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3 years ago

The ____ in an arithmetic sequence can be found by subtracting the first term from the second term

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

7 0

The [common difference, d, ] in an arithmetic sequence can be found by subtracting the first term from the second term

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<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%5E%7B2%7D%20%2B4x-4%7D%7Bx%5E%7B2%7D%20-2x-8%7D" id="TexFormula1"

givi [52]

i) The given function is

$f(x)=\frac{x^2+4x-4}{x^2-2x-8}$

We can rewrite in factored form to obtain;

$f(x)=\frac{x^2+4x-4}{x^2-2x-8}$

$f(x)=\frac{(x+2\sqrt{2}+2)(x-2\sqrt{2}+2)}{(x-4)(x+2)}$

The domain is

$(x-4)(x+2)\ne0$

$(x-4)\ne0,(x+2)\ne0$

$x\ne4,x\ne-2$

ii) To find the vertical asymptotes equate the denominator to zero.

$(x-4)(x+2)=0$

$(x-4)=0,(x+2)=0$

$x=4,x=-2$

iii) To find the roots, equate the numerator to zero.

$(x+2\sqrt{2}+2)(x-2\sqrt{2}+2)=0}$

$(x+2\sqrt{2}+2)=0,(x-2\sqrt{2}+2)=0}$

$(x=-2\sqrt{2}-2,x=2\sqrt{2}-2)}$

iv) To find the y-intercept, substitute $x=0$ into the equation.

$f(0)=\frac{0^2+4(0)-4}{0^2-2(0)-8}$

We simplify to obtain;

$f(0)=\frac{-4}{-8}$

$f(0)=\frac{1}{2}$

v) The horizontal asymptote is

$lim_{\to \infty}\frac{x^2+4x-4}{x^2-2x-8}=1$

The equation of the horizontal asymptote is y=1

vi) The function does not have a variable factor that is common to both the numerator and the denominator.

The function has no holes in it.

vii) The given function is a proper rational function.

Proper rational functions do not have oblique asymptotes.

7 0

3 years ago

Is algebra.

gulaghasi [49]

Answer:

2(x - 9.46)(x + 2.54)

Step-by-step explanation:

2(x² - 12x + 24)

since there are no factors that multiply to 24 and add to -12 then i used the quadratic formula to get:

6+2 $\sqrt{3}$ , 6-2 $\sqrt{3}$

7 0

3 years ago

Find the value of x

nataly862011 [7]

Answer:

x = 128°

Step-by-step explanation:

123 + 109 + x = 360

x = 360 - (123 + 109)

x = 360 - 232

x = 128°

7 0

3 years ago

8.508 8.58 7.5 7.058 what is the decreasing order

Ostrovityanka [42]

First 8.58
Second 8.508
Third 7.5
Fourth 7.058

3 0

3 years ago

Students were asked how many books they were carrying in their backpacks. The data is shown in the frequency table. What is the

maxonik [38]

Answer:

Some students were asked how many books they were carrying in their backpacks. The data is given in this frequency table. What is the mean number of pens carried by these students in their backpacks?

Pens Frequency

0 4

1 5

2 8

3 4

4 3

5 1

A.2

B.3.5

C.4

D.5.5

3 0

3 years ago