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3 years ago

Discriminant of 9x^2+12x+4=0

2 answers:

7 0

$9x^2+12x+4=0\\\\(3x)^2+2\cdot3x\cdot2+2^2=0\\\\(3x+2)^2=0\iff3x+2=0\\\\3x=-2\ \ \ /:3\\\\x=-\frac{2}{3}\\\\-------------------------------\\\\(a+b)^2=a^2+2ab+b^2$

BartSMP [9]3 years ago

4 0

$the\ discriminant\ of\ ax^2+bx+c=0:\ \ \ \ \Delta=b^2-4\cdot b\cdot c \\---------------------------\\9x^2+12x+4=0\ \ \ \Rightarrow\ \ \ \Delta=12^2-4\cdot9\cdot4=144-144=0\\\\\Delta=0\ \ \ \Rightarrow\ \ \ x_0=- \frac{b}{2a} =- \frac{12}{2\cdot9} =- \frac{2\cdot2\cdot3}{2\cdot3\cdot3}= - \frac{2}{3} \\\\Ans.\ The\ discriminant\ is\ \Delta=0$

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Chance knows the length of a football field (including end zones) is 120 yards. The width of the football field is 53.33 yards.

Ira Lisetskai [31]

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6 0

3 years ago

Read 2 more answers

Suppose for some value of x the solution to the equation 2.5(y−x)=0 is y = 6. What must be true about x?

Varvara68 [4.7K]

Step-by-step explanation:

In this case, you input the value of y (y = 6) into the equation ( 2.5(y-x)= 0)

2.5(6-x) = 0

Open the bracket,

(2.5×6)-2.5x= 0

Collect like terms.

2.5x= 2.5×6

Divide both sides by the coefficient of x (2.5)

x = 6

So,

x= 6 is true.

Substituting 6 for x in the equation,

2.5(6-6)= 0

2.5•0 = 0

0= 0

Which is also true.

7 0

2 years ago

The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32

myrzilka [38]

Answer:

a) $(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

b) $t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

Step-by-step explanation:

Data given and notation

$\bar X_{A}=14.68$ represent the mean for Pirates

$\bar X_{B}=18.77$ represent the mean for Splash Mountain

$s_{A}=11.87$ represent the sample standard deviation for the sample Pirates

$s_{B}=16.79$ represent the sample standard deviation for the sample Slpash Mountain

$n_{A}=32$ sample size selected for Pirates

$n_{B}=30$ sample size selected for Splash Mountain

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a

The confidence interval would be given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 32+30-2 = 60$

Since we want 98% of confidence the significance level is $\alpha =1-0.98 =0.02$ and $\alpha/2 =0.01$ , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

$t_{\alpha/2}= 2.39$

And replacing we got for the confidence interval:

$(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

the statistic is given by:

$t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

6 0

3 years ago

A superhero can fly from New York to Los Angeles in 30 minutes. The distance from New York to Los Angeles is approximately 2,450

kow [346]

<h3>Answer: 4900 mph</h3>

Work Shown:

30 min = 30/60 = 0.5 hours

distance = rate*time

rate = distance/time

rate = (2450 miles)/(0.5 hours)

rate = (2450/0.5) mph

rate = 4900 mph

For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.

7 0

2 years ago

Solve the proportion

Vanyuwa [196]

W is equal to 19/4 or 4.75

Hope this helps! :)

7 0

3 years ago