How to divide polynomials by long division.

Applying limits, it is found that since [tex]a \neq 0, \frac{a}{2} \neq 0[/tex], and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.

The function is given by:

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

The horizontal asymptote is the limit of the function as x goes to infinity, hence:

[tex]y = \lim_{x \rigtharrow \infty} F(x) = \lim_{x \rigtharrow \infty} \frac{(ax - 3)(x - 2)}{2(x + 3)(x - 2)}[/tex]

Considering only the terms with the highest exponents:

[tex]y = \lim_{x \rigtharrow \infty} \frac{ax^2}{2x^2} = \frac{a}{2}[/tex]

Since [tex]a \neq 0, \frac{a}{2} \neq 0[/tex], and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.

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Answer:

it's b

Step-by-step explanation:

because it is sum and difference of 3x and 5

Answer:

Step-by-step explanation:

If 3 is width and 2 is length 3 units right 1 unit up

If 2 is width and 3 is length 2 units right 3 units up

Answer:

£120

Step-by-step explanation:

original_price = discounted_price / (1 - discount / 100)

78/(1-35/100)=120

Answer:

65

Step-by-step explanation:

let's place 9 in place of p and 4 in place of q. I will use a star in place of that symbol for the sake of my convenience having to look for it, apologies.

[tex]9 \star 4 = 9^2-4^2 = 81-16 = 65[/tex]

Answer:

65

Step-by-step explanation:

9^2-4^2=65

Answer:

Smaller angle : 30 degrees

Bigger Angle : 65 degrees

Step-by-step explanation:

85+6x+13x=180, 85+19x=180,19x=95,x=5

Smaller angle : 30

Bigger Angle : 65

Answer:12

Step-by-step explanation:

if 4y=12

then y=3

4y=2x

then as 4y=12 then 2x=12

Answer: 2x=12

Step-by-step explanation:

so if 4y=2x we know that 2x is also equal to 12

2x=12

Answer:

h(x) = (1/3)x + 6

Step-by-step explanation:

yeah-ya ....... right?

Answer:

-9?????????????????????????

Step-by-step explanation:

Answer:

16c+24

Step-by-step explanation:

4c+4c+7+7+8c+10=16c+24

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{4}[/tex] x - 4 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

Parallel lines have equal slopes

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here (a, b ) = (- 1, 7 ) , then

y - 7 = [tex]\frac{3}{4}[/tex] (x - (- 1) ) , that is

y - 7 = [tex]\frac{3}{4}[/tex] (x + 1) → A

Answer:

The answer is C

Step-by-step explanation:

The range of the function plotted on the graph is [-6, 9].

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is the graph of a function shown in the image.

Range of a function is the set of {y} - values that exist for the values in the domain of the function. We can see from the graph that the values of {y} range from {y} = - 6 to {y} = 9 over the entire domain. See the black dots, that black dots mean that the both the numbers -6 and 9 are included in the range. So, in the set form, we can write the range of the function as -Range : [-6, 9].

Therefore, the range of the function plotted on the graph is [-6, 9].

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Answer:

The key to developing a great credit score is not a formula, but there are certain general recommendations that may be followed. Make on-time payments on your debts on a consistent basis. One strategy to ensure that your payments are made on time is to set up automated payments or electronic reminders for your accounts. If you've fallen behind on your payments, get up to date and remain up to date.

Step-by-step explanation:

Hope it helps if this is what you mean;)

Answer:

y <  -3/2x + 1

Step-by-step explanation:

Points (-2,4) and (2, -2) are on the graph.

The graph crosses the y-axis at 1 so the y-intercept is 1

Slope = (change in the y-value)/(change in the x-value.

Slope = (-2 - 4)/ [2 - (- 2)]

Slope = -6/4

Slope = -3/2  

The equation of the line : y = -3/2x + 1

Now the graph is dotted and it is shaded down.

Therefore the inequality is y <  -3/2x + 1

hope this help

pls mark as brainliest

Answer:

B. 12 per 16 minutes

Step-by-step explanation:

4x4=16, so multiply 3×4 to get 12.

Answer:

a=12

Step-by-step explanation:

brainlest if this helped so much !

Answer:

Its A. 12

Step-by-step explanation:

Hope this helps!

Step-by-step explanation:

option D is correct.

hope this answer helps you dear! take care

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The additional information to prove the Triangles congruent is ~

The Triangles are congruent by SAS congruency criteria ~

Answer:

60 miles

Step-by-step explanation:

1 hour = 25 miles. To find how much the shark can swim during 2.4 hours, we just have to multiply 25 by 2.4, which is 60, and that's your answer.

Tell me if I'm wrong :)

Answer:

x-2y=12

Solve for y

x-2y=12

Subtract x on both sides

-2y=-x + 12

Divide both sides by -2

y=\frac{1}{2}x - 6y=21x−6

the domain is {-3,-1,0,2,5}

Domain are the set of x values

Range are the set of y values

We are given with domain x, we need to find out y values using the equation y=\frac{1}{2}x - 6y=21x−6

when x=-3 , y=\frac{1}{2}(-3)-6=\frac{-15}{2}=-7.5y=21(−3)−6=2−15=−7.5

when x=-1 , y=\frac{1}{2}(-1)-6=\frac{-13}{2}=-6.5y=21(−1)−6=2−13=−6.5

when x=0 , y=\frac{1}{2}(0)-6=-6y=21(0)−6=−6

when x=2 , y=\frac{1}{2}(2)-6=-5y=21(2)−6=−5

when x=5 , y=\frac{1}{2}(5)-6=\frac{-7}{2}=-3.5y=21(5)−6=2−7=−3.5

Range is {-7.5, -6.5, -6 , -5, -3.5}

Step-by-step explanation:

solve the equation ? 1 equation with 2 variables ? that is not possible.

what you mean is probably find the range.

x - 2y = 12

-2y = -x + 12

2y = x - 12

y = (x - 12)/2 = (1/2)x - 6

x = -3

y = 1/2 × -3 - 6 = -1.5 - 6 = -7.5

x = -1

y = 1/2 × -1 - 6 = -0.5 - 6 = -6.5

x = 0

y = 1/2 × 0 - 6 = -6

x = 2

y = 1/2 × 2 - 6 = 1 - 6 = -5

x = 5

y = 1/2 × 5 - 6 = 2.5 - 6 = -3.5

so, the corresponding range of the function is

{-7.5, -6.5, -6, -5, -3.5}

Answer:

Step-by-step explanation:

K, but what's the question?

Answer:

y = 1.25x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 1.25 and (0, - 3 ) ⇒ c = - 3

y = 1.25x - 3 ← equation of line

Darrel has 50 grapes in all.

Lia has 72 green grapes, and she shares them equally between 8 friends. To find out how many grapes each friend receives, divide the total number of grapes by the number of friends:

Number of grapes each friend receives = 72 / 8 = 9

Now, Darrel adds 41 green grapes to his share, so the total number of grapes he has is:

Total grapes for Darrel = Number of grapes Darrel received initially + Additional grapes added by Darrel

Total grapes for Darrel = 9 + 41 = 50

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Answer: x=2

Step-by-step explanation:

Answer:

I don't know but

1+2=3

3+3=6

6+4=10

10+5=15

if this helps you make any sense of it.. tell me

Step-by-step explanation:

Answer:

These are triangular numbers.

Step-by-step explanation:

The explicit formula for the nth term of the sequence id 1/2n(n+1).

So for, example, the 6th term =  1/2*6(6+1)

= 21.

They all fit exactly into equilateral triangles.

Option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

The distance across a circle through the centre is called the diameter.

Diameter = 2 × radius

In the given figures, option B has a diameter of 20

so radius = diameter /2

=20/2

=10 units

Hence, option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

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Answer:In each step the number is double that of the previous step.

Step-by-step explanation:

In each step the number is double that of the previous step.

0    5

1    10

2   20

3   40

4    80

This can be written as 5*(2)^n, where n is the step number.  e;g;, 5*2^0 = 5 for step 0.  For step 4:  5*2^4 = 80.

Step-by-step explanation:

According to the given we have following inequalities:

See the graph attached below.

Solution region is within the triangle with marked vertices.

Answer:

here is the answer

Step-by-step explanation: