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3 years ago

Which of the following terms best describes the graph of the exponential function given below? F(x)=9*((1)/(7))^(x)

Mathematics

2 answers:

Monica [59]3 years ago

6 0

The correct answer should be B, a decreasing function.

goblinko [34]3 years ago

3 0

Answer:

B. Decreasing

Step-by-step explanation:

We have been given formula of a function $F(x)=9\cdot (\frac{1}{7})^x$ . We are supposed to determine the type of our given function.

We know that an exponential function is in form $y=a\cdot b^x$ , where,

a = Initial value,

b = If $b>1$ , then the function is growth function. If $b$ , then the function is decay function.

Upon looking at our given function we can see it is in form of exponential function.

Upon comparing our given function with standard exponential function, we can see that the value of a is 9 and value of b is $\frac{1}{7}$ .

Since $\frac{1}{7}$ , therefore, our function is decreasing and option B is the correct choice.

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Which phrases can be represented by the algebraic expression x + 14? Select three options.

Snezhnost [94]

Answer:

a number plus 14

fourteen more than a number

a number increased by 14

Step-by-step explanation:

The phrases which can be represented by the algebraic expression x + 14 are

Let x = the unknown number

a number plus 14

= x + 14

fourteen more than a number

= x + 14

a number increased by 14

x + 14

4 0

3 years ago

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Question 4 (1 point)

igomit [66]

Answer:

x = 15

Step-by-step explanation:

We want to solve for x in 3*(2x + 5) = 3x + 4x

First simplify.

3*(2x + 5) = 7x

Next, distribute the 3.

3*2x + 3*5 = 7x

6x + 15 = 7x

15 = 7x - 6x

15 = x

4 0

3 years ago

Hello again! This is another Calculus question to be explained.

podryga [215]

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions

Function Notation

Exponential Property [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Property [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

We are given the following and are trying to find the second derivative at x = 2:

$\displaystyle f(2) = 2$

$\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}$

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

$\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}$

When we differentiate this, we must follow the Chain Rule: $\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]$

Use the Basic Power Rule:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')$

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]$

Simplifying it, we have:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]$

We can rewrite the 2nd derivative using exponential rules:

$\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}$

To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:

$\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}$

When we evaluate this using order of operations, we should obtain our answer:

$\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

5 0

3 years ago

When sample size increases Group of answer choices

Olenka [21]

Answer:

Option A)

Confidence interval decreases

Step-by-step explanation:

If we increase the sample size, then,

The standard error of the interval decrease.
If the standard error increase, the margin of error of the interval decrease.
If the margin of error decreases, the width of the confidence level decreases, hence, the confidence interval become narrower.

Thus, the correct answer is

Option A)

Confidence interval decreases

3 0

3 years ago

Identify the terms and like terms in the question 3n+7-n-3

Temka [501]

Answer:

like terms: (3n,-n),(7,-3)

Step-by-step explanation:

4 0

2 years ago

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