-2x + 2y = 2 4x –4y= 4A.No solutionB.One solution: x = _____ y = ___C.Infinitely many solutionsBONUS: A customer at a concession stand bought 2 boxes of popcorn and 3 drinks for $12. Another customerbought 3 boxes of popcorn and 5 drinks for $19. How much does a box of popcorn cost? _____________How much does a drink cost?__________________

Answers

Answer 1

Answer:

See answers below

Step-by-step explanation:

1) Given the simultaneous equation;

-2x + 2y = 2 .... 1  * 2

4x –4y= 4...2 * 1

____________

-4x + 4y = 4 .... 1

4x –4y= 4...2

Add both equations

4y-4y = 4-4

0y = 0

y = 0/0

Let x = k

Substitute x = k into 1

From 1: -2x + 2y = 2

-x+y = 1

-k + y = 1

y = 1+k

Hence the solution to the system of equation (x, y) is (k, 1 + k) where k is any integer.

The presence of k shows that the equation has many solutions since k can take any value

2) Let a box of popcorn be x

Let the cost of a drink be y

If a customer at a concession stand bought 2 boxes of popcorn and 3 drinks for $12, then;

2x + 3y = 12 ... 1

Also, if another customer bought 3 boxes of popcorn and 5 drinks for $19, then;

3x + 5y = 19 ...2

Solve 1 and 2 simultaneously

2x + 3y = 12 ... 1  * 3

3x + 5y = 19 ...2  * 2

_________________

6x + 9y = 36  

6x + 10y = 38

Subtract

9y - 10y = 36 - 38

-y = -2

y = 2

Recall that 2x + 3y = 12

2x + 3(2) = 12

2x + 6 = 12

2x = 12-6

2x = 6

x = 6/2

x= 3

Hence a box of popcorn cost $3 and a drink cost $2


Related Questions

Can someone help me? The first person to get it correct gets brainliest.

Answers

50 because 2(5)^2 equals to 2 (5x5) which equals 2(25) which is 50.

PLEASE HELP ASAP WILL GIVE 25 POINTS PLUS WILL MARK AS BRAINLIEST PLEASE EXPLAIN ANSWER TOO!

Answers

Answer: 5.1

Step-by-step explanation:

use SOHCAHTOA

so its y/8  = cos(50)

y= cos(50) x 8

y = 5.1

Hope this helps!!

I’m answering for the points and so you can mark the person above as brainliest

You have $15. a. How much money do you have left if you ride each ride once? You have $ left. b. Do you have enough money to ride each ride twice? Explain. It costs $ to ride each ride once, and you have $ left.

Answers

Answer:

a.) Money left = $1

b) No

Step-by-step explanation:

Given - You have $15. It costs $ to ride each ride once,

To find - a. How much money do you have left if you ride each ride once?

              b. Do you have enough money to ride each ride twice? Explain.

Proof -

As it is not given in the question that, how much cost to ride each ride once.

Let us assume that,

The cost for each ride = $2

Total rides  = 7

Now,

Total money we have = $15

a.)

Given, cost for 1 ride = $2

⇒ Cost for 7 rides = 7×$2 = $14

∴ Money left =  $15 - $14 = $1

b.)

Given,

Cost for 1 ride = $2

Cost of 1 ride if we ride twice = 2×$2 = $4

Cost of 7 rides if we ride twice = 7×$4 = $28

As $28 > $15

So, we cannot ride each ride twice.


If the cost of petrol is R10,05 per litre, calculate how far the
car will be able to travel if R150,00 worth of petrol is filled in the car.

Answers

Answer:

I dont know lol...........

∠3 and ∠6 are _______ angles

Answers

Alternate interior angles are congruent. so ∠3 = ∠6 -------> by alternate interior angles.

________________

Hope this makes sense!

-Lexi

plz help, I will mark brainliest

Answers

X > 10 Because if you remove the parenthesis and distribute 4 through the parentheses - 8x + 8 + 12. Then you add 8 and 12 which equals 20. Then you move the constant to the right-hand side and change its sign. You calculate 100 - 20 which give you 80 and divide then which gives you 10.

Hopefully this helps! <3

What is the slope of a trend line that passes through the points (1, 3) and (10, 25)?
O -15/2
O -1/2
O 22/9
O 24/7​

Answers

-15/2 you go up then down

Sorry for asking again.
The options are cut out so it says
2
3
4
5

Answers

Answer:

2

Step-by-step explanation:

For A and B, count to the y axis (vertical line)

How many ounces in 5 gallons?
O A. 128 ounces
O B. 320 ounces
O C. 640 ounces
O D. 1280 ounces
please hhelp I'll be posting a lot of questions ;-;​

Answers

The answer is 640 ounces

Find a10 of the sequence 4, 28, 196, 1372



*Formula: a_n=a_1r^{n-1}a
n

=a
1

r
n−1

Answers

Answer:

[tex] \purple { \bold{ a_{10}=161414428}}[/tex]

Step-by-step explanation:

Given sequence is: 4, 28, 196, 1372

28/4 = 7

196/28 = 7

1372/196 = 7

Since, the ratio of any two consecutive terms is same, so it is a geometric sequence.

Therefore,

Common ratio r = 7

First term a = 4

nth term of a geometric sequence is given as:

[tex]a_n=ar^{n-1} \\ \\\implies \\ \\ a_{10}=4.7^{10-1} \\ \\ a_{10}=4.7^{9} \\ \\ a_{10}=4.7^{9} \\ \\ a_{10}=4(40353607) \\ \\ \red{ \bold{ a_{10}=161414428}}[/tex]

The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.

Answers

Answer:

59.85

Step-by-step explanation:

The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.

We solve the above question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 70

σ is the population standard deviation = 7

z = -1.45

Hence:

-1.45 = x - 70/7

Cross Multiply

-1.45 × 7 = x - 70

-10.15 = x - 70

x = -10.15 + 70

x = 59.85

Add 4 kg 250 g, 2 kg 90 g and 19kg 3 g.

Answers

Answer:

=25343 grams or 25 kg 343 g.

Step-by-step explanation:

1 kg = 1000 g

∴ 4 kg = 4000 grams

and the 4 kg 250 g would equal = 4250 grams.

∴ 2 kg = 1000 g

2 kg 90 g = 2000 grams + 90 g = 2090 grams

∴ 19 kg = 19000 grams

and 19 kg 3 grams = 19000 grams + 3 grams = 19003 grams

now we will add all of the values together to get the final answer.

4250 grams + 2090 grams + 19003 grams = 25343 grams or 25 kg 343 g.

Hope this helps!!

2 The length of this rectangle is x cm.
a The width of the rectangle is 2 cm less than the length.
Write down an expression for the width of the rectangle, in centimetres.
b The perimeter of the rectangle is 84 cm. Write down an equation to show this.
c Solve the equation.
d Find the area of the rectangle.

Answers

Answer:

a. The width of the rectangle is x-2cm

b. length is 21.5 cm and breadth is 19.5cm

c. area is 419.25 cm sq.

Step-by-step explanation:

Let the length be x and the breadth be x-2

perimeter = 84 = 2(l+b) = 2×(x+x-2)

2×(2x-2)=84

4x-2 = 84

4x = 86

x= 86/4

x= 21.5

length is 21.5 and breadth is 21.5-2 = 19.5

area = l×b

= 21.5 ×19.5

= 419.25cmsq.

hope it helps

) The diagram shows a quadrant of a circle . If the curved edge is 15 cm long, what is the length of a straight edge?

Answers

Answer:

9.55 cm

Step-by-step explanation:

A quadrant of a circle is 1/4 of a circle.

Since the curved edge is 15 cm, a full circle would be 60 inches.

60/Pi = diameter

diameter = 60/3.14 = 19.11 cm

diameter/2 = radius

radius = 19.22/2 = 9.55 cm which is the length of a straight edge.

Please simplify the expression to standard form:
−1/2(8x −4) + (−5 + 3x)

Answers

Photomath can do that
It’s -x-3. You can use photo math

Elia rode her bicycle from her house to the beach at a constant speed of 18 1818 kilometers per hour, and then rode from the beach to the park at a constant speed of 15 1515 kilometers per hour. The total duration of the rides was 1 11 hour and the distances she rode in each direction are equal. Let b bb be the number of hours it took Elia to ride from her house to the beach, and p pp the number of hours it took her to ride from the beach to the park.

Answers

Answer: hello your question is not well written but it seems you are asking for the Total distance covered during the rides hence i will give you a general solution

Total distance travelled during rides = 16.36 km

Total duration of rides = 1 hour

Step-by-step explanation:

Given that :

b = number of hours from house to beach

p = number of hours from beach to park

since the total duration of the rides = 1 hour

hence: b + p = 1 ------ ( 1 )

Also ; speed from house to beach = 18 km/hr

         speed from beach to park = 15 km/hr

Given that distance covered in both directions are equal and distance = s * t

Hence distance covered :   18b = 15p ------  ( 2 )

determine the total distance travelled

b + p = 1 ------ ( 1 )

18b = 15 p ----- ( 2 )

from equation 1 : b = 1 - p

18 ( 1 - p ) = 15p

18 = 15p + 18p

p = 18 / 33 = 6/11

back to equation 1

b + 6/11 = 1

hence b = 1 - 6/11 = 5/11

Distance covered in one direction

18 ( 5/11 ) = 15 ( 6/11 )

90 / 11  = 90 /11

hence Total distance covered = ( 90 / 11 ) * 2 = 16.36 km

Help me please and thank you

Answers

Answer:

i think your answer would be 12

Step-by-step explanation:

there are 12 dots, so 12 robots were built

hope this helps! have a nice day!

There are 15 counters. One-third of the counters are yellow. How many
counters are yellow? *

Answers

Answer:

3

Step-by-step explanation:

15*1/5= 3

Write a system of linear equations for the problem below(you do not have to solve it) Twenty-six students attended the community service event. The number of girls was 4 fewer than twice the number of boys. How many boys attended the community service event?

Answers

Answer:

Number of boys who attended the community service event = 10

Step-by-step explanation:

Let [tex]x[/tex] denotes number of girls and [tex]y[/tex] denotes number of boys.

Twenty-six students attended the community service event.

So,

[tex]x+y=26[/tex]

The number of girls was 4 fewer than twice the number of boys.

[tex]x=2y-4[/tex]

Put [tex]x=2y-4[/tex] in [tex]x+y=26[/tex]

[tex]2y-4+y=26\\3y=26+4\\3y=30\\y=10[/tex]

So,

Number of boys who attended the community service event = 10

The sum of the first n terms of a sequence is given by Sn = 3m+1 - 6
3.1.
Determine the sum of the first 12 terms.

Answers

Answer:

i need points sry i needa ask a question

Step-by-step explanation:

PLEASE ANSWER THIS FAST-Name the angles and sides of each pair of triangles that are congruent.

Answers

Answer:

1. Gh is congruent to Gh. Hf is congruent to HL. Gf is congruent to GL. Angle G is congruent to angle G. Angle h is congruent angle h. Angle F is congruent to angle L.

2. Cb is congruent to Jk. Bd is congruent to KL. Cd is congruent to JL. Angle c is congruent to angle j. Angle b is congruent to angle j. Angle d is congruent to angle L.

3. Wx is congruent to Dc. Xy is congruent to Cy. Wc is congruent to Dy. Angle w is congruent to angle d. Angle c is congruent to angle x. Angle y is congruent angle y.

Tip: Label the statement 1 , 2, 3 and do the same to the other one. It will make your life so much easier.

A truck can carry a 3.5 ton load. How many packs of roof shingles weighing 80 lb each can it carry?

Answers

Answer:

25

Step-by-step explanation:

it can carry 25 packs of shingles because

1 ton = 2000 ponds

and 80 can go into 2000 25 times

hope this helps!

Please I need help please!!!!!!!

Answers

Answer:

1/3= 137.51 so b

Step-by-step explanation:

Answer:

B, θ=137,51°

Step-by-step explanation:

[tex]\alpha =\frac{l}{r}[/tex]

alpha are the angle in radian.

l= lenght of de arc=12cm

r=radius=5cm

[tex]\alpha =\frac{12}{5} \\\\[/tex]

Converting the radian angle to degrees:

α--->θ

π--->180°

θ=(180°*α)/π

using the fact that: α=12/5

θ=(180°*12)/5

θ=432°/π

θ=137,5098°

θ=137,51°

find the area of the regular polygon with the given apothem a and side length s. a=28. s=18.2 round to the nearest decimal place as needed​

Answers

The formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.

someone please help me

Answers

Answer:

can't see the question ⁉️

PLZZZ HURRYY. i will thank you. Q- Explain the transformations that map the polygon A to polygon B.

Answers

It went down 3 and reflected across y axis

Find the value of x and y.

Answers

Answer:

x= 73

y= 13

Step-by-step explanation:

The sum of the angles opposite the exterior angle = the exterior angle so

x= 141-68

x= 73

The angle sum of a triangle= 180.

180-68-73= 39

since there are 3 "y"s we need to divide 39 by 3

39/3= 13

The answer is Y=13 and x=73

question in photo—————————-

Answers

Answer:

there is two solutions to that problem. you can find x is equal to two numbers.

Need help!!!! PLZ I don't know

Answers

Answer:

Step-by-step explanation:

First factor the polynomials and reduce the fractions.

Marty has a driveway that is 200 feet long. The tires on her car have a diameter of 18 inches. What is the fewest number of tire rotations a tire will make tot travel the entire distance of the driveway?​

Answers

The the fewest number of tire rotations is 42 to travel the entire distance of the driveway.

It is given that the driveway that is 200 feet long and the tire diameter is 18 inches.

It is required to find the fewest number of tire rotations a tire will make to travel the entire distance of the driveway.

What is a circle?

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

Driveway length = 200 feet

Diameter of the tire = 10 inches

For converting it to feet divide by 12.

Now the diameter of tire = 18/12 = 1.5 feet

Radius of the tire = 0.75 feet

We know the perimeter of the circle:

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

P = 2(π)(0.75)

P = 4.71 feet   ( π =3.14 and P = 0.75)

[tex]\rm number \ of \ tire \ rotations = \frac{Driveway \ length}{Perimeter \ of tire}[/tex]

[tex]= \frac{200}{4.71}[/tex]

Number of tire rotation = 42.462 ≈ 42

Thus, the the fewest number of tire rotations is 42 to travel the entire distance of the driveway.

Learn more about circle here:

brainly.com/question/11833983

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