For what values of x is the inequality 2/3 + x/3 >1 true?

Mathematics

1 answer:

Travka [436]2 years ago

6 0

Answer:

Step-by-step explanation:

$\frac{2}{3}$ + $\frac{x}{3}$ > 1 ( multiply through by 3 to clear the fractions )

2 + x > 3 ( subtract 2 from both sides )

x > 1

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Enter an expression equivalent to (3x^2+2y^2-3x) + (2x^2+y^2-2x) - (x^2 + 3y^2 +x)

11111nata11111 [884]

Answer:

4x² - 6x

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right<u> </u>

Distributive Property

<u>Algebra I</u>

Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

(3x² + 2y² - 3x) + (2x² + y² - 2x) - (x² + 3y² + x)

<u>Step 2: Simplify</u>

[Distributive Property] Distribute negative: 3x² + 2y² - 3x + 2x² + y² - 2x - x² - 3y² - x
Combine like terms (x²): 4x² + 2y² - 3x + y² - 2x - 3y² - x
Combine like terms (y²): 4x² - 3x - 2x - x
Combine like terms (x): 4x² - 6x

4 0

3 years ago

Find the exact value of sin2 theta given sin theta =5/13, 90°<theta <180°

Zepler [3.9K]

Now, we know that 90°< θ <180°, that simply means the angle θ is in the II quadrant, where sine is positive and cosine is negative.

$\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}$

$\bf \pm\sqrt{13^2-5^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a \implies \stackrel{II~quadrant}{-12=a}
\\\\\\
therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}
\\\\
-------------------------------\\\\
sin(2\theta )\implies 2sin(\theta )cos(\theta )\implies 2\left(\frac{5}{13} \right)\left( \frac{-12}{13} \right)\implies -\cfrac{120}{169}$

3 0

3 years ago

Express in the form <br> 1<br> :<br> n<br> .<br> Give <br> n<br> as a decimal.<br> 10<br> :<br> 4

Brut [27]

Answer:

n=0.4

Step-by-step explanation:

10:4=5:2

to make 5 as 1, we will divide both 5 and 2 by 5