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3 years ago

PLEASE HELP EASY MATH

Mathematics

1 answer:

Alexxx [7]3 years ago

7 0

Answer:90

Step-by-step explanation:

When the sum of two angles is 90°, then the angles are known as complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles.

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If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(

timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

2 years ago

What does the unit rate represent

Furkat [3]

Answer: rate is a ratio that is used to compare different kinds of quantities. A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

7 0

3 years ago

A piece of blue yarn is 5/ 3/7 yards long. A piece of pink yarn is 5 times as long as the blue yarn. How much longer is the pink

MaRussiya [10]

Answer:

27 1/7

Step-by-step explanation:

Multiply 5×5=25 and afterwards multiply 3/7×5=2 1/7

8 0

3 years ago

*will give brainliest*

andriy [413]

I think the answer is one solution

3 0

2 years ago

What is the domain and range of y=x^2?

r-ruslan [8.4K]

Hi there! the best way of solving this is picturing out what the graph might look like. Let's assume you had the graph of a parabola y=x^2. You know that for every x you substitute, there'd always be a value for y. Thus, the domain is ALL REAL NUMBERS or from -INFINITY to + INFINITY. The range on the other hand is different. We know that any number raised to the second power will always yield a positive integer or 0. Thus, y=x^2 won't have any negative y-values as the graph opens upward. Therefore, the range is: ALL REAL NUMBERS GREATER THAN OR EQUAL TO 0. or simply: 0 to +INFINITY.

<span>On the other hand, a cubic function y=x^3 is quite different from the parabola. For any x that we plug in to the function, we'd always get a value for y, thus there are no restrictions. And the domain is ALL REAL NUMBERS or from -INFINITY to + INFINITY. For the y-values, the case would be quite similar but different to that of the y=x^2. Since a negative number raised to the third power gives us negative values, then the graph would cover positive and negative values for y. Thus, the range is ALL REAL NUMBERS or from -INFINITY to + INFINITY. Good luck!!!:D</span>

3 0

3 years ago

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