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Mashutka [201]
3 years ago
8

Find the least common denominator for these two rational expressions. x²/x²+2x+1 and 5/x²+4x+3

Mathematics
1 answer:
iVinArrow [24]3 years ago
5 0
Factor each denominator:

x^2 + 2x + 1 = (x+1)^2

x^2 + 4x + 3 = (x+3)(x+1)

Now take the common and non common factors with the highest exponents and multiply them.

(x+3).(x+1)^2 is the least common denominator.

If you expand that product you will get x^3 + 5x^2 + 7x +3
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How to evaluate the limit
anzhelika [568]
\displaystyle\lim_{x\to2}\frac{x^2-x+6}{x+2}

Both the numerator and denominator are continuous at x=2, which means the quotient rule for limits applies:

\dfrac{\displaystyle\lim_{x\to2}(x^2-x+6)}{\displaystyle\lim_{x\to2}(x+2)}=\dfrac{2^2-2+6}{2+2}=\dfrac84=2

Perhaps you meant to write that x\to-2 instead? In that case, you would have

\displaystyle\lim_{x\to-2}\frac{x^2-x+6}{x+2}=\lim_{x\to-2}\frac{(x+2)(x-3)}{x+2}=\lim_{x\to-2}(x-3)=-2-3=-5
4 0
3 years ago
If the temperature is 45 degrees and it decreases by 15 degrees, what is the final temperature? I​
Hoochie [10]

Answer:

30

Step-by-step explanation:

45-15

7 0
2 years ago
Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3).
marissa [1.9K]

Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:

A=\frac{3\sqrt{3}}{2} a^2

Where A is the area of the regular hexagon

a is the side length of the regular hexagon

Also, it's Perimeter is given by:

P=6a

Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.

A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.

Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.

Let us now find the distance between the points D and E using the distance formula which is as:

d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

Where d is the distance.

(x_1,y_1) and (x_2,y_2) are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance d)

Applying the above formula we get:

d=\sqrt{(8-4)^2+(0-0)^2} =\sqrt{4^2}=4

\therefore d=4

We know that this distance is the side length of the given regular hexagon.

\therefore d=a=4

Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:

a_{small}=4-\frac{40}{100}\times 4=2.4

Thus, the area of the smaller hexagon will be:

A_{small}=\frac{3\sqrt{3}}{2} a_{small}^2=\frac{3\sqrt{3}}{2} (2.4)^2\approx14.96 unit squared

and the new smaller perimeter will be:

P_{small}=6a_{small}=6\times 2.4=14.4 unit

Which are the required answers.

5 0
3 years ago
Y’all I am terrible at math please help me
aniked [119]
GCF = 3a^2b
Solution: A, u are correct :)
5 0
2 years ago
Read 2 more answers
Which of the following represents a valid first step to solving this system of equations using the substitution method?
Phoenix [80]

Answer:

2(2y - 1) - y = 7

Step-by-step explanation:

I guess the 2 equations are

2x - y = 7

x = 2y - 1

substitution message that you use one equation to express one variable by the other, and then you use that in the other equation to get one equation for one variable. then you solve for that, and use that result in the first equation to since for the second variable.

the equations are already defined that way, that the second equation directly defines x as an excision of y.

so, this needs to be used then in the first equation.

and that makes

2(2y - 1) - y = 7

the correct first step.

7 0
2 years ago
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