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1 year ago

Using the quadratic formula to solve 5x = 6x²-3, what are the values of x?

Mathematics

1 answer:

Salsk061 [2.6K]1 year ago

8 0

Answer:

$\boxed{\sf{x = \frac{5 \pm \sqrt{97} }{12} }}$

Step-by-step explanation:

$\sf{5x = 6 {x}^{2} - 3 }$

$\sf{0 = 6 {x}^{2} - 3 - 5x }$

$\sf{0 = 6 {x}^{2} - 5x - 3 }$

a = 6
b = - 5
c = - 3

$\sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }$

$\sf{x = \frac{ - ( - 5) \pm \sqrt{ { - 5}^{2} - 4(6)( - 3)} }{2(6)} }$

$\sf{x = \frac{5 \pm \sqrt{ 25 + 72} }{12} }$

$\sf{x = \frac{5 \pm \sqrt{97} }{12} }$

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Number of shares
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After one year share value
10×(1+0.13)=11.3
After the second year share value
11.3×(1−0.05)=10.735
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2 years ago

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2 years ago

A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in

erica [24]

Answer:

$\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54$

The degrees of freedom are:

$df=n-1=10-1=9$

Now we can calculate the p value using the alternative hypothesis:

$p_v =2*P(\chi^2 >13.54)=0.279$

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

Step-by-step explanation:

Assuming the following data:"12.14 12.05 12.27 11.89 12.06

12.14 12.05 12.38 11.92 12.14"

We can calculate the sample deviation with this formula:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$n=10$ represent the sample size

$\alpha=0.05$ represent the confidence level

$s^2 =0.0217$ represent the sample variance

$\sigma^2_0 =0.12^2= 0.0144$ represent the value to verify

Null and alternative hypothesis

We want to determine whether the standard deviation differs from 0.12 ounce, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 = 0.0144$

Alternative hypothesis: $\sigma^2 \neq 0.0144$

The statistic can be calculated like this;

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

$\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54$

The degrees of freedom are:

$df=n-1=10-1=9$

Now we can calculate the p value using the alternative hypothesis:

$p_v =2*P(\chi^2 >13.54)=0.279$

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2 years ago

How is domain of the function f(x)=sinx restricted so that its inverse function exists?

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Answer:

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Step-by-step explanation:

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3 years ago

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stiv31 [10]

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