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3 years ago

use the elimination method to solve the system of equations. choose the correct ordered pair. 6x-4y=-8 and 11x+4y=76

Mathematics

1 answer:

nika2105 [10]3 years ago

4 0

Answer:

(4,8)

Step-by-step explanation:

6x-4y=-8

11x+4y=76 eliminate y

6x+11y=-8+76

17 x=68

x=68/17=4

substitute x :

6x-4y=-8

6(4)-4y=-8

-4y=-8-24

y=-32/-4

y=8

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

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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

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Function Notation

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Calculus

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

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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

2 years ago

What is the slope of the line through (1,-1)(1,−1)left parenthesis, 1, comma, minus, 1, right parenthesis and (5,-7)(5,−7)left p

Alexeev081 [22]

Answer:

None of the points is a solution

The question doesn't look logical correct, check closely

Step-by-step explanation:

With the points ;

(1,-1)(1,−1)

The slope is = ( -1-( -1))/( 1-1)= infinity

Similarly if you do same with

5,-7)(5,−7) ; the slope would be infinity

6 0

3 years ago

use the elimination method to solve the system of equations. choose the correct ordered pair. 6x-4y=-8 and 11x+4y=76​

use the elimination method to solve the system of equations. choose the correct ordered pair. 6x-4y=-8 and 11x+4y=76