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Bumek [7]
3 years ago
7

Complete the square: ax^2 + x + 3.

Mathematics
2 answers:
RUDIKE [14]3 years ago
8 0

Answer:

The value of a is \frac{1}{12}.

Step-by-step explanation:

The given expression is

ax^2+x+3

A quadratic expression ax^2+bx+c is complete square if b^2-4ac=0

For the given expression a=a,b=1 and c=3.

(1)^2-4(a)(3)=0

1-12a=0

Add 12a on both sides.

1=12a

Divide both sides by 12.

\dfrac{1}{12}=a

Therefore, the value of a is \frac{1}{12}.

\frac{1}{12}x^2+x+3

(\frac{1}{2\sqrt{3}}x)^2+2(\frac{1}{2\sqrt{3}}x)(\sqrt{3}+(\sqrt{3})^2

(\frac{1}{2\sqrt{3}}x+\sqrt{3})^2           [\because (a+b)^2=a^2+2ab+b^2]

Usimov [2.4K]3 years ago
7 0

Answer:

a(x+\frac{1}{2a})^2)-\frac{1}{4a}+3

Step-by-step explanation:

We have been given an expression ax^2+x+3. We are asked to complete the square for the given expression.

First of all, we will factor our a as:

a(x^2+\frac{x}{a})+3  

a(x^2+\frac{1}{a}x)+3

Now, we need to add and subtract half the square of the middle term, that is (\frac{1}{2a})^2:

a[x^2+\frac{1}{a}x+(\frac{1}{2a})^2-(\frac{1}{2a})^2]+3      

a[x^2+\frac{1}{a}x+(\frac{1}{2a})^2-(\frac{1}{4a^2})]+3    

a(x^2+\frac{1}{a}x+(\frac{1}{2a})^2)+3-a*\frac{1}{4a^2}  

a(x+\frac{1}{2a})^2)-\frac{1}{4a}+3

Therefore, our required square would be a(x+\frac{1}{2a})^2)-\frac{1}{4a}+3.

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Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
Leona [35]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is X: flexural strength of concrete beams.

Data:

7.3 6.8 8.6 9.7 11.6 9.7 6.8 7.7 11.8 7.4 8.1 8.7 6.3 7.9 7.0 7.9 7.8 6.5 6.3 7.0 7.5 7.7 7.2 11.3 9.0 10.7 5.1

a.

The point estimate of the mean value is the sample mean. You calculate it using the following formula:

X[bar]= ∑X/n= 219.40/27= 8.1259≅ 8.13

b)x

b.

The point estimate that divides the sample in 50%-50% is the measure of central tendency called Median(Me).

To reach the median you have to calculate it's position (PosMe)

For uneven samples PosMe= (n+1)/2= (27+1)/2= 14 ⇒ This means that the Median is the 14th observation of the data set.

So next is to order the data from lower to heighest and identify the value in the 14th position:

5,1 ; 6,3; 6,3; 6,5 ; 6,8; 6,8; 7; 7; 7,2; 7,3; 7,4 ; 7,5 ; 7,7 ; 7,7 ; 7,8 ; 7,9 ; 7,9 ; 8,1 ; 8,6 ; 8,7 ; 9 ; 9,7 ; 9,7 ; 10,7 ; 11,3 ; 11,6 ; 11,8

Me= 7.7

d) x tilde

c.

The point estimate of the population standard deviation is the sample standard deviation. The standard deviation is the square root of the variance, so the first step is to calculate the sample variance:

S^2= \frac{1}{n-1}*[sumX^2-\frac{(sumX)^2}{n} ]

∑X²= 1858.92

S^2= \frac{1}{26}*[1858.92-\frac{219.40^2}{27} ] = 2.926

S= √2.926= 1.71

The standard deviation is a measurement of variability, it shows how to disperse the data is concerning the sample mean.

d. This estimate describes the spread of the data.

I hope it helps!

7 0
3 years ago
Pls help me on this!
Ira Lisetskai [31]

Answer:

5 2/3

Step-by-step explanation:

So because it is a mixed number that means you want to have a whole plus a fraction. You keep the 5 as the whole and because 2/3=.666666. You add them together making 5 2/3.

3 0
3 years ago
If the perimeter of the adult pinball machine is 172 inches, what is the length, in inches of G’A’?
quester [9]
If you have ever seen a pinball machine, you would know that it is shaped like a rectangular box. Since a rectangle has two sets of equal parallel lines, then you would have to know the length and the width. Its perimeter is equal to the total length of all sides. Thus, the equation is 2L + 2W = 172 inches. However, since there is no other data other than the perimeter, I can't give a definite numerical answer. The only answer I could give is in variables. Thus, the length of the pinball machine is

2L = 172 - 2W

L= 86 - W
8 0
3 years ago
Three of the following statements are true. Which one is NOT true? <br> |-12| &gt; 1
san4es73 [151]
|-12| is greater than 1

The absolute value brackets make the -12 positive, 12>1.

True
5 0
1 year ago
Read 2 more answers
Help pretty pretty please !!❤️
insens350 [35]

Answer:

HEYOOO

The answer must be that it has a MAX

Step-by-step explanation:

Its because the graph has a MAXIMUM "peak" of the line--the maximum point on the graph of which it reaches!

HOPE THIS HELPS!

4 0
3 years ago
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