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2 years ago

Use the quadratic formula to solve 4x²-9x=2x²-2x-4

1 answer:

5 0

$4x^2-9x = 2x^2 -2x -4\\\\\implies 4x^2 -9x -2x ^2 +2x +4 =0\\\\\implies 2x^2 -7x +4=0\\\\\text{Apply quadratic formula,}~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}.\\\\\text{In this case,} ~a =2, b = -7 ~ \text{and}~ c =4\\\\\\x =\dfrac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 4}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{17}}4\\\\\\\text{Hence,}~ x = \dfrac{7 +\sqrt{17}}4~ \text{and}~x = \dfrac{7 -\sqrt{17}}4$

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N an

Lostsunrise [7]

<h3>Answer:</h3>

$C)\ a_n=2a_{n-1}-1$

<h3>Explanation:</h3>

You can try the choices to see which one works. The differences between an values double each time. They have the sequence 1, 2, 4, 8. So, you know that choices A) and D) do not work. They show the difference to be constant at 1 or 8. Since the differences are multiplied by 2, C) is a reasonable choice. Trying that, we find it describes the sequence perfectly:

a2 = 2·2 -1 = 3

a3 = 2·3 -1 = 5

a4 = 2·5 -1 = 9

a5 = 2·9 -1 = 17

___

Trying choice B on the last term, we have

... a5 = 3·a4 -3 = 3·9 -3 = <em>24 ≠ 17</em>

7 0

3 years ago

Which expression is a polynomial?<br><br> –13

olasank [31]

Polynomials are <em>algebraic</em> expressions whose <em>standard</em> form is defined below:

$p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}$

The expression p(x) = - 13 represents a <em>zeroeth</em> polynomial.

<h3>What is a polynomial?</h3>

Herein we must present what the form of polynomials are. Polynomials are <em>algebraic</em> expressions whose <em>standard</em> form is defined below:

$p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}$ (1)

Where:

$c_{i}$ - i-th coefficient
n - Grade
x - Independent variable

An example is the expression p(x) = - 13, <em>real </em>numbers can be define as <em>zeroeth</em> polynomials. In this regard, the example can be seen as:

p(x) = 0 · xⁿ + 0 · xⁿ⁻¹ + ... + 0 · x² + 0 · x - 13

<h3>Remark</h3>

The statement is incomplete. We decided to re-define the statement to what polynomials are.

To learn more on polynomials: brainly.com/question/11536910

#SPJ1

5 0

2 years ago

Find the distance round to the nearest tenth (-8, -6) (-3,-2)

lina2011 [118]

Answer:

$\displaystyle d \approx 6.4$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Coordinates (x, y)

<u>Algebra II</u>

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

<u>Step 1: Define</u>

Point (-8, -6)

Point (-3, -2)

<u>Step 2: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates into the distance formula to find distance <em>d</em>

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(-3+8)^2+(-2+6)^2}$
[√Radical] (Parenthesis) Add: $\displaystyle d = \sqrt{(5)^2+(4)^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{25+16}$
[√Radical] Add: $\displaystyle d = \sqrt{41}$
[√Radical] Evaluate: $\displaystyle d = 6.40312$
Round: $\displaystyle d \approx 6.4$