All categories

3 years ago

Determine if the statement is always, sometimes, or never true: A scalene triangle is an acute triangle.

Mathematics

2 answers:

Lana71 [14]3 years ago

7 0

Always true.....……................

Marina86 [1]3 years ago

3 0

Answer:

it is true

Step-by-step explanation:

You might be interested in

- 9.9t = - 9.9 solve for t

vampirchik [111]

T=1

Hope that helps bud!

5 0

3 years ago

What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?

scoray [572]

Answer:

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to c} x = c$

Special Limit Rule [L’Hopital’s Rule]:
$\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]:
$\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$
Derivative Rule [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:

Step 1: Define

Identify given limit.

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}$

Step 2: Find Limit

Let's start out by directly evaluating the limit:

[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \frac{\sqrt{3 + 1} - 2}{3 - 3}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \frac{\sqrt{3 + 1} - 2}{3 - 3} \\& = \frac{0}{0} \leftarrow \\\end{aligned}$

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

[Limit] Apply Limit Rule [L' Hopital's Rule]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\\end{aligned}$
[Limit] Differentiate [Derivative Rules and Properties]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \leftarrow \\\end{aligned}$
[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \leftarrow \\\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \\& = \boxed{ \frac{1}{4} } \\\end{aligned}$

∴ we have evaluated the given limit.

___

Learn more about limits: brainly.com/question/27807253

Learn more about Calculus: brainly.com/question/27805589

___

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

3 0

2 years ago

3. Which ordered pair is a solution of the equation y=x-3?

Vlada [557]

The answer is B (-5,2)

3 0

3 years ago

Uma balconista vendeu 70 centímetros de tecido a um freguês. Essa balconista preencheu corretamente a nota fiscal, escrevendo:

Evgesh-ka [11]

Answer:

Step-by-step explanation:

A clerk sold 70 centimeters of fabric to a customer. This clerk correctly filled out the invoice, writing:

1 point

a) 0.07 m

b) 0.070 m

c) 0.070 cm

d) 0.70 m

The clerk sold 70cm of fabrics

So, she want to filled the invoice but it length of fabrics sold must be in metre.

From metric units

100cm = 1m

Then,

70 cm = x

100cm = 1m

Cross multiply

70 cm × 1m = x × 100cm

Divide both side by 100cm

Then,

x = 70 cm × 1 m / 100cm

cm cancel out

x = 70 × 1m / 100

x = 70m / 100

x = 0.7m.

So, the correct answer is D.

To Portuguese

O funcionário vendeu 70cm de tecidos

Então, ela deseja preencher a fatura, mas o comprimento dos tecidos vendidos deve estar em metros.

De unidades métricas

100cm = 1m

Então,

70 cm = x

100cm = 1m

Multiplicação cruzada

70 cm × 1 m = x × 100 cm

Divida os dois lados por 100cm

Então,

x = 70 cm × 1 m / 100 cm

cm cancelar

x = 70 × 1m / 100

x = 70m / 100

x = 0,7 m.

Então, a resposta correta é D.

7 0

3 years ago

What are reasons A,B,and C in the proof?

Vlad [161]

Answer:

Option D is correct.

Explanation:

Commutative Property of Multiplication define that two numbers can be multiplied in any order.

i.e $a\times b =b \times a$

Distributive property of multiplication states that when a number is multiplied by the sum of two numbers i.e, the first number can be distributed to both of those numbers and multiplied by each of them separately.

$a \times (b+c) = a\times b+ a\times c$