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Vladimir79 [104]
2 years ago
6

5. Change the following mixed numbers to improper

Mathematics
1 answer:
bonufazy [111]2 years ago
3 0
A.23/6
b.23/8
c.26/5
d.64/9
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Find the value of x.<br> M<br> (Round to the nearest degree as needed)
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Answer:

28

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=4%20%20%20%7B%7D%5E%7Bx%20%7D%20%20%2B%206%20%7B%7D%5E%7Bx%7D%20%3D%209%20%7B%7D%5E%7Bx%7D%20%
Nookie1986 [14]

So, the value of x is 1.19

The question is an exponential equation

<h3>What is an exponential equation?</h3>

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

<h3>How to find x?</h3>

Since 4^{x} + 6^{x} = 9^{x},

Dividing through by 4ˣ, we have

\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} }  = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} }  = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} }  = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} }  = (\frac{3}{2})^{2x} }

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or  \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or  \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or  \frac{3.236}{2}\\= -0.618 or 1.618

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

Learn more about exponential equation here:

brainly.com/question/11832081

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1 year ago
What is the ratio of 3/20
Sveta_85 [38]
The ratio of 3/20 is 3:20
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3 years ago
(-5,-1); 2y=2x-4 help me ASAP please
PIT_PIT [208]

Answer:

u trrahs at fritnote

Step-by-step explanation:

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