Determine the perimeter of the following figures

mr Goodwill [35]

Answer: 2.813 .......

7 0

3 years ago

Which expressions are equivalent to 2 ln a 2 ln b - ln a? Check all that apply. Ln ab2 - ln a ln a 2 ln b ln a2 ln b2 - ln a 2 l

marysya [2.9K]

Equivalent expressions are expressions with same simplified form. Equivalent expressions for the given expression are;

Expression 2: $\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)$
Expression 3: $\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)$
Expression 5: $\ln(ab^2)$

<h3>What are equivalent expressions?</h3>

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

$a^b = c$

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

$b = log_a(c)$

Some properties of logarithm are:

$log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1\\\\ log_a(b) + log_b(c) = log_a(c)$

Log with base e = 2.71828.... is written as $\ln(x)$ simply.

The expression given is $2\ln(a) + 2\ln(b) - \ln(a)$

We get its simplified form as

$2\ln(a) + 2\ln(b) - \ln(a) = \ln(a) + \ln(b^2) = \ln(ab^2)$

Simplifying given expressions:

Expression 1: $\ln(ab^2) - \ln(a) = \ln(ab^2/a) = \ln(b^2)$

This isn't same as simplified form of original

. Thus , this expression is not equivalent to the given expression.

Expression 2: $\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)$

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

Expression 3: $\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)$

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

Expression 4: $2\ln(ab) = \ln((ab)^2) = \ln(a^2b^2)$

This isn't same as simplified form of original expression. Thus , this expression is not equivalent to the given expression.

Expression 5: $\ln(ab^2)$

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

Thus, equivalent expressions for the given expression are;

Expression 2: $\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)$
Expression 3: $\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)$
Expression 5: $\ln(ab^2)$

Learn more about equivalent expressions here:

brainly.com/question/10628562

4 0

2 years ago

Who can see if they can help me with this

goldfiish [28.3K]

Answer:

vertical angles, Vertical Angles are the angles opposite each other when two lines cross. "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.

Complementary angles are two angles with a sum of 90º. Supplementary angles are two angles with a sum of 180º. Vertical angles are two angles whose sides form two pairs of opposite rays. We can think of these as opposite angles formed by an X.

Step-by-step explanation:

6 0

3 years ago

726 ÷3 use place value disks

alexandr402 [8]

Hello. I’d you were to divide seven-hundred and twenty six (726) by three (3) You would receive the complete answer being 242. Hope this helps! :)

7 0

3 years ago

Read 2 more answers

I NEED HELP! simplify this expression

ioda

Answer:

25

Step-by-step explanation:

36-1*16+5 (PEMDAS, exponents first)

36-16+5 (PEMDAS, multiplication)

20+5 (PEMDAS, add and subtract left to right)

25 (PEMDAS, add and subtract left to right)

7 0

3 years ago