Jason is playing a trivia game with his friends. At the end of each round, his score updates to the square of 1 less than the previous round’s score. If he has 8 points in the first round, which of the following recursive formulas can be used to determine his score at the end of future rounds? Assume that the number of rounds is unlimited, and n is the number of rounds.

Answer:

2x^2 - x + 1

Step-by-step explanation:

This is polynomial long division:

Divide x + 3 into 2x^3 + 5X^2 - 2x + 3:

  Divide 2x^3 by x = 2x^2

  Multiple 2x^2 by (x + 3) =  2x^3 + 6x^2

  Subtract that from 2x^3 + 5X^2 - 2x + 3 = -x^2 -2x + 3

  Divide -x^2 by x = -x

  Multiple -x by (x + 3) = -x^2 - 3x

  Subtract that from -x^2 - 2x + 3 =  x + 3

  Divide x by x = 1

  Multiple 1 by (x + 3) = x + 3

  Subtract from x + 3 = 0

Answer:

b

Step-by-step explanation:

you need to round 2.51 to 3 because it was the correct answer

Answer:

360 different permutations.

Step-by-step explanation:

It goes 6*5*4*3 because as you pick the pens the amount of pens in the jar would obviously decrease. Picking one leaves you with 5 new options. If you repeat that 4 times then you are left with 360 options.

The number of permutations of picking 4 pens from the box is 6P4, or 6!/(6-4)! = 654×3 = 360.

We have 6 pens and we are picking 4 of them. The order in which we pick the pens matters, so we are dealing with permutations.

The number of permutations of n objects is given by n!, or n factorial. So, the number of permutations of 6 objects is 6!.

However, we need to divide by the number of permutations of the 2 pens that we are not picking. There are 2 pens that we are not picking, so the number of permutations of those pens is 2!.

Therefore, the number of permutations of picking 4 pens from the box is 6!/(6-4)! = 654×3 = 360.

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Answer:

Fist if all u will draw ur Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Secondly u will draw ur Parallel lines or angle.

Answer:

a c e

Step-by-step explanation:

Answer:

2:5

Step-by-step explanation:

The structure of a ratio is x:y.

So all you have to do is place the former as the first digit and the latter as the second and separate them by a colon.

Answer:

k+2 or k=2

Step-by-step explanation:

combine -5 and 7 to get your answer

Answer:

K+2

Step-by-step explanation:

K - 5 + 7 ....add -5 and 7

K+2

Answer:

[tex]\boxed{-9x^3-18x^2 + 15x}[/tex]

Step-by-step explanation:

(3x²+6x-5)(-3x)

Apply distributive law.

-3x(3x²)-3x(6x)-3x(-5)

Simplify.

-9x³ - 18x² + 15x

Answer:

[tex] \boxed{\red{ - 9 {x}^{3} - 18 {x}^{2} + 15x}}[/tex]

Step-by-step explanation:

[tex] ( - 3x)(3 {x}^{2} + 6x - 5) \\ - 3x(3 {x}^{2} ) - 3x(6x) - 3x( - 5) \\ = - 9 {x}^{3} - 18 {x}^{2} + 15x[/tex]

Answer:

The length of segment A'E' is 5 units

Explanation:

From the included graph the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A- (0, 0)

E- (0, 2)

The length of the segment AE = √((2-0)² + (0 - 0)²) = √2² = 2

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;

Length of segment A'E' = 5/2 × Length of segment AE

Therefore;

Length of segment A'E' = 5/2 ×2 = 5 units.

The length of segment A'E' is 5 units.

This question is based on distance formula.The length of segment A'E' is 5 units.

Given:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

From the given  graph, the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A- (0, 0)

E- (0, 2)

The length of the segment AE = [tex]\sqrt{(2-0)^{2} +(0-0)^{2} }=\sqrt{2^{2} } =2[/tex]

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;

Length of segment A'E' = 5/2 × Length of segment AE

Therefore;

Length of segment A'E' = 5/2 ×2 = 5 units.

Therefore, the  length of segment A'E' is 5 units.

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Answer:27.78% ; Twi; 1/3

Step-by-step explanation:

Given the data :

Language - - - - - - - Number of students

Nzema - - - - - - - - - - - 5

Ga - - - - - - - - - - - - - - - 20

Twi - - - - - - - - - - - - - - - 30

Ewe - - - - - - - - - - - - - - - 25

Fante - - - - - - - - - - - - - - 10

1.) To prepare pie chart:

Total number of students :

(5 + 20 + 30 + 25 + 10) = 90 students

Nzema: (5/90) × 360 = 20

Ga : (20/90) × 360 = 79.99 = 80

Twi : (30/90) × 360 = 119.99 = 120

Ewe : (25/90) × 360 = 79.99 = 100

Fante : (10/90) × 360 = 39.99 = 40

Total = 360

Pie chart is attached in the picture below

2)Percentage students that speak Ewe = (25/90) * 100 = 27.78%

Or (100/360) * 100 = 27.78%

3.) Modal language : This is the language spoken by majority of the students = Twi

4.) Fraction of student that speak either GA or Fante :

(GA or Fante) = (20 + 10) / 90 = 30/90 = 1/3

Answer:

Which statement about the function is true?

The function is positive for all real values of x where

x > –4. <<<CORRECT

The function is negative for all real values of x where

–6 < x < –2.

The function is positive for all real values of x where

x < –6 or x > –3.

The function is negative for all real values of x where

x < –2.

Step-by-step explanation:

November Edge 2021

Function f(x) is positive for the values x ≤ -6 and x ≥ -2 and negative in the interval -6 ≤ x ≤ -2.

A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves.

The graph of the function f(x) = (x + 2)(x + 6) is a downward facing parabola that intersects the x-axis at x = -6 and x = -2.

Therefore, we can conclude that the function is negative for all real values of x where x < -6 or x > -2 (outside the x-intercepts).

The function is positive for all real values of x where x lies between the x-intercepts, which means -6 < x < -2.

Therefore, the statement that is true is: "The function is negative for all real values of x where x < -6 or x > -2. The function is positive for all real values of x where -6 < x < -2."

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Your question seems incomplete, the probable complete question is:

Which statement about the function is true?

O The function is positive for all real values of x where

The function is negative for all real values of x where

-6exs-2.

O The function is positive for all real values of x where

X-6 orr-3

O The function is negative for all real values of x where

x<-2

Answer:

second option

Step-by-step explanation:

Answer:

Check below

Step-by-step explanation:

Hi, let's check

1.[tex](7x+20) + 12 \:and\: 7x +(24+12)\\[/tex]

In this case we have the Associate Property, since we can associate two, or even three terms without modify the final result.

2.[tex]21x+28y \:=\: 7(3x + 4y)[/tex]

Distributive Property, note that that the right side is the left side rewritten as a product, with the GCF outside the brackets.

3. Commutative Property

[tex]7y + 6x \:and\: 6x + 7y[/tex]

The order of these sum does not compromise the result.

4. [tex]x+4y-Sy \:and\: x-5y[/tex]

Combining like terms, similar terms are operated together.

Answer:

6n or 6 x n

Step-by-step explanation:

Answer:

B. 1296 in.^2

Step-by-step explanation:

The rectangles are similar, and sides ST and YZ are corresponding sides.

The linear scale factor is k = YZ/ST = 24/8 = 3

The area scale factor is k^2 = 3^2 = 9

A = 144 sq in. * k^2 = 144 sq in. * 9 = 1296 sq in.

Answer: B. 1296 in.^2

Answer:

4)1,296in^2

5)510.4ft

Step-by-step explanation:

4)

24/8=3 This is the dilation

144/8=18 This is the side length for QRST

18*3=54 The side length for WXYZ

24*54=1296 The area of WXYZ

5)

319*8/5 Your fence with a scale factor of 8/5

319*1.6 Changing 8/5 into fraction form

319*1.6=510.4 The length of the friend's fence.

Hope this helps. I could not see the end of the last question so I am sorry if it is not written properly.

Have a good day!

The discount is 15%, multiply the price y 15%:

5000 x 0.15 = 750

The discount is 750

Answer:

0.5346

Step-by-step explanation:

Find the z-scores.

z = (x − μ) / σ

z₁ = (89 − 100) / 15

z₁ = -0.73

z₂ = (111 − 100) / 15

z₂ = 0.73

Find the probability.

P(-0.73 < Z < 0.73)

= P(Z < 0.73) − P(Z < -0.73)

= 0.7673 − 0.2327

= 0.5346

Answer: rotate 180 degrees and reflection across the line y=2

Step-by-step explan

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Here in this question, we want to select which of the options particularly represents what was given in the question.

Mathematically 10^4 means that we are raising 10 into a continued exponential raising up to 4 times.

So 10^4 is pronounced as the first option in the question.

10 raised to power 10 , raised to power 10 etc

Answer:

to find the slope of a linear function, there is only one formula

this formula requires two points, which are stated in tables and graphs alike

these points do not need to be one after the other as it is slope and slope predicts what the next point graphed will be.

Formula for Slope:

this should help. take any two points and substitute for each; y values in the correct spots and x values in their correct spots

make sure to put the values of second point where it is labelled y2 and x2 And make sure to substitute first point values in those labelled y1 and x1

It is important to remember that if this becomes a fraction, SIMPLIFY

We can write the slope of the function as -

{m} = (9 - 5)/(4 - 0).

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 a table for the function as -

{x}   0   4

{y}   5   9

We can write the slope of the function as -

{m} = (9 - 5)/(4 - 0)

Therefore, we can write the slope of the function as -

{m} = (9 - 5)/(4 - 0).

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Answer:

$14,580

Step-by-step explanation:

To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form

-In doing that, you get 2,000

-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000

-the value of the car after one year is now $18,000

Now, let's move to the second year.  This time find 10% of 18,000

-multiply 18,000 by 0.1 to get 1,800

-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200

-the value of the car after two years is now $16,200

Finally, let's look at the value of the car after three years.  Only this time, we will now find 10% of 16,200

-multiply 16,200 by 0.1 to get 1,620

-since value is being depreciated, or lessened, we will once again be subtracting.  Subtract 1,620 from 16,200 to get 14,580

Therefore, the value of the car after three years is now $14,580.

Answer:

[tex]\huge\boxed{(2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}=4x^5}[/tex]

Step-by-step explanation:

[tex](2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}\qquad\text{use}\ (ab)^n=a^nb^m\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{3}{2}(x^3)^\frac{3}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^{(3)(\frac{3}{2})}=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^\frac{9}{2}\\\\\text{use the commutative and associative property}\\\\=\left(2^\frac{1}{2}\times2^\frac{3}{2}\right)\left(x^\frac{1}{2}\times x^\frac{9}{2}\right)\qquad\text{use}\ a^n\times a^m=a^{n+m}[/tex]

[tex]=2^{\frac{1}{2}+\frac{3}{2}}x^{\frac{1}{2}+\frac{9}{2}}=2^\frac{1+3}{2}x^{\frac{1+9}{2}}=2^\frac{4}{2}x^\frac{10}{2}=2^2x^5=4x^5[/tex]

Answer:

[tex] 4x^5 [/tex]

Step-by-step explanation:

[tex] (2x)^\frac{1}{2} \times (2x^3)^\frac{3}{2} = [/tex]

[tex]= (2x)^\frac{1}{2} \times (2x \times x^2)^\frac{3}{2}[/tex]

[tex]= [(2x)^\frac{1}{2} \times (2x)^\frac{3}{2}] \times (x^2)^\frac{3}{2}[/tex]

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

[tex]= (2x)^{\frac{4}{2}} \times x^{\frac{6}{2}}[/tex]

[tex] = 2^2x^2 \times x^3 [/tex]

[tex] = 4x^5 [/tex]

Answer:

i) x = 65°       ii)  x = 60°     iii)  x = 34°

  y = 50°           y = 80°           y = 124°

Step-by-step explanation:

i) x = 180-115= 65°

  y = 65+65= 130

     =  180-130= 50°  

ii) x = 90+30= 120

         180-120= 60°

   y = 60+20= 80

         180-80 = 100

         180-100= 80°

iii) y = 34+90= 124

    x = 180-124= 56

           56+90= 146

           180-146= 34°

I hope this helped, mark me brainliest please :)

Answer:

[tex]AB = 10 units[/tex]

Step-by-step explanation:

The line of segment AB can be calculated using distance formula, [tex] d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} [/tex] , to calculate the distance between point A(6, 2) and point B(0, 10).

A(6, 2) can be (x1, y1),

B(0, 10) can be (x2, y2)

[tex] d = \sqrt{(0 - 6)^2 + (10 - 2)^2} [/tex]

[tex] d = \sqrt{(-6)^2 + (8)^2} [/tex]

[tex] d = \sqrt{36 + 64} [/tex]

[tex] d = \sqrt{100} [/tex]

[tex] d = 10 [/tex]

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations: [tex]a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2[/tex]

They coincide if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]

They are parallel if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]

They intersect if [tex]\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}[/tex]

Given equations: [tex]8 x + 10 y = 30\\ 12 x + 15 y = 60[/tex]

Here,

[tex]\dfrac{a_1}{a_2}=\dfrac{8}{12}=\dfrac{2}{3}\\\\ \dfrac{b_1}{b_2}=\dfrac{10}{15}=\dfrac{2}{3}\\\\ \dfrac{c_1}{c_2}=\dfrac{30}{60}=\dfrac{1}{2}[/tex]

⇒[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

[tex]y=-\dfrac{8}{10}x+\dfrac{30}{10}\Rightarrow\ y=-0.8x+3[/tex]

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

[tex]y=-\dfrac{12}{15}x+\dfrac{60}{15}\Rightarrow\ y=-0.8x+4[/tex]

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations:  

They coincide if  

They are parallel if  

They intersect if  

Given equations:  

Here,

⇒  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer:

  1 : 2

Step-by-step explanation:

The ratio is ...

  small dia : large dia = 1 : 2 = small circumference : large circumference

__

Further explanation

The diameter of the small circle is the radius of the large circle. Since the large circle's diameter is twice the length of its radius, the ratio of circle diameters is ...

  small : large = 1 : 2

We multiply the diameter by π to get the circumference. Multiplying both these numbers by π will give the ratio of the circumferences. In order to reduce the ratio to lowest terms we must divide by π again:

  dia ratio = circumference ratio = lowest terms ratio

  1 : 2 = π : 2π = 1 : 2

Answer: 1:2

Step-by-step explanation:

Answer:

[tex]x=37\,\sqrt{2}[/tex]

Step-by-step explanation:

Notice you are dealing with a right angle triangle, since one of the angles measure [tex]90^o[/tex]. Now, what you are asked to find is the hypotenuse of that triangle, given an angle of [tex]45^o[/tex] and the opposite side: 37 units. Then, we can use for example the sine function which relates opposite, and hypotenuse:

[tex]sin(45^o)=\frac{opposite}{hyp} \\hyp=\frac{opposite}{sin(45^o)} \\hyp=\frac{37}{\sqrt{2}/2}\\hyp=37\,\sqrt{2}[/tex]

Answer:

64.08

Step-by-step explanation:

3^16.90+1*20.50-7.12

Answer:

I believe the unit price would be 2.39 per unit

Step-by-step explanation:

Answer:

1) 24Z^2 - 177.

2) 16d^2 - 32d.

6) 30x - 24.

7) 6q - 4.

Step-by-step explanation:

1) 3(8Z^2 - 52 - 7)

= 3(8Z^2 - 59)

= 24Z^2 - 177

2) 8d(2d - 4)

= (8d * 2d) - (8d * 4)

= 16d^2 - 32d

6) 6(5x - 4)

= (6 * 5x) - (6 * 4)

= 30x - 24

7) Already simplified. 6q - 4.

Hope this helps!

Answer:

  B. 18.6

Step-by-step explanation:

The 'rule of 69' says the value will be doubled in 69/i years, where i is the annual interest rate in percent (compounded continuously). The interest rate is given as 3.7%, so the prediction is

  n = 69/3.7 = 10.649

  n ≈ 10.6