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kenny6666 [7]
3 years ago
12

What is the value of the bisecting angle, x, marked on this square?

Mathematics
2 answers:
lord [1]3 years ago
5 0

The four corners of a square are 90 degrees.

They are evenly split by the diagonal lines, so each corner is now two 45 degree angles.

The lines form triangles, which have 3 angles that need to equal 180 degrees.

Two of the angles are 45, so 45 + 45 = 90 degrees.

X = 180 -90 = 90 degrees.

Norma-Jean [14]3 years ago
4 0

Answer:

90 degrees

By 90 * 4 is 360

Step-by-step explanation:

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First you have to identify the black line at the bottom so it means it's 180 degrees. No notice the red box it means it's 90 degrees. We can conclude from this that the other side of the red box should also equal 90 degrees. So to find x you have to set up this equation: 6x+4+32=90. Then you solve for x which ends up being 9.

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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

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2 years ago
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