Find the vertical asymptote of f(x)=2x^2+3x+6/x^2-1 I'm having trouble with this one, seems simple tho I just don't want to make a stupid mistake,,, And here are the choices:

Answer:

[tex]\large \boxed{\sf \ \ \ -1, \ -5, \ -\dfrac{1}{4} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's determine the possible rational zeros of this polynomial function using the rational zeros theorem:

[tex]P(x) = 4x^4 + 13x^3-49x^2-73x-15[/tex]

First of all, what is the rational zeroes theorem?

If P(x) is a polynomial with integer coefficients

and if (p and q being integer)

[tex]\dfrac{p}{q}[/tex]

is a zero of P(x), meaning

[tex]P(\dfrac{p}{q})=0[/tex]

then p is a factor of the constant term of P(x) and

q is a factor of the leading coefficient of P(x).

How to apply it here?

The constant term of P(x) is -15

The leading coefficient of P(x) is 4

so p is a factor of -15

q is a factor of 4

15 = 1 * 5 * 3

4 = 2 * 2 * 1

q can be 1, 2, 4

-p can be 1, 3, 5, 15

so it gives the following potential solutions

-1, -3, -5, -15

[tex]\dfrac{-1}{2}, \dfrac{-3}{2}, \dfrac{-5}{2}, \dfrac{-15}{2}[/tex]

[tex]\dfrac{-1}{4}, \dfrac{-3}{4}, \dfrac{-5}{4}, \dfrac{-15}{4}[/tex]

Let's compute P(x) for x in this list of potential solutions

x P(x)

-1 0

-3 -264

-5 0

-15 148680

-0.5 7.875

-1.5 -39.375

-2.5 -185.625

-7.5 4948.125

-0.25 0

-0.75 7.96875

-1.25 -15.9375

-3.75 -324.84375

It gives -1, -5 and -0.25

Conclusion

The possible rational zeroes of P(x) are

-1

-5

[tex]\dfrac{-1}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The correct option is;

As x → ∞ f(x) → -∞, and  as x → -∞ f(x) →∞

Step-by-step explanation:

The values given are;

x,      f(x)

-4,     18

-3,     9

-2,     6

-1,      3

0,      0

1,      -3

2,     -6

3,     -9

4,     -18

Based on the table, as the magnitude of x increases in the positive direction,  the magnitude of f(x) increases in the negative direction

Therefore, the correct option that best predicts the end behavior of the graph of f(x) is As x → ∞ f(x) → -∞, and  as x → -∞ f(x) →∞.

it's a quadrilateral

interior angles add up to 360

x + 2x - 75 + x + x - 35 = 360

5x - 110 = 360

5x = 360 + 110

x = 470 ÷ 5

x = 95

and x - 35 = 60

2x - 75

= 190 -75

= 115

Answer:

see explanation

Step-by-step explanation:

The sum of the interior angles of a quadrilateral = 360°

Sum the given angles and equate to 360

x + x + x - 35 + 2x - 75 = 360, that is

5x - 110 = 360 ( add 110 to both sides )

5x = 470 ( divide both sides by 5 )

x = 94 , then

x - 35 = 94 - 35 = 59

2x - 75 = 2(94) - 75 = 188 - 75 = 113

Thus

The 4 angles are 59°, 94°, 94°, 113°

Answer:MLK

Step-by-step explanation:

The angle that is placed sideways with <JKM is <MKL

The adjacent interior angle of a triangle are angles placed sideways with each other.

For the given diagram attached, you can see interior angles of the triangle are <LMK, <MKL and <KLM

Among the listed interior angles, the angle that placed sideways with <JKM is <MKL

Learn more on interior angles here: https://brainly.com/question/24966296

Answer:

$600

Step-by-step explanation:

1800/300 = 6

6 x 100 = $600

Answer:

$600

Step-by-step explanation:

1800/300 = 6

6 x 100 = $600

Answer:

Lucy needs to invest $55,194.16

Step-by-step explanation:

The given information are;

The interest rate of the account = 7% compounded daily

The amount at the end of 6 years = $84,000

The time duration = 6 years

The amount Lucy

The formula for compound interest is

[tex]A(t) = P \times \left ( 1 + \dfrac{r}{n} \right )^{n \times t}[/tex]

Where;

r = The interest rate = 7% = 0.07

n = The number of times a year = 365

t = The number years = 6 years

A(t) =  The amount after 6 years = $84,000

P = The initial amount invested

Therefore, we have;

[tex]\$ 84,000 = P \times \left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}[/tex]

[tex]P = \dfrac{\$84,000}{\left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}} =\dfrac{\$84,000}{1.522} = \$55,194.16[/tex]

Therefore, Lucy needs to invest $55,194.16.

Answer:

tan A has the ratio a/c

Step-by-step explanation:

Pleased to help u...

Answer:

No

Step-by-step explanation:

I believe at the point of (1,1)  there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous.

Continuous means that there is no abrupt changes (google) and im sure you know this already (im just saying no offence to anyone's intelligence)

The given function is not continuous. The correct option is D.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value.

The point of (1,1)  there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous. Continuous means that there are no abrupt changes.

It is shown in the graph that the function is reducing continuously at the point ( 1,-1) and after that, there is a sudden change in the function after that it becomes constant or parallel to the x-axis.

Because there is a sudden change in the function it will be termed a discontinuous function.

Hence, the function is not continuous, and the correct option is D.

To know more about continuous function follow

https://brainly.com/question/18102431

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[tex]\dfrac{2ax+3}{ax+3}=-1[/tex]

Rewrite -1 as a fraction

[tex]\dfrac{2ax+3}{ax+3}=\dfrac{-1}{1}[/tex]

Cross multiply

[tex]2ax+3=-1(ax+3)[/tex]

Distribute the -1

[tex]2ax+3=-ax-3[/tex]

Add both sides by ax

[tex]3ax+3=-3[/tex]

Subtract both sides by 3

[tex]3ax=-6[/tex]

Divide both sides by 3a

[tex]x=-\dfrac{6}{3a}[/tex]

Simplify

[tex]=-\dfrac{2}{a}[/tex]

That's the value of x respect to a. Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

[tex]\frac{2ax+3}{ax+3} =-1\\2ax+3=-ax-3\\2ax+ax=-3-3\\3ax=-6\\x=-\frac{2}{a}[/tex]

Answer:

1/6

Step-by-step explanation:

I think this is tricky.

when you randomly choose the 1st two times, it doesn't matter as long as Na was not chosen, otherwise the probability would become ZERO for the 3rd one be Na.

So, after 1st two is removed, there are only 4 left in the pool, so picking Na at the 3rd draw is 1/4 probability.

But, come to think of it, when 1st draw, you have to draw the other 5 out of 6, 2nd draw the 4 out of 5, then 3rd is 1 Na out of the 4.

So, 5/6 x 4/5 x 1/4 = 1/6

Answer: 46 eggs

Step-by-step explanation:

There are 12 eggs in a dozen.  Thus, there are 3 5/6*12, or 46 eggs.

Hope it helps <3

Answer:

C. snowball sampling

Step-by-step explanation:

Snowball sampling also known as referral sampling or chain sampling is a sampling method in research where the participants in the research are recruited to find new participants. This is a non-probability sampling method because participants choose other participants through their own insight.  Just as a ball takes up more snow as it rolls by, so also this research method takes up more participants as it progresses.

So, when the field researcher who wanted to learn about a political organization's recruiting pattern begins by interviewing a participant who in turn suggests another participant, he has applied the snowball sampling method.

Answer:

x=3

Step-by-step explanation:

To solve for x, we will follow the steps below:

First note that exterior angle =two  opposite interior angle

From the diagram below

(25x) ° + (57 + x)°   = (45x)°

25x° + 57° + x° = 45x°

next step is to collect the like term

45x° - 25 x°  - x°  =  57°

19x° = 57°

Divide both-side of the equation by 19

19x°/ 19 = 57° /19

On the left-hand side of the equation 19 will cancel out 19 leaving us with just x°  while on the right-hand side of the equation 57 will be divided by 19

x  =   3

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

1. Relations are the set of y (output) and x (input) values that are related. A function is when each input has a relation with one output.

2. The mathematical formula is the formula of Pythagoras theorem. Where the length c (hypotenuse) is equal to the square root of the sum of the legs squared.

Answer:

b^8

Step-by-step explanation:

When multiplying exponents with the same base, we can add the exponents

b^2 * b^6

b^ (2+6)

b^8

Answer:b8 x

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "b6"   was replaced by   "b^6".  1 more similar replacement(s).

STEP

1

:

Multiplying exponential expressions

1.1    b2 multiplied by b6 = b(2 + 6) = b8

Final result :

 b8x

Answer:

3.88 feet

Step-by-step explanation:

let the length the ladder reaches be x

[tex] \tan(57) = \frac{x}{8} [/tex]

[tex]x = 8 \tan(57) [/tex]

x = 3.8775938143

Answer: 2.73 cm

Step-by-step explanation:

Given that :

Side (a) of cube = 4.4cm

Volume of a cube (V) = a^3

V = 4.4^3

V = 85.184cm^3

Therefore, volume of the sphere made = 85.184cm^3

Volume of sphere = 4/3 πr^3

Where r = radius

85.184 = (4/3)*(22/7)*r^3

85.184 = (88/21)*r^3

85.184 = 4.1905 * r^3

r^3 = 85.184 / 4.1905

r^3 = 20.327884

Take the cube root of both sides

r = 2.73 cm

Answer:

-0.704 (corrected to 3 significant figures).

Step-by-step explanation:

Standardized score = (actual score - mean) / standard deviation

Standardized score = (60% - 65%) / 7.1%

= -0.704 (corrected to 3 significant figures).

Standardized score = (actual score - mean) / standard deviation

= (60% - 65%) / 7.1%

= -0.704 (corrected to 3 significant figures).

A regular distribution is an association of facts set in which maximum values cluster in the center of the range and the relaxation taper off symmetrically in the direction of either intense.

Peak, beginning weight, studying potential, activity satisfaction, or SAT scores are only some examples of such variables. due to the fact that commonly distributed variables are so not unusual, many statistical checks are designed for commonly disbursed populations.

Learn more about the normal distribution here: https://brainly.com/question/4079902

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Hey there! I'm happy to help!

When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D

0.3n=45

To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.

0.3n÷0.3=45÷0.3

n=150

Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!

Have a wonderful day! :D

Answer:

5/14

Step-by-step explanation:

I assume after testing the 1st car, it is not placed back into the pool.

So, 1st test orange is 5/8

2nd test orange is 4/7.

Both had to be true, so 5/8 x 4/7 = 5/14

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]

Required

Why is the function not continuous at x = 3

First substitute 3 for x at the denominator

[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]

Factorize the numerator and the denominator

[tex]f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}[/tex]

[tex]f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}[/tex]

[tex]f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}[/tex]

Divide the numerator and denominator by (x - 3)

[tex]f(x) = \frac{x+2}{x+3}[/tex]

Substitute 3 for x

[tex]f(3) = \frac{3+2}{3+3}[/tex]

[tex]f(3) = \frac{5}{6}[/tex]

Because [tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex] is defined when x = 3;

Then the function is continuous

Answer:

A: f is not defined at x = -3

Step-by-step explanation: EDGE 2020

Step-by-step explanation:

An arithmetic sequence is given by relation as follows :

[tex]A(n)=-6+(n-1)\dfrac{1}{5}[/tex]

For the first term, put n = 1. So,

[tex]A(1)=-6+(1-1)\dfrac{1}{5}\\\\A(1)=-6[/tex]

For fourth term, put n = 4. So,

[tex]A(4)=-6+(4-1)\dfrac{1}{5}\\\\A(4)=\dfrac{-27}{5}\\\\A(4)=-5\dfrac{2}{5}[/tex]

For tenth term, put n = 10. So,

[tex]A(10)=-6+(10-1)\dfrac{1}{5}\\\\A(10)=-6+\dfrac{9}{5}\\\\A(10)=\dfrac{-21}{5}\\\\A(10)=-4\dfrac{1}{5}[/tex]

Hence, the correct option is (C).

Answer:

the answer in C)-6, -5 2/5, -4 1/5

Answer:

yeah....same!

Step-by-step explanation:

I'm having the same problem I thought it was just me

Answer: 32 copies of hardcover version.

Step-by-step explanation: Suppose the quantity of hardcover version copies sold is H and the paperback copies is P.

1) A store sells a total of 70 copies:

H + P = 70

2) One hardcover is sold for $15 and one paperback for $11.50. In one month was charged $917:

15H + 11.5P = 917

Solving the system of equations:

H + P = 70 (I)

15H + 11.5P = 917 (II)

Since it is asked for the hardcover version, find H.

Multiply equation (I) by -11.5:

-11.5H - 11.5P = - 805 (III)

Add (II) and (III):

-11.5H - 11.5P = - 805

  15H + 11.5P = 917

  3.5H            = 112

H = 32

In one month, it was sold 32 hardcover version of a book.

Answer:

The answer is option B.

Step-by-step explanation:

To find Angle A we use cosine

cos ∅ = adjacent / hypotenuse

From the question

The adjacent is 14

The hypotenuse is 26

So we have

cos A = 14/26

cos A = 7/13

A = cos-¹ 7/13

A = 57.42

Hope this helps you

Answer:

57 deg

Step-by-step explanation:

(see attached for reference)

we are given a right triangle together with the lengths of one side (= 14 units) and the hypotenuse (= 26 units)

Using the trigonometry formulas, we can find angle A

cos A = adjacent length / hypotenuse

cos A = 14 / 26

A = cos⁻¹ (14/26)    (use calculator)

A = 57.42 deg

A = 57 deg (rounded to nearest whole degree)

Answer:

140/221.

Step-by-step explanation:

For the triangle containing  angle α:

The adjacent side is -√(13^2-5^2) = -12.

For the triangle containing angle β:

Hypotenuse = √(-8)^2 + (15)^2) =  17.

cos(α - β) = cos α  cos β   + sin α   sin β

= ((-12/13) * (-15/17) + (-5/13)* (8/17)

= 180/221 + - 40/221

= 140/221.

Hi there! :)

Answer:

a = 12 units.

Step-by-step explanation:

Using the Pythagorean Theorem (c² = a² + b²), where

c = length of the Hypotenuse

a = length of the shorter leg

b = length of the longer leg

We can calculate the length of "a" by substituting in the values into the equation:

c = 15

a = "x"

b = 9

----------------

15² = x² + 9²

Simplify the squares:

225 = x² + 81

225 - 81 = x²

144 = x²

Take the square root of both sides:

√144 = x

x = 12 units.

Therefore, the length of a = 12 units.

Answer:

a= 12

Step-by-step explanation:

Pythagorean Theorem: a²+b²=c²

b= 9

c= 15

a= x = what we are looking for

For this problem, we need to set c² equal to x² and b², which would look like:

15²= x²+9²

225= x²+81

Subtract 81 from both sides

144=x²

Square root both sides

x=12

a= 12

Answer:

48 mph.

Step-by-step explanation:

You need to calculate the average. So,

42 + 54 = 96

Because there are two quantities, 42 and 54, divide 96 by 2.

The average speed is 48.

Answer:

w²-30w+210=0

Step-by-step explanation:

2w + 2l = 60 , w + l = 30, l = 30 - w

wl = 210

w(30-w) -210 = 0

30w - w²-210 = 0

w²-30w+210=0

Answer:

x=7

2x+45=59

3x+55=76

Step-by-step explanation:

Answer:

7°, 59°, 76°

Step-by-step explanation:

The equation for the sum of the angles:

Solving for x:

The angles: