All categories

3 years ago

Rewrite the function by completing the square F(x)=2x^2+3x-2

Mathematics

2 answers:

Lady bird [3.3K]3 years ago

6 0

y = 2 ( x + 3/4 )^2 − 25 8

siniylev [52]3 years ago

5 0

Answer:

$\boxed{ \ 2(x+\dfrac{3}{4})^2-\dfrac{25}{8}\ }$

Step-by-step explanation:

we should write this function

$2x^2+3x-2$

this way $a(x-b)^2+c$

let s check the first terms in $x^2$ and x

$2x^2+3x$

this is the beginning of

$2(x+\dfrac{3}{4})^2$

indeed

$2(x+\dfrac{3}{4})^2=2x^2+3x+2(\dfrac{3}{4})^2=2x^2+3x+\dfrac{9}{8}$

so we can write that

$2x^2+3x=2(x+\dfrac{3}{4})^2-\dfrac{9}{8}$

then

$2x^2+3x-2=2(x+\dfrac{3}{4})^2-\dfrac{9}{8}-2=2(x+\dfrac{3}{4})^2-\dfrac{9+16}{8}=2(x+\dfrac{3}{4})^2-\dfrac{25}{8}$

You might be interested in

Heather can rake and fill 6.8 bags of leaves each hour how many bags of leaves will heather rake and fill in 17 hours

Sergeu [11.5K]

Answer:

115.6

Step-by-step explanation:

115.6, this would be your answer because 17 hours × 6.8 would get you 115.6

so 17 × 6.8 = 115.6

6 0

3 years ago

Witch order pair is a solution<br><br> -2x+6y=16. -4x-3y=2

Bezzdna [24]

Answer:

The ordered pair solution is (-2,2)

Step-by-step explanation:

Here, we want to get the ordered pair solution to the system of linear equations

From the first equation, we can have it that;

-2x = 16-6y

Now, we can substitute this into the second equation as follows;

From; -4x -3y = 2

2(-2x) - 3y = 2

2(16-6y) - 3y = 2

32 - 12y - 3y = 2

32-15y = 2

-15y = 2-32

-15y = -30

y = -30/-15

y = 2

Recall;

-2x + 6y = 16

substitute for the value of y

-2x + 6(2) = 16

-2x + 12 = 16

-2x = 16-12

-2x = 4

x = 4/-2

x = -2

7 0

3 years ago

Six times the difference of 2a and B increased by 4B

prisoha [69]

6(2a-b)+46 Then when you simplify it : 12a-6b+46

5 0

3 years ago

Read 2 more answers

I need help again please

Verdich [7]

A variety of different religions

5 0

3 years ago

Read 2 more answers

The Late Show with David Leterman is seen by a relatively large percentage of household members who record the show for viewing

Zanzabum

Answer:

a) Null hypothesis: $\mu \leq 40000$

Alternative hypothesis: $\mu > 40000$

b) $t=\frac{41182-40000}{\frac{19990}{\sqrt{1700}}}=2.438$

c) The first step is calculate the degrees of freedom, on this case:

$df=n-1=1700-1=1699$

Since the sample size is large enough we cna use the z distribution as an approximation for the statsitic on this case.

Since is a one right tailed test the p value would be:

$p_v =P(t_{(1699)}>2.438)=0.0074$

d) If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis at 1% of signficance. So we can conclude that the true mean is higher than 40000 at the significance level assumed.

Step-by-step explanation:

Data given and notation

$\bar X=41182$ represent the sample mean

$s=19990$ represent the sample standard deviation

$n=1700$ sample size

$\mu_o =40000$ represent the value that we want to test

$\alpha=0.01$ 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: State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is greater than 40000, the system of hypothesis would be:

Null hypothesis: $\mu \leq 40000$

Alternative hypothesis: $\mu > 40000$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b: Calculate the statistic

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

$t=\frac{41182-40000}{\frac{19990}{\sqrt{1700}}}=2.438$

Part c: P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=1700-1=1699$

Since the sample size is large enough we cna use the z distribution as an approximation for the statsitic on this case.

Since is a one right tailed test the p value would be:

$p_v =P(t_{(1699)}>2.438)=0.0074$

Part d: Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis at 1% of signficance. So we can conclude that the true mean is higher than 40000 at the significance level assumed.

3 0

3 years ago