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Maru [420]
3 years ago
14

20%29%29%20%2B%20%20%7B2%7D%5E%7B2%7D%20%20%3D%200" id="TexFormula1" title=" {2}^{x} - 3( {2}(^{x} + \frac{1}{2} )) + {2}^{2} = 0" alt=" {2}^{x} - 3( {2}(^{x} + \frac{1}{2} )) + {2}^{2} = 0" align="absmiddle" class="latex-formula">
Can someone solve this equation?​
Mathematics
1 answer:
8_murik_8 [283]3 years ago
4 0

Answer:   \huge\boxed{x=log_2\frac{12\sqrt{2}+4}{17}}

Step-by-step explanation:                                                                       \displaystyle\ \bigg{2^x-3(2^{x+\frac{1}{2} }})+2^2=0 \qquad  ; \ \ \boxed{t=2^x} \\\\t-3t\sqrt{2} +4=0  \\\\ t(1-3\sqrt{2} )=-4 \\\\ t=\frac{4}{3\sqrt{2} -1} \cdot \frac{3\sqrt{2}+1 }{3\sqrt{2}+1 } =\frac{12\sqrt{2}+4}{17}  \\\\\\2^x=\frac{12\sqrt{2}+4}{17} \\\\x=log_2 \ \ \frac{12\sqrt{2}+4}{17}

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Answer:

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If we plug in $60 as s (school clothes) and $20 as g (gym clothes), the statement is true.

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60 ≥ 60. These numbers make the linear system true.

If you have trouble with this, an easy way to find this answer is simply creating the linear system that represents the problem, (he will buy 3 times more school clothes than gym clothes) s ≥  3g and plug in each variable from the answer choices until you find the variables that make the linear system true.


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Two vertical poles of lengths 11 ft and 14 ft stand 16 ft apart. A cable reaches from the top of one pole to some point on the g
Alex17521 [72]

We are given

total length of cable is 30 feet

and this cable is on hypotenuse sides of the triangles

so, we can draw triangle as

Let's assume those hypotenuse as 'a' and 'b'

so, we will have

a+b=30

now, we can find 'a' and 'b' from triangle

Smaller triangle:

a=\sqrt{x^2+11^2}

Larger triangle:

b=\sqrt{(16-x)^2+14^2}

we know that

a+b=30

so, we can plug this value

and we get

\sqrt{x^2+11^2}+\sqrt{(16-x)^2+14^2} =30

now, we can solve for x

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so,

The point should be located 4.510 feet , 9.627 feet from the smaller pole to use 30 feet cable............Answer

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