what is thecentre and diameter of the circle with equation
[tex]x {2} + {y2} - 2y + 1 = 16[/tex]
​

The statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity

If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.

For the considered case, the function is:

[tex]f(x) = \dfrac{2x}{1-x^2}[/tex]

The missing options are:

So we need to find the limit of the function as x approaches infinity.

[tex]lim_{x\rightarrow \infty}f(x) = lim_{x\rightarrow \infty}\dfrac{2x}{1-x^2} = lim_{x\rightarrow \infty}\dfrac{2x/x^2}{1/x^2 - 1} = lim_{x\rightarrow \infty}\dfrac{2/x}{1/x^2 - 1}\\\\lim_{x\rightarrow \infty}f(x) = \dfrac{lim_{x\rightarrow \infty}(2/x^2)}{lim_{x\rightarrow \infty}(1/x^2 - 1)} = \dfrac{0}{0-1} = \dfrac{0}{-1} = 0[/tex]

Since the value of the function approaches 0 as x approaches infinity, so as its graph will do.

Thus, the statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity

Learn more about limits of a function here:

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Answer:

a) four friends bought each ticket for $80 and also

bought a Jersey for $15

b) 4(95)

= 380

c) 8.95 - the answer is in decimal

teddy bears = 80

hope it helps..!!!

Answer:

a=12 times

b=156 times

Step-by-step explanation:

4 weeks=month

4*3=12

52 weeks=1 year

52*3=156

Therefore he goes 12 times a month, and 156 times a year.

Answer:

They both equal 20 when you do the butterfly method. They are all factors of 20.

Step-by-step explanation:

2/4 5/10

2x10=20

4x5=20

Answer:

x = 1, 3

Explanation:

[tex]\sf f(x)=x^2-4x+3[/tex]

[tex]\rightarrow \sf x^2-4x+3=0[/tex]

[tex]\rightarrow \sf x^2-3x-x+3=0[/tex]

[tex]\rightarrow \sf x(x-3)-1(x-3)=0[/tex]

[tex]\rightarrow \sf (x-1)(x-3)=0[/tex]

[tex]\rightarrow \sf x-1=0, \ x-3=0[/tex]

[tex]\rightarrow \sf x=1, \ x=3[/tex]

Thus, there are two solutions and the values are 1 and 3

Let's see

[tex]\\ \rm\rightarrowtail f(x)=0[/tex]

[tex]\\ \rm\rightarrowtail x^2-4x+3=0[/tex]

[tex]\\ \rm\rightarrowtail x^2-3x-x+3=0[/tex]

[tex]\\ \rm\rightarrowtail x(x-3)-1(x-3)=0[/tex]

[tex]\\ \rm\rightarrowtail (x-1)(x-3)=0[/tex]

[tex]\\ \rm\rightarrowtail x=1,3[/tex]

Answer:

Step-by-step explanation:

Answer:

800n+1050

Step-by-step explanation:

800(n+1)+250 = 800n+800+250 = 800n+1050.

Hope this helps!

Good luck with your test + I hope you do well on it.

Please mark me as brainliest!

Answer:

£17,253.53

Step-by-step explanation:

9.5% of 19,064.67 is 1,811.14 (rounded to the nearest hundredth.)

Subtract 1,811.14 from 19,064.67, and this will give you 17,253.53. This is a 9.5% decrease.

Step-by-step explanation:

for the trip restaurant to the bus stop he had to go 2 blocks down and 3 blocks to the left - in total 5 blocks.

for the trip from the bus stop to the stadium he had to go 3 blocks to the left and then 8 blocks up. in total 11 blocks.

so, the whole trip took 5 + 11 = 16 blocks.

Answer:

The scale is 11 feet per one inch.

Step-by-step explanation:

[tex]\frac{165feet}{15inches} = 11feet / inch[/tex]

Step-by-step explanation:

The distance from the radius to a point on the circle is equal to the radius. After using the distance formula, we get that the radius is 5.

Using the fact that the circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2, we get that the equation is:

(x+5)^2 + (y-6)^2 = 25

Answer:

10.3 cm

Step-by-step explanation:

By sine rule

[tex] \frac{x}{ \sin \: 50 \degree} = \frac{13}{ \sin \: 75 \degree} \\ \\ \implies \: x = \frac{13\sin \: 50 \degree}{\sin \: 75 \degree} \\ \\\implies \: x = \frac{9.9585777605}{0.9659258263} \\ \\ \implies \: x = 10.3098783\\\\\implies \: x = 10.3\: cm[/tex]

To find the area of the shaded part we have to subtract the rectangle area from the triangle area :

[tex]s = \frac{1}{2} \times (8x + 2)(6x) - (x)(3x + 1) \\ [/tex]

[tex]s = \frac{1}{2} \times (48 {x}^{2} + 12x) - (3 {x}^{2} + x) \\ [/tex]

[tex]s = \frac{48}{2} {x}^{2} + \frac{12}{2} x - 3 {x}^{2} - x \\ [/tex]

[tex]s = 24 {x}^{2} + 6x - 3 {x}^{2} - x[/tex]

[tex]s = 24 {x}^{2} - 3 {x}^{2} + 6x - x[/tex]

[tex]s = 21 {x}^{2} + 5x[/tex]

And we're done

Have a great day ♡

Answer:

A= 130

B= 25

Step-by-step explanation:

A is 130 because the amount of degrees that are in a triangle is 180 degrees. From that we can substract 25 from 180 and get 155.

Since B is congruent with 25, B is also 25 degrees. Therefore, A is 130 because 180 - 50 is 130.

Hope this helps.

Answer:198000 maybe

Sorry if it’s wrong

Answer:

7.96

Step-by-step explanation:

C=2πr undo it

R=C/2π=50/2×π≈7.5775 rounded is 7.96

Hope this helps!

Have a nice day!! :D

The radius of the circle is 7.96 cm.

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by ‘R’ or ‘r’.

The circumference of the circle is given by;

[tex]\rm Circumference = 2\pi r[/tex]

Where r is the radius of the circle.

Substitute all the values in the formula

[tex]\rm Circumference = 2\pi r\\\\50 = 2\pi r\\\\r = \dfrac{50}{2\times 3.14}\\\\r=7.96[/tex]

Hence, the radius of the circle is 7.96 cm.

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Answer:

It is actually very simple:

Notice that they don't actually do the square of 49 and 64. For some reason, they do the square root of the values without squaring them. If we were to do it in the right way, the answer would be:

[tex]49^{2} +64^{2} = c^{2}[/tex]⇔ 2401+4096 = [tex]c^{2}[/tex] ⇔ 6497 = [tex]c^{2}[/tex] ⇔ [tex]\sqrt{6497}[/tex] = [tex]\sqrt{c^{2} }[/tex] ⇔ 80,6 ≈ c

I believe this is the answer. I hope I had helped :)

The result of the recursive function mystery (m) is k.

In computer science, functions are collections of code that can be used and re-utilised in greater codes. Functions are formed by inputs, a procedure and an output.

In this question we must analyze a recursive function, recursive functions are functions that creates a loop with the function itself, that is, the function uses itself as an output, until desired output is done.

After performing desktop testing, we conclude that the result of the recursive function mystery (m) is k. [tex]\blacksquare[/tex]

This is a Computer Science problem, whose complete statement is described below:

Consider the following recursive method:

public static int mystery (int n)

{

    if (n <= 1)

    {

         return 0;

    }

    else

    {    

         return 1 + mystery(n/2);

    }

}

Assuming that k is a nonnegative integer and m = 2ⁿ, what value is returned as a result of the call mystery (m)?

To learn more on recursive functions, we kindly invite to check this verified question: https://brainly.com/question/25762866

The result of the recursive function mystery (m) is k.

In computer science, functions are collections of code that can be used and re-utilized in greater codes. Functions are formed by inputs, a procedure, and an output.

In this question we must analyze a recursive function, recursive functions are functions that create a loop with the function itself, that is, the function uses itself as an output until the desired output is done.

After performing desktop testing, we conclude that the result of the recursive function mystery (m) is k.

Consider the following recursive method:

public static int mystery (int n)

{

   if (n <= 1)

   {

        return 0;

   }

   else

   {    

        return 1 + mystery(n/2);

   }

}

Hence, the result of the recursive function mystery (m) is k.

To learn more about recursive functions; brainly.com/question/25762866

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Answer:

Let the amount invested at 3% = x

Let the amount invested at 6% = y.

From the total amount invested, we get this equation.

x + y = 18

Now we look at the interest earned.

The 3% account earns 0.03x

The 6% account earns 0.06y

5% on the entire amount is 0.05 * 18 = 0.9

This gives us the second equation.

0.03x + 0.06y = 0.9

Now we have a system of 2 equations in 2 unknowns.

x + y = 18

0.03x + 0.06y = 0.9

Solve the first equation for y:

y = 18 - x

Replace 18 - x for y in the second equation.

0.03x + 0.06y = 0.9

0.03x + 0.06(18 - x) = 0.9

0.03x + 1.08 - 0.06x = 0.9

-0.03x + 1.08 = 0.9

-0.03x = -0.18

x = 6

Answer: He invested $6 at 3%

Answer:

y = (2/15) x -(117/15)

Step-by-step explanation:

To write the equation we should know the slope m and the y-intercept b .

m= (y2-y1)/(x2-x1)

For points (x1 = -9, y1 = -9) and (x2 = 6, y2 = -7)

m = (-7 - - 9)/(6 - - 9) = (-7 + 9)/(6 +9) = 2 / 15

The general equation of a line is

y= mx + b

Our equation is

y = (2/15) x +b

To find b, substitute one of the two points, we know are on the line, in our equation. For example, we can substitute point (-9,-9)

-9 = (2/15) (-9) +b , multiply -9 by 2/15

-9 = - (18/15) +b, add -18/15 on both sides

-9 + (18/15) = b, find common denominator and add

[(-9 ·15) +18]/15 = b , simplify

-117/15 = b

So our equation is:

y = (2/15) x -(117/15)

The distance I can see from the  top of the sears tower in Chicago is 46.41 mi.

The equation for direct proportionality = y = b√x

where:

b = y /√x

41 / √1135

b = 1.217

y = 1.217√1454

y = 46.41 mi

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Answer:

12 classrooms

Step-by-step explanation:

We know that there are 3 math classrooms, and three math classrooms is 25% of all of the classrooms. We need to know the total number of classrooms, which is 100% of the classrooms, so we do 25% times 4. Because we did 25 times 4, we have to do 3 classrooms times 4, and we get 12 classrooms.

Here's a ratio explanation.:

Percent of classrooms : Classrooms

25                                  : 3

100                                : 12

Answer:

3b. [tex]\displaystyle 10; Mental\:Mathematics[/tex]

3a. [tex]\displaystyle \frac{5}{8} \times 16[/tex]

Explanation:

Dividing a mixed number\fraction is in similarity to multiplying its multiplicative inverce, which is what you see in the above answer. However, I did not figure it out this way. I did this:

[tex]\displaystyle \boxed{10} = \frac{5}{\frac{1}{2}} \Rightarrow \boxed{10} = \frac{5}{8} \div \frac{1}{16}[/tex]

Either way is fine, as long as you know what you are doing.

I am joyous to assist you at any time.

Answer: x=12, (MR)=55

Step-by-step explanation:

Answer:

14,085m³

Step-by-step explanation:

9*5*13

9*5=45

45*313=14,085

14,085

Answer: 6

Step-by-step explanation:

I assume you meant to write 8xy − 9x2y − 5x + 6. The constant term in an expression is defined as a number by itself that contains no variables. Therefore, the answer is 6.