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SVEN [57.7K]
3 years ago
6

Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.

Mathematics
2 answers:
allochka39001 [22]3 years ago
7 0

Answer:

(x + 1/4)^2 = -15/16

Step-by-step explanation:

Gelneren [198K]3 years ago
5 0
<span>divide both sides of the equation by 2 to get: 

(x + 1/4)^2 = -7/16 ***** this is your solution. 

continue further to solve for x if you care to, but the problem did not require you to do this. 

take the square root of both sides of the equation to get: 

x + 1/4 = plus or minus sqrt(-7/16) 

subtract 1/4 from both sides of the equation to get x = -1/4 plus or minus sqrt(-7/16). 

since sqrt(-7/16) is the same as sqrt(7/16) * i, your solution becomes: 

x = -1/4 plus or minus sqrt(7/16) * i. 

your problem was to convert it to the form of (x + p)2 = q. 

the solution to that is: 

</span><span>(x + 1/4)^2 = -7/16 </span><span>subtract 1 from both sides of the equation to get: 

2x^2 + x = -1 

factor out a 2 on the left side of the equation to get: 

2 * (x^2 + x/2) = -1 

complete the squares on x^2 + x/2 to get: 

2 * ((x+1/4)^2 - (1/16)) = -1 

simplify by distibuting the multiplication to get: 

2 * (x+1/4)^2 - 2*(1/16) = -1 

simplify further to get: 

2 * (x+1/4)^2 - 1/8 = -1 

add 1/8 to both sides of the equation to get: 

2 * (x + 1/4)^2 = -7/8 .



</span>
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77julia77 [94]

Answer:

a) Y= 90 +46.50(5) +0.35 (340) =441.50

b) The accountant should not question the voucher as the request is much higher than expected.

c) We can add the following variables

d) The percentage of variation in the trip cost that can be explained by the model​ = (0.64)^2 =0.4096 or 40.96%

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Step-by-step explanation:

Part a

For this case we have the multiple regression model given by:

Y= 90 +46.50 x_1 +0.35 x_2

Where x_1 represent the number of days on the road and x_2 the distance traveled in miles.

And we want to find the expected amount from a 340​-mile trip that took her out of town for 5 ​days, so we just need to replace x1= 5 and x2=340 and we got:

Y= 90 +46.50(5) +0.35 (340) =441.50

Part b

The expected value taking in count that x1 = 5 and y = 340 is:

Y= 90 +46.50(55) +0.35 (340) =441.50

And the difference from the obtained value is : 685-441.50=243.5

So then the correct answer would be:

The accountant should not question the voucher as the request is much higher than expected.

Part c

We can add the following variables

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

The coefficient of determination "is a measure used in statistical analysis that assesses how well a model explains and predicts future outcomes. It is indicative of the level of explained variability in the data set".

The percentage of variation in the trip cost that can be explained by the model​ = (0.64)^2 =0.4096 or 40.96%

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Step-by-step explanation:

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