 3) lie on the line

x1 = -4 and x2 = 0

x2 = 0 and y2 = 3

∵ Δx = 0 - (-4) = 0 + 4 = 4

∵ Δy = 3 - 0 = 3

→ By using the rule of the slope above

m = [tex]\frac{3}{4}[/tex]

∵ The average rate of change of the function = the slope of the line

The average rate of change of the function for the interval [-4, 0] is  [tex]\frac{3}{4}[/tex]


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Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6.

Answers

Answer:

The 45th term is equal to -209.

Step-by-step explanation:

I got stuck on this question for six attempts. Therefore I started trying other methods. I started with a10=1 and then subtracted 6 to get a11=-5. I continued this process until I reached a45=-209

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The 45th term for the arithmetic sequence is -209.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

aₙ = a₁ + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

Given that the 10th term of the arithmetic series is 1, while the common difference of the arithmetic series is -6. Therefore, 10th term of the series can also be written as,

aₙ = a₁+(n-1)d

1 = a₁+(10-1)(-6)

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1 = a₁ - 54

a₁ = 55

Now, the 45th term for the arithmetic sequence is,

aₙ = a₁ + (n-1)d

a₄₅ = 55 + (45-1)(-6)

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Hence, the 45th term for the arithmetic sequence is -209.

Learn more about Arithmetic Sequence here:

https://brainly.com/question/3702506

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2(x + 3)2 – 3(x + 3) + 8
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Answers

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solve the equation
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Answers

48=y+5y

pretend that there is a 1 in front for the y

48=1y+5y

add the like terms first

1y+5y=6y

48=6y

divide both sides by 6 to get y by itself

48/6=6y/6

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answer:

y=8

Answer:

y = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Step-by-step explanation:

Step 1: Define equation

48 = y + 5y

Step 2: Solve for y

Combine like terms:                    48 = 6yDivide 6 on both sides:               8 = yRewrite:                                        y = 8

Step 3: Check

Plug in y into the original equation to verify it is a solution.

Substitute in y:                    48 = 8 + 5(8)Multiply:                               48 = 8 + 40Add:                                     48 = 48

Here we see that 48 does indeed equal 48.

∴ y = 8 is a solution of the equation.

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Step-by-step explanation:

So for number 33, we see that 2x+28=90 degrees so you just simplify the equation to 2x=62, x=31.

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For number 35, according to the vertical angle theorem, 43=2x+1, so we simplify that too and we get 42=2x, 21=x, x=21.

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Answer:

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Step-by-step explanation:

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For this case we have the following expression:
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Answer:
the simplified form of p ^ 0 is:
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Part B: What is the growth or decay percentage for this function? (2 points)

Part C: What does the y-intercept of the graph of the function f(n) represent? (2 points)

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Answers

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Step-by-step explanation:

Given the function :

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Answers

Answer:

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Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

The slope is in the given line. It is the number in front of the x which is 3.

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Step-by-step explanation:

Parallel lines never intersect.

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Step-by-step explanation:

lmk if you need work

and remember that when it is negative, the value that is closer to 0 is greater

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Answers

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Answers

Answer: 2x+y+11=0

Step-by-step explanation:

The equation of given line is x-2y-2=0

Slope of given line is (m1)= - coefficient of x÷coefficient of y

m1= -1÷-2 =1÷2

Let slope of required line be m2.

Since the two lines are perpendicular,

So,

m1×m2= -1

or, 1÷2×m2 = -1

m2 = -2

The required line is passing through (4,-3)

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y-y1 = m(x-x1)

or, y-(-3)= -2(x+4)

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or, 2x+y+3+8 = 0

2x+y+11 = 0 which is required equation of line.

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How do you write the equation of a line in point slope form and slope intercept form given point (6, -3) and has a slope of 1/2?

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Answer:  g(x) = (x-2)^2 + 1. Choice C

===========================================================

Explanation:

The graphs have the same shape, which means they have the same 'a' value.

In this case, a = 1.

The vertex of the red graph is (0,0).

The vertex of the blue parabola is (2, 1)

The red curve has been shifted 2 units to the right and 1 unit up.

Since the vertex of the blue graph is (2,1), this means h = 2 and k = 1.

Plug a = 1, h = 2 and k = 1 to get...

y = a(x-h)^2 + k

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Answer:

C.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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