Can someone help me with this ASAP?

<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.

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:

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5 0

1 year ago

15% of $9 is $ this is a question on my math worksheet please respond quick and show the steps on how to do it please and thank

Vladimir79 [104]

9 times .15 = 1.35
15% of $9 is $1.35

5 0

3 years ago

Read 2 more answers

Area of a Triangle

jek_recluse [69]

Answer:

3.51 (round to the nearest hundreds)

Step-by-step explanation:

PART A

slope of the line passing through AC : (6-1)/(1-2) = 5/-1 = -5

equation of the line passing through B and perpendicular to AC:

y-3 = 1/5(x-3)

y-3 = 1/5x -3/5

y = 1/5 x - 3/5 + 3

y = 1/5 x + (-3+15)/5

y = 1/5 x + 12/5

PART B

line that passes through the points A and C

y-1 = -5(x-2)

y = -5x+10 + 1

y = -5x + 11

Interception of the lines

y = 1/5x + 12/5

y = -5x + 11

-5x + 11 = 1/5x + 12/5

-25x +55 = x + 12

26x = 43

x = 43/26

y = -5(43/26) + 11

y= -215/26 + 11

y = (-215+286)/26 = 71/26

D (1.65, 2.73)

PART C

AC = $\sqrt{(1-2)^2 + (6-1)^2} = \sqrt{1 + 25} = \sqrt{26}$ = 5,09902

BD = $\sqrt{(3-1.65)^2 + (3-2.73)^2}$ = 1,376735

PART D

AREA = (5,09902 * 1.376735)/2 = 3,509999

8 0

3 years ago

If x=7+4√3,find the value of √x+¹/√x

Tcecarenko [31]

<h2><em>Answer:</em></h2><h2><em>Answer:x = 7+4√3</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√3</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we get</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we get1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we get1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =1/√x = 2-√3</em></h2><h2 /><h2><em>Answer:x = 7+4√3To find √x we proceed,√x = √(7+4√3)√x = √(7+2x2√3)√x = √(7+2√3x4)√x = √(3+4+2√3x4)….. {writing 7 = 3+4}If we observe RHS of √x we observe form of√(a² + b² +2ab) where a=√3 and b =√4Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3√x = 2+√31/√x = 1/(2+√3)Multiplying both numerator and denominator by 2 - √3, we get1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =1/√x = 2-√3Hence √x +1/√x = 2+√3 +2 -√3 = 4</em></h2><h2 />

4 0

3 years ago

Evaluate each function in the table for f(3)

kogti [31]

Answer:

Function 1:

We have 3x + 5, so we plug in 3 for x to get 9 + 5 = $\boxed{14}$