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3 years ago

Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.

Mathematics

1 answer:

kifflom [539]3 years ago

8 0

N/D =(x²+4x+4)/(x² - 4)

N= x²+4x+4 = (x+2)²
D = x²-4 =(x-2)(x+2)

N/D = (x+2)²/(x-2)(x+2); simplify by (x+2)

N/D = (x+2)/(x-2)

Domain of x ={x∈R≠3} ; in short x =( -2) should be excluded

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Evaluate 1x + y, for x = 8 and y=-15. 7 -7 23 -23

statuscvo [17]

Answer:

B) -7

Step-by-step explanation:

x+y

8+(-15)=8-15=-7

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3 years ago

The sum of the two digits of a number is 16. The number formed by reversing the digits is 18 more than the original number. Dete

nydimaria [60]

9u-9t=18

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reversed no. is 10u+t

so its (10u+t)-(10t+u)=18
which gives 9u-9t=18

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3 years ago

The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

Makovka662 [10]

Answer:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

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.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

8 0

3 years ago

Yeah I don’t get this

umka2103 [35]

using pythagorean theorem

a^2 + b^2 = c^2

(12x)^2 + (16x)^2 = 10^2

square each term

144x^2 + 256x^2 = 100

combine like terms

400 x^2 = 100

divide by 400 on each side

x^2 = 1/4

take the square root on each side

x = 1/2

Answer: x=1/2

8 0

3 years ago

What is an equation of the line that passes through the points (6, -3) and (-6, -5)?

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

The standard form of an equation for a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

We can calculate the slope from the two given points, (6,-3) and (-6,-5). Slope is Rise/Run, where Rise is the change in y and Run is the change in x.

From the two given points, starting at (-6,-5) and going to (6,-3):

Rise = (-3 - (-5)) = +2

Run = (6 - (-6)) = 12

Rise/Run (slope) = 2/12 or 1/6

The equation becomes y = (1/6)x + b

We can find b by enterieng either of the two given points and solving for b. I'll pick (6,-3):

y = (1/6)x + b

-3 = (1/6)*(6) + b

-3 = 1 + b [Now you can see why I chose (6,-3)]

b = -4

The equation is y = (1/6)x - 4

Check this with a DESMOS graph (attached).

6 0

2 years ago