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3 years ago

Solve the rational equation 2x/x-3 - 2x-5/x^2-8x+15 = -3/x-5

1 answer:

4 0

Answer:2\cdot \frac{x}{x}-3-2x-\frac{5}{x^2}-8x+15=-\frac{3}{x}-5\quad :\quad x=\frac{1}{2},\:x=\frac{7+\sqrt{149}}{10},\:x=\frac{7-\sqrt{149}}{10}\quad \left(\mathrm{Decimal}:\quad x=0.5,\:x=1.92065\dots ,\:x=-0.52065\dots \right)

Step-by-step explanation:

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What is the name of the point of concurrency of the angle bisectors of a triangle?

scoray [572]

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4 years ago

Which expression shows the result of applying the distributive property of 3(2x – 6)?

jok3333 [9.3K]

Answer:

6x - 18

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Step-by-step explanation:

<u>Step 1: Define</u>

3(2x - 6)

<u>Step 2: Expand</u>

Distribute 3: 3(2x) + 3(-6)
Multiply: 6x - 18

5 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=Given%20%5C%3A%20cotA%20%3D%20%5Csqrt%7B%5Cdfrac%7B1%7D%7B3%7D%7D" id="TexFormula1" title="Giv

ruslelena [56]

<h3>Given :</h3>

$\tt cotA = \sqrt{ \dfrac{1}{3}}$

$\tt \implies cotA = \dfrac{1}{\sqrt{3}}$

All other trigonometric ratios, which are :

sinA
cosA
tanA
cosecA
secA

<h3>Solution :</h3>

Let's make a diagram of right angled triangle ABC.

Now, From point A,

AC = Hypotenuse

BC = Perpendicular

AB = Base

$\tt We \: are \: given, \: cotA = \dfrac{1}{\sqrt{3}}$

$\tt We \: know \: that \: cot \theta = \dfrac{base}{perpendicular}$

$\tt \implies \dfrac{base}{perpendicular} = \dfrac{1}{\sqrt{3}}$

$\tt \implies \dfrac{AB}{BC} = \dfrac{1}{\sqrt{3}}$

$\tt \implies AB = 1x \: ; \: BC = \sqrt{3}x \: (x \: is \: positive)$

Now, by Pythagoras' theorem, we have

AC² = AB² + BC²

$\tt \implies AC^{2} = (1x)^{2} + (\sqrt{3}x)^{2}$

$\tt \implies AC^{2} = 1x^{2} + 3x^{2}$

$\tt \implies AC^{2} = 4x^{2}$

$\tt \implies AC = \sqrt{4x^{2}}$

$\tt \implies AC = 2x$

Now,

$\tt sin \theta = \dfrac{perpendicular}{hypotenuse}$

$\tt \implies sinA = \dfrac{BC}{AC}$

$\tt \implies sinA = \dfrac{\sqrt{3}x}{2x}$

$\tt \implies sinA = \dfrac{\sqrt{3}}{2}$

$\Large \boxed{\tt sinA = \dfrac{\sqrt{3}}{2}}$

$\tt cos \theta = \dfrac{base}{hypotenuse}$

$\tt \implies cosA = \dfrac{AB}{AC}$

$\tt \implies cosA = \dfrac{1x}{2x}$

$\tt \implies cosA = \dfrac{1}{2}$

$\Large \boxed{\tt cosA = \dfrac{1}{2}}$

$\tt tan \theta = \dfrac{perpendicular}{base}$

$\tt \implies tanA = \dfrac{BC}{AB}$

$\tt \implies tanA = \dfrac{\sqrt{3}x}{1x}$

$\tt \implies tanA = \sqrt{3}$

$\Large \boxed{\tt tanA = \sqrt{3}}$

$\tt cosec \theta = \dfrac{hypotenuse}{perpendicular}$

$\tt \implies cosecA = \dfrac{AC}{BC}$

$\tt \implies cosecA = \dfrac{2x}{\sqrt{3}x}$

$\tt \implies cosecA = \dfrac{2}{\sqrt{3}}$

$\Large \boxed{\tt cosecA = \dfrac{2}{\sqrt{3}}}$

$\tt sec \theta = \dfrac{hypotenuse}{base}$

$\tt \implies secA = \dfrac{AC}{AB}$

$\tt \implies secA = \dfrac{2x}{1x}$

$\tt \implies secA = 2$

$\Large \boxed{\tt secA = 2}$

5 0

4 years ago

Read 2 more answers

What is the slope of a line perpendicular to the line y = 2x + 5?

Setler79 [48]

2x is the slope, I think.

7 0

3 years ago

Plzz help solve the given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no

zloy xaker [14]

Answers:

<h3>x = 3</h3><h3>One solution</h3><h3>Identity</h3>

Step-by-step explanation:

In algebra, the goal is always to isolate the variable, so that its value can be determined.

<h3>Step 1: Use distributive property to remove parentheses</h3>

2x + 4x - 4 = 2 + 4x

<h3>Step 2: Add like terms</h3>

6x - 4 = 2 + 4x

<h3>Step 3: Subtract 4x</h3>

We need all variables on one side to solve, so subtract 4x from both sides.

2x - 4 = 2

2x = 6

<h3>Step 5: Divide by 2</h3>

x = 3

<h3>Step 6: Check</h3>

2(3) + 4(3) - 4 = 2 + 4(3)

6 + 12 - 4 = 2 + 12

14 = 14 ✔

<h3>Step 7: How many solutions?</h3>

The given equation has only one solution.

<h3>Step 8: Identity, a contradiction or neither?</h3>

The given equation is an identity.

<h3>Step 9: Answers</h3>

x = 3

One solution

Identity

I'm always happy to help :)

3 0

3 years ago