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3 years ago

(AM GIVING BRAINLIEST) Find all values of x such that x/(x - 5) =4/(x - 4)

Mathematics

2 answers:

Irina18 [472]3 years ago

4 0

Answer:

x = imaginary number

x₁ = 2i

x₂ = 6i

Step-by-step explanation:

x/(x - 5) =4/(x - 4)

x(x-4) = 4(x-5)

x*x + x*-4 = 4*x * 4*-5

x² -4x = 4x - 20

x² -4x - 4x + 20 = 0

x² - 8x + 20 = 0

x = {-(-8)±√((-8²)-(4*1*20))} / (2*1)

x = {8±√(64-80)} / 2

x = {8±√-16} / 2

√(-16) ∈ i

i = set of imaginary numbers

√-16 = -4i

then:

x = {8±(-4i) } / 2

x₁ = {8+(-4i)}/2 = {8-4i)/2 = 4i/2 = 2i

x₂ = {8-(-4)}/2 = {8+4i}/2 = 12i/2 = 6i

lesya [120]3 years ago

3 0

Answer:

$\boxed{\sf x = 4 \pm 2i}$

Step-by-step explanation:

$\sf Solve \: for \: x: \\ \sf \implies \frac{x}{x - 5} = \frac{4}{x - 4} \\ \\ \sf Cross \: multiply: \\ \sf \implies x(x - 4) = 4(x - 5) \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \sf \implies {x}^{2} - 4x = 4(x - 5) \\ \\ \sf Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ \sf \implies {x}^{2} - 4x = 4x - 20 \\ \\ \sf Subtract \: 4 x \: from \: both \: sides:\\ \sf \implies {x}^{2} - 4x - 4x = 4x - 20 - 4x \\ \\ \sf \implies {x}^{2} - 8x = - 20\\ \\ \sf Add \: 16 \: to \: both \: sides: \\ \sf \implies {x}^{2} - 8x + 16 = - 20 + 16 \\ \\ \sf\implies {x}^{2} - 8x + 16 = -4 \\ \\ \sf Write \: the \: left \: hand \: side \: as \: a \: square: \\ \sf\implies {x}^{2} - 4x - 4x + 16 = -4 \\ \\ \sf\implies x(x - 4) - 4(x - 4) = -4 \\ \\ \sf\implies (x - 4)(x - 4) = -4 \\ \\ \sf\implies {(x - 4)}^{2} = - 4 \\ \\ \sf Take \: the \: square \: root \: of \: both \: sides: \\ \sf\implies \sqrt{ {(x - 4)}^{2}} = \sqrt{ - 4} \\ \\ \sf\implies x - 4 = \pm 2i \\ \\ \sf Add \: 4 \: to \: both \: sides: \\ \sf\implies x - 4 + 4= \pm 2i + 4 \\ \\ \sf\implies x = 4\pm 2i$

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Answer:

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Step-by-step explanation:

Answers above! Hoped this helped :)

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3 years ago

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shepuryov [24]

Answer:

Step-by-step explanation:

The recommended sample size n for point estimates is:

n = NX / (N + X - 1)

where N is the population size, and X is defined as:

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where Z is the critical value, p is the sample proportion, and E is the margin of error.

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n = (2000) (73) / (2000 + 73 - 1)

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Rounding, the recommended sample size is 70.

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3 years ago

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write a function g whose graph represents a translation 2 units to the right followed by a horizontal stretch by a factor or 2 o

Alenkinab [10]

$\bf f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}\\\\
f(x)=&{{ A}} \left|{{ B }}x+{{ C}} \right|+{{ D}}
\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see,

$\bf f(x)=|x| \implies \begin{array}{lllccll}
f(x)=&1|&1x&+0|&+0\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

so, to shift it to the right by 2 units, simply set C = 2.
to stretch it by 2, set A = 1/2.

the smaller A is, the wider it opens, the larger it is, the more it shrinks.

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3 years ago

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natulia [17]

Answer:

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c) 0.018

d) 0.982

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Step-by-step explanation:

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