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3 years ago

Solve the system of equations.y= 2x + 4y = x2 + x - 2

Mathematics

1 answer:

bezimeni [28]3 years ago

3 0

Answer:

Step-by-step explanation:

$y=2x+4$

$y=x^2+x-2$

Both equations are solved for y so I'm just going to substitute

the 1st y (the 2x+4) into the second equation's y.

$2x+4=x^2+x-2$

I'm going to get everything on one side so I have 0=ax^2+bx+c.

Subtract 2x and subtract 4 on both sides:

$0=x^2-x-6$

Since the coefficient of x^2 is 1, all we have to do is find two numbers that multiply to be -6 and add up to be -1.

These numbers are -3 and 2.

So the factored form of our equation is:

$0=(x-3)(x+2)$

This means we have x-3=0 or x+2=0.

x-3=0

Add 3 on both sides:

x=3

x+2=0

Subtract 2 on both sides:

x=-2

So now we need to find y. I'm going to choose to use the easier equation:

y=2x+4.

If x=3, then y=2(3)+4=6+4=10. The ordered pair (3,10) is a solution.

If x=-2, then y=2(-2)+4=-4+4=0. The orded pair (-2,0) is a solution.

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Someone please help for brainiest and thanks.. No fake answers or you get reported

bagirrra123 [75]

Hello from MrBillDoesMath!

Answer:

12/5

Discussion:

Note that 10 is a common denominator of both denominators:

9/5 = (9*2)/(5*2) = 18/10

- ( -6/10) = + (6/10)

So the original problem is equivalent to

18/10 + 6/10 =

(18 +6)/10 =

24/10 =

(2*12)/ (2*5) => cancelling the common factor "2"

12/5 =

2 and 2 fifths =

22/5 (though this looks like (22)/5!)

Thank you,

MrB

6 0

3 years ago

The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 9,

Airida [17]

Answer:

Step-by-step explanation:

Mean: 9+6+18+2+13+3+5= 56/7 = 8

Median: 2,3,5,6,9,13,18 the middle number is 6

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7 0

2 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

2 years ago

Anybody know the answer (and please dumb it down) 4y + 2 = 2y + 4 + 3y

Anna11 [10]

36y + 7 stars are great but I don’t have a bad experience

7 0

2 years ago

To add or subtract fractions, what must you have?

antiseptic1488 [7]

Answer:

You need a common denominator.

Step-by-step explanation:

3/4+2/3

9/12+8/12

4 0

3 years ago

Read 2 more answers

Solve the system of equations.y= 2x + 4y = x2 + x - 2​

Solve the system of equations.y= 2x + 4y = x2 + x - 2