Carolyn was asked to solve the following system of equations. Her work is shown. What is the solution to the system of linear equations?

Answer:

50 - 6x = leftover value

Step-by-step explanation:

X is the amount of movies he has seen (pays $6 for each movie)

Carl can use the function → a(n) = 56 - 6n determine the value left on his card after each movie he sees.

We have Carl's grandparents who gave him a $50 gift card to a local movie theater. The theater charges $6 admission for each movie.

We have to check how can Carl use an arithmetic sequence to determine the value left on his card after each movie he sees.

An arithmetic sequence is a sequence of numbers in which every term (except the first term) is obtained by adding a constant number to the previous term is called an arithmetic sequence.

According to the question, we have -

Amount in Gift card = $50

Charges for Admission to every new movie = $6

Therefore, we can create a arithmetic sequence with -

a = 50  and  d = -6

Therefore -

a(n) = a + (n - 1)d

a(n) = 50 + (n - 1)(-6)

a(n) = 50 - 6n + 6

a(n) = 56 - 6n

where n denotes the number of movies he watch and a(n) is money remained after watching the movies.

Hence, Carl can use the function a(n) = 56 - 6n determine the value left on his card after each movie he sees.

To solve more questions on Arithmetic sequences, visit the link below-

https://brainly.com/question/21406026

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Work Shown:

For any given suit, there are 3 face cards: Jack, Queen, King.

There are 4 suits, leading to 4*3 = 12 face cards out of 52 total.

The probability of pulling out a face card is 12/52.

After that card is selected, we have 12-1 = 11 face cards left and 52-1 = 51 cards left overall. This is assuming a replacement is not made, or the card is not put back.

The probability of getting another face card, given the first selection was a face card, is 11/51.

Multiplying the two fractions gives:

P(2 face cards) = P(1st facecard)*P(2nd facecard given 1st facecard)

P(2 face cards) = (12/52)*(11/51)

P(2 face cards) = (12*11)/(52*51)

P(2 face cards) = (3*4*11)/(13*4*3*17)

P(2 face cards) = (11)/(13*17)

P(2 face cards) = 11/221

Step-by-step explanation:

line that is perpendicular to the given line :

y = 2/3x + 5

m1 × m2 = -1

m1 = the coefficient of x

m1 = 2/3

remember : m1 × m2 = -1

2/3 x m2 = -1

2m2 ÷ 3 = -1

(let m2 = x)

2x ÷ 3 = -1

(cross multiply)

2x = 3 × -1

2x = -3

(divide both sides by the coefficient of x)

x = -3/2

Remember : m2 =x

m2 = -3/2

The line that passes through the point (4,2) ;

( note : x¹ = 4 , y¹ = 2)

m = (y - y1) ÷ (x - x1 )

-3/2 = (y - 2) ÷ (x - 4)

(cross multiply)

-3(x - 4) = 2 (y - 2)

-3x +12 = 2y - 4

(make y the subject of formula )

-3x + 12+ 4 = 2y

-3x + 16 = 2y

(

(divide through by the coefficient of y)

-3x/ 2 + 16/2 = y

-3/2x + 8 = y

HOPE IT WAS HELPFUL

Answer:

..

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph below is how you label the points, where to put them and the line that you need to draw to get the points.

Everything is laid out for you to copy. Start at the lower right and go to the to the upper left on your table.

Answer:

[tex]\frac{x^2}{25} -\frac{y^2}{200} =1[/tex]

Step-by-step explanation:

Recall that the equation of  hyperbola centered at the origin with transverse horizontal axis has the general form:

[tex]\frac{x^2}{a^2} -\frac{y^2}{b^2} =1\\and\,\,\,\, with\\c=\sqrt{a^2+b^2}[/tex]

since we know that a = 5 ,and c = 15,we can solve for b:

[tex]15=\sqrt{5^2+b^2} \\15^2=25+b^2\\b^2=200\\[/tex]

then the equation of the hyperbola becomes:

[tex]\frac{x^2}{5^2} -\frac{y^2}{200} =1\\\frac{x^2}{25} -\frac{y^2}{200} =1[/tex]

Answer:x = 6

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Add  5 to both sides of the equation:

2x -5 = 7

2x -5 +5 =7 +5

Simplify:

2x=12

Divide both sides of the equation by the same term:

2x = 12

2x/2 = 12/2

Simplify again:

x=6

Answer:

x = 6

Answer:

60

Step-by-step explanation:

Since equalateral. The angles are the same.

Answer:

(-20, 0, 0)

(0, 12, 0)

(0, 0, -30)

Answer:

(-20, 0, 0)

(0, 12, 0)

(0, 0, -30)

Answer:

I don't know how to expand but I can simplify please mark me

Step-by-step explanation:

2(x + 7) + 3(x + 1)

=2x + 14 + 3x + 3

=2x-3x + 3-14

=x+11

Answer:

The person is 5.28 feet tall

Answer:

Step-by-step explanation:

total area = rectangle + semi circle

                = (11 x 5) + (1/2 * π * 2.5²)

               = 55 + 9.8

               = 64.8 sq. units

Answer:

the slope is 1

Step-by-step explanation:

i cant tell if the y-intercept is 1 or -1

Note: Your option 'b' is somewhat ambiguous, so I am assuming you meant to write the equation y=2x+3 for the 'b' option.

Answer:

the equation y = 2x + 3  has slope m=2 and the y-intercept is 3, and also PASSES through the point (2, 7).

Step-by-step explanation:

Given the point (2, 7) from which the equation passes through.

so checking all the equations in the options to check whether any equation passes through or not.

Checking the option 'a':

y = 3x - 2

Putting (2, 7)

7=3(2)-2

7=6-2

7=4

L.H.S is not equal to R.H.S

Therefore, the option 'a' is NOT correct.

So, the equation y = 3x - 2 will NOT PASS through the point (2, 7)

Checking the option 'b':

y = 2x + 3

Putting (2, 7)

7=2(2)+2

7=7

7=7

L.H.S is equal to R.H.S

Therefore, option 'b' is the CORRECT option.

So, the equation y = 2x + 3 will PASS through the point (2, 7)

Checking the option 'c':

y = x-6

Putting (2, 7)

7=2-6

7=-4

L.H.S is not equal to R.H.S

Therefore, the option 'c' is NOT correct.

So, the equation y = x-6 will NOT PASS through the point (2, 7)

Checking the option 'd':

y + 2x = 8

Putting (2, 7)

7+2(2)=8

7+4=8

11=8

L.H.S is not equal to R.H.S

Therefore, the option 'd' is NOT correct.

So, the equation y + 2x = 8 will NOT PASS through the point (2, 7)

Therefore, considering the above analysis, we conclude that:

Option 'b' is the CORRECT option.

So, the equation y = 2x + 3 will PASS through the point (2, 7).

also

The slope-intercept form of the equation is

[tex]y=mx+b[/tex]

where m is the slope and b is the y-intercept.

Therefore, the equation y = 2x + 3  has slope m=2 and the y-intercept is 3, and also PASSES through the point (2, 7).

Answer:

0.25 and 0.33?

Step-by-step explanation:

Answer:

[tex]P(x,y) = (0,\frac{11}{5})[/tex]

Step-by-step explanation:

Given

[tex]A = (-2,1)[/tex]

[tex]B = (3,4)[/tex]

[tex]m:n = 2:3[/tex]

Required

Determine the coordinates of P

The coordinate of a point when divided into ratio is:

[tex]P(x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]

Where

[tex](x_1,y_1) = (-2,1)[/tex]

[tex](x_2,y_2) = (3,4)[/tex]

[tex]m:n = 2:3[/tex]

This gives:

[tex]P(x,y) = (\frac{2 * 3 + 3 * -2}{2 + 3},\frac{2 * 4 + 3 * 1}{2 + 3})[/tex]

[tex]P(x,y) = (\frac{6 - 6}{5},\frac{8 + 3}{5})[/tex]

[tex]P(x,y) = (\frac{0}{5},\frac{11}{5})[/tex]

[tex]P(x,y) = (0,\frac{11}{5})[/tex]

The answers are A and C.

Answer:

c+2

Step-by-step explanation:

Im not 100% sure I understand what you mean by this but anytime it says and in a statement it means + so c+2 would be the answer.

Answer:

1 + 1 = 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1+1 =2

Answer:

110 db

Step-by-step explanation:

Answer: 3h+18

Step-by-step explanation:

2h+6+h+12

add like terms (add all the the h’s) which equals 3h and add 6+12 which equals 18 so your answer is 3h+18

Answer:

you have to post the equation

Step-by-step explanation:

Answer:

(4, -5) should be the correct answer

Step-by-step explanation:

I hope this helps, please mark brainliest if correct!

Answer:

Step-by-step explanation:

Y should still be 10 since x is 540