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3 years ago

PLEASE HELP!!!! and show your work

Mathematics

1 answer:

Goryan [66]3 years ago

4 0

The answer would be

4.41

my work is in the image below

hope this helps :)

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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.

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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5 0

1 year ago

P(7, then a number greater than 16)

krek1111 [17]

Can u give more details

5 0

3 years ago

Please help <br><br> asap plz!!

Anuta_ua [19.1K]

Answer:

$2x + 4 = 22$

$or \: 2x = 22 - 4$

$or \: 2x = 18$

$or \: x = \frac{18}{2}$

$therefor \: x = 9$

7 0

2 years ago

Read 2 more answers

Factor out the highest common factor.<br><br>

saw5 [17]

The highest common factor is found by multiplying all the factors which appear in both lists

a.(13-4b)(a+6)

13a-24b

13 and 24

so we have to factor this

13 =13×1

24=12×2=12 is 6×2=6 is 3×2=3 is 3×1=3×1

Therefore 1 and 1 get canceled

13×3=39

(a )39

like this we have to solve........

4 0

3 years ago

Keith asked 30 people whether they knew how to play whist or dominoes. Fifteen of them knoew how to play whist and 20 knew how t

adelina 88 [10]

Ok so, 15 of them know how to play whist (I have no idea what that is) and 20 of them know how to play dominoes, 5 of them do not. So, if you add up 20+15=35, take off 10 35-10=25 so it must mean that 10 is the answer. (Also if you add 5 to that 25+5=30)
The Answer is 10

7 0

3 years ago