What is the discriminant of 9х2 + 2 = 10x?

1 answer:

5 0

$\bf 9x^2+2=10x\implies 9x^2-10x+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-10}x\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}~~\checkmark\\ negative&\textit{no solution} \end{cases} \\\\\\ (-10)^2-4(9)(2)\implies 100-72\implies 28$

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Step-by-step explanation:

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3 years ago

What are the remaining angle measures if the figure is to be a parallelogram?

goldfiish [28.3K]

The correct answer is

m∠B ==101°,

m∠C =79°,

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Step-by-step explanation:

As we know that, it is a parallelogram opposite angels are congruent
Therefore, m∠A = m∠C and m∠B =m∠B

As we know that, If side a=79 then side c must also be equal to 79

When we consider all the angles and add them it must be equal to 360°
When we add 79+79 = 158°, which mean a=c= 158°

By subtracting all the sides of parallelogram which is 360- 158= 202°
If we divide it by 2 then we will get the value of the other side of the angle which is b and d.
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$\frac{202}{2}$ = 101°
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3 years ago

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Suppose a sample of 80 with a sample proportion of 0.58 is taken from a

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99.7% confidence interval is $[0.4162,0.7437]$

Step-by-step explanation:

The formula for a confidence interval for a population proportion is $CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }$ where $\hat{p}$ is the sample proportion, $n$ is the sample size, and $z^*$ is the critical score for the desired confidence level.

We are given a sample size of $n=80$ and a sample proportion of $\hat{p}=0.58$ . Our critical score for a 99.7% confidence level would be $z^*=normalcdf(0.9985,0,1)=2.9677$

Therefore, the approximate 99.7% confidence interval for the population parameter is $CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }=0.58\pm 2.9677\sqrt{\frac{0.58(1-0.58)}{80} }=[0.4162,0.7438]$