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Andru [333]
2 years ago
6

Also need help with this one

Mathematics
1 answer:
katen-ka-za [31]2 years ago
8 0
Let the width of table B be w, and since area of table A = area of table B, then 6 2/3 x 3 1/2 = 4 1/4 x w    [this is the required equation]
20/3 x 7/2 = 17/4 w
17/4 w = 70/3
w = 70/3 / 17/4 = 70/3 x 4/17 = 280/51 = 5 25/51
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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

#SPJ1

5 0
1 year ago
Is 5/8 more than 2/3
Andre45 [30]
No. 2/3 is bigger than 5/8 because if you convert them to where the denominator is the same, 5/8= 15/24 and 2/3 is equal to 16/24
8 0
3 years ago
ANSWER FAST!!! Which property was used to write the equation in step 2?
k0ka [10]

Answer:

ummm what step?

whats the equation?

Step-by-step explanation:

4 0
3 years ago
PLEASE HELP ILL MARK BRAILEST
lbvjy [14]

Answer:

it is around 51

Step-by-step explanation:

sorry i'm doing this again, my answer got deleted :(

5 0
3 years ago
Read 2 more answers
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5/4x-
dimaraw [331]

Answer:

has only one solution: x=8, y=3

Step-by-step explanation:

\left \{ {{\frac{5x}{4} -\frac{2y}{3}=8(equation 1)} \atop {\frac{x}{4} +\frac{5y}{3} =7(equation 2)}} \right\\

substract  \frac{1}{5}×(equation 1) from equation2

\left \{ {{\frac{5x}{4} -\frac{2y}{3}=8(equation 1)} \atop {0x +\frac{9y}{5} =\frac{27}{5}(equation 2)}} \right\\

from equation 2 we obtain

y=\frac{27}{9} =3

and we replace 3 in equation 1

\frac{5x}{4} -\frac{2(3)}{3} =8\\\\\frac{5x}{4} =10\\\\x=\frac{40}{5} =8

5 0
3 years ago
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