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3 years ago

What number should be added to both sides of the equation to complete the square X2+3x=6

Mathematics

2 answers:

Paladinen [302]3 years ago

5 0

Answer:

$\frac{9}{4}$

Step-by-step explanation:

Here we will first split the middle term in such way that it is a product of 2 and some factor. In this case 3 can be splitter as product of 2 and 3/2.

We then add the square of 3/2 on both sides. Let us see how:

$x^2+3x=6\\x^2+2*\frac{3}{2}*x=6\\x^2+2*\frac{3}{2}*x+(\frac{3}{2})^2=6+(\frac{3}{2})^2\\(x+\frac{3}{2})^2=6+\frac{9}{4}\\(x+\frac{3}{2})^2=\frac{33}{4}$

harina [27]3 years ago

3 0

Answer:

add 6

Step-by-step explanation:

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Karolina [17]

The regression equation is $\^y = 1.56\^x + 1.29$ , and it will take 31 weeks to have $50.00

<u>(a) The linear regression equation</u>

To do this, we make use of a graphing calculator;

From the graphing calculator, we have the following calculation summary:

The sum of X = 45
The sum of Y = 83
Mean X = 4.5
Mean Y = 8.3
Sum of squares (SSX) = 82.5
Sum of products (SP) = 128.5

The regression equation is then represented as:

$\^y = b\^x + a$

Where:

$b = \frac{SP}{SSX}$ and $a = M_Y - bM_X$

So, we have:

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$b = 1.55758$

Approximate

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$a= 8.3 - (1.56 \times 4.5)$

$a= 1.29091$

Approximate

$a= 1.29$

This means that, the regression equation is $\^y = 1.56\^x + 1.29$

<u>(b) Predict the time to have $50.00</u>

This means that:

$\^y = 50$

So, we have:

$50 = 1.56\^x + 1.29$

Subtract 1.29 from both sides

$48.71 = 1.56\^x$

Divide both sides by 1.56

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Rewrite as:

$\^x = 31.22$

Approximate

$\^x = 31$

Hence, it will take 31 weeks to have $50.00

Read more about linear regression models at:

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