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Kazeer [188]
2 years ago
5

What is the equation of this line in standard form? (-4, -1) & (1/2, 3)

Mathematics
1 answer:
BabaBlast [244]2 years ago
4 0

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{\frac{1}{2}}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{\frac{1}{2}}-\underset{x_1}{(-4)}}}\implies \cfrac{3+1}{\frac{1}{2}+4}\implies \cfrac{4}{~~\frac{9}{2}~~}\implies \cfrac{4}{1}\cdot \cfrac{2}{9}\implies \cfrac{8}{9}

\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{8}{9}}[x-\stackrel{x_1}{(-4)}]\implies y+1=\cfrac{8}{9}(x+4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{9}}{9(y+1)=9\left( \cfrac{8}{9}(x+4) \right)}\implies 9y+9=8(x+4)\implies 9y+9=8x+32 \\\\\\ 9y=8x+23\implies -8x+9y=23\implies 8x-9y=-23

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2 years ago
Why are the solutions to the proportions 40/8 = x/10 and x/40 = 10/8 the same?
romanna [79]

Answer:

Both proportions are equivalent.

Step-by-step explanation:

We have been given two proportions \frac{40}{8}=\frac{x}{10} and \frac{x}{40}=\frac{10}{8}. We are asked to find why the solutions to our given proportions are equal.

We can solve proportions by cross multiplying them.

After cross multiplying our both proportions we will get same equation that is:

40*10=8*x

400=8x

8*x=40*10

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Since we get same equation after cross multiplying both proportions, therefore, the solutions to the given proportions would be same.

4 0
3 years ago
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how many ounces of water must be added 100 oz. of 60% iodine to produce a 55% solution ? round your answer to the nearest hundre
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Step-by-step explanation:

8 0
2 years ago
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The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds
Bumek [7]
Answer: 11.5% 

Explanation:


Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds. 

Now, we get the z-score for 720 seconds by the following formula:

\text{z-score} =  \frac{x - \mu}{\sigma}

where 

t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
\\ \mu = \text{average time for the auditor to finish his work } = 600 \text{ seconds}
\\ \sigma = \text{standard deviation } = 100 \text{ seconds}

So, the z-score of 720 seconds is given by:

\text{z-score} = \frac{x - \mu}{\sigma}
\\
\\ \text{z-score} = \frac{720 - 600}{100}
\\
\\ \boxed{\text{z-score} = 1.2}

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

P(t \ \textgreater \  720) 
\\ = P(z \ \textgreater \  1.2)
\\ = 1 - P(z \leq 1.2)
\\ = 1 - 0.885
\\  \boxed{P(t \ \textgreater \  720)  = 0.115}

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice. 
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Answer:

Answer is 36

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