Jason and Henry go to the movie theater and purchase refreshments for their friends. Jason spends a total of $66.75 on 12 drinks and 1 bag of popcorn. Henry spends a total of $82.50 on 3 drinks and 10 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of popcorn, to the nearest cent.

Answers

Answer 1

Answer:

The cost of one drink is $5

Step-by-step explanation:

3x-120x=82.50-667.5

120x-3x=667.50-82.50

117x=585

x=5


Related Questions

What is an equation of the line that passes through the point (- 8, 0) and is parallel to the line x - 2y = 10 ?

Answers

4x+2y+10 = 0 can be rewritten as 2y = -4x-10 and dividing by 2 yields the slope/intercept form of y = mx+b

y = -2x-5

where -2 is the slope (m) and -5 the y-intercept (b)

the line we seek has that same slope, will pass through (7,3), but will have a different y-intercept. Plugging in 7 and 3 for x and y gives us

3 = -2(7)+b => 3 = -14+b => 17 = b making our new line’s equation:

y = -2x+17

An equation of the line that passes through the point (- 8, 0) and is parallel to the line x - 2y = 10 is y = -2x+17.

How to get the slope intercept form of a straight line equation?

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = mx +c

To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

We know that 4x+2y+10 = 0 can be rewritten as 2y = -4x-10

Thus, dividing by 2 yields the slope/intercept form of y = mx+b

y = -2x-5

where, -2 is the slope (m) and -5 the y-intercept (b)

Now the line we has that same slope, will pass through (7,3), but will have a different y-intercept.

Then Plugging in 7 and 3 for x and y gives us;

3 = -2(7)+b

3 = -14+b

17 = b

Therefore, our new line’s equation:

y = -2x+17

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Un robot en Marte tiene los siguientes desplazamientos antes de lograr encontrar el lugar con las coordenadas indicadas para empezar a analizar . Su desplazamiento es de: 25 m al Sur, 35 m a 15° partiendo del Este hacia el Norte y por último 20 m a 37° partiendo del Oeste hacia el Norte. Encuentra el desplazamiento de su recorrido

Answers

Answer:

El desplazamiento total del robot es de aproximadamente 17.4 m 12.35° al sur del este

Step-by-step explanation:

El movimiento del robot en Marte se da como sigue;

1) El desplazamiento sur = 25 m

2) El desplazamiento 15 ° al norte del este = 35 m

3) El desplazamiento 37 ° al norte del oeste = 20 m

Por lo tanto, tenemos la moción en forma vectorial;

1) -25[tex]\hat j[/tex]

2) 35·cos(15°)[tex]\hat i[/tex] + 35·sin(15°)[tex]\hat j[/tex]

3) -20·cos(37)[tex]\hat i[/tex] + 20·sin(37°)[tex]\hat j[/tex]

Por lo tanto, tenemos el desplazamiento resultante total, R, del robot está dado por la suma de los vectores como sigue;

R =  (35·cos(15°) - 20·cos(37)) [tex]\hat i[/tex] + (35·sin(15°) + 20·sin(37°) - 25)[tex]\hat j[/tex]

R = 17.8346937192 [tex]\hat i[/tex] - 3.9050329583 [tex]\hat j[/tex]  

La magnitud de R = √ ((17.8346937192) ² + (-3.9050329583) ²) ≈ 17.4 m

La magnitud de R ≈ 17,4 m

La dirección de R = Arctan ((- 3.9050329583) / (17.8346937192)) ≈ -12.35 °

La dirección de R ≈ -12,35 °

La dirección es aproximadamente 12,35 ° al sur del este

El desplazamiento total del robot es de aproximadamente 17.4 m 12.35 ° al sur del este

Use the subway train schedule below to answer the question. Train ScheduleTrainArrives Every...Red line4 minutesBlue line5 minutesYellow line6 minutes All three trains just arrived at the station. When will they next all arrive at the station at the same time? They will all arrive at the station in minutes.

Answers

Answer:

60 minutes

Step-by-step explanation:

Given the schedule above :

Red line arrives every 4 minutes

Blue line arrives every 5 minutes

Yellow line arrives every 6 minutes

All three just arrives at the train station ; when next will they all arrive at the train station at the same time.

Obtain the lowest common multiple of each arrov time :

Lowest common multiple of 4, 5, 6

_2___4___5___6

_2___2___5___3

_3___1___ 5 __ 3

_5___1___ 5 __ 1

_____1 ___1 ___1

Hence, lowest common multiple :(2 * 2 * 3 * 5) = 60

Hemce, they all arrive at the train station at the same time after 60 minutes

Isabella is having a party with 45 balloons. She needs 6 feet of string to attach to
each balloon. How much string would she need if it is sold by the yard? (Hint: 1
yard = 3 feet.)

Answers

Answer:

90 yards of string

Step-by-step explanation:

You multiply the 45 Balloons and 6 feet of string. Then u divide it by 3 bc there are 3 yards is a feet.

Factor 3y3 – 9y2
The factored polynomial is

Answers

Answer:

Factor 3y23y2 out of 3y33y3.

3y2(y)−9y23y2(y)-9y2

Factor 3y23y2 out of −9y2-9y2.

3y2(y)+3y2(−3)3y2(y)+3y2(-3)

Factor 3y23y2 out of 3y2(y)+3y2(−3)3y2(y)+3y2(-3).

3y2(y−3)

Step-by-step explanation:

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Solve x-6y = 13 for y.

Answers

Answer:

y = 1/6x -13/6

Step-by-step explanation:

x-6y = 13

Subtract x from each side

x-x-6y =-x+ 13

-6y = -x+13

Divide each side by -6

-6y/-6 = -x/-6 + 13/-6

y = 1/6x -13/6

write the fraction 18/24 in its simplest form​

Answers

Here 6 is the highest common factor so if you divide both top and bottom by 6 you would get 3/4 :)

Answer:

3/4

Step-by-step explanation:

Divide the numerator and the denominator by the greatest common factor of 18 and 24, 6.

[tex] \frac{18}{24} [/tex]

[tex] \frac{18 \div 6}{24 \div 6} [/tex]

[tex] \frac{3}{4} [/tex]

Find the distance between the points
(9,-7) and
(5,-4).


25
5
V137
V7

Answers

Answer:

5

Step-by-step explanation:

5 is the 100% correct answer.....Hopes to get BRAINLIEST.....

Thank you ☺️☺️

-2(x -3) what number should be distributed

Answers

Answer:

-2

Step-by-step explanation:

-2 needs to be distributed to the rest of the equation so that gives you -2x+6

-2

-2 is on the outside of the parentheses, meaning it should be distributed to everything inside the parentheses

so, -2(x-3) is actually (-2x) + (-2 *-3)

Absolute value is DISTANCE. How many units a number is away from zero.

a.) 3
b.)4
C.) -3
d.) -4

Answers

I believe it is B) 4

The number line is going by .5 per space and there are 8 spaces in the red line segment. You can then do 8 x .5 and you will get 4.

what Else would need to be congruent to show

Answers

Answer:

A

Step-by-step explanation:

RiDdLE oF ThE DaY: PaRt 2- Mr.White had been missing and the only evidence he left behind was a paper that said "The first of July, the fourth of January, the first of December and the eighth of February" the police questioned the people that were in the house at that time. Judy said she was at her parents house, Logan was Mr.Whites secretary said he was working on a report for his boss and haven't left his room and Rose, Mr. Whites daughter said she was having guest and never left the living room. Can you crack the case?

Answers

Answer:

Step-by-step explanation:

1st of July: J

4th of January: U

1st of December: D

8th of February: Y

Answer: JUDY!

Answer:

Child  this has to be one the most hard riddles I ever did

Step-by-step explanation:

Melanie connected a brown garden hose, a green garden hose, and a black garden hose to make one long hose. The brown hose is 10.75 feet long, the green hose is 16.4 feet long, and the black hose is 8.5 feet long. What is the farthest distance the one long hose can reach? 18.65 ft 24.65 ft 34.84 ft 35.65 ft

Answers

Answer:

35.65 feet

Step-by-step explanation:

Melanie connected a brown garden hose , a green garden hose and a black garden hose to make one long hose

The brown hose is 10.75 feet

The green hose is 16.4 feet

The black hose is 8.5 feet

Therefore the farthest distance that the one hose can reach can be calculated as follows

= 10.75 + 16.4 + 8.5

= 35.65 feet

Hence the farthest distance that one hose can reach is 35.65 feet

The United States Census collects data on many variables about individuals and households.

Which variables are quantitative?

Select all that apply.


Years living in the U.S.


How many adults are registered to vote in the upcoming election?


Number of adults over 18.


Number of minors in the household


Family role of respondent


Number of family members residing at the address


Ethnicity


Zip code

Answers

Answer:

Years living in the U.S.

How many adults are registered to vote in the upcoming election?

Number of adults over 18

Number of minors in the household

Number of family members residing at the address

Zip code

Step-by-step explanation:

Given the following :

Select the variables which are quantitative :

Quantitative variables may be explained as those variables which are represented numerically or possess numerical attributes. The are usually expressed in numbers. Quantitative variables in the options below are those which will take Numeric inputs.

Years living in the U.S. = quantitative

How many adults are registered to vote in the upcoming election? = quantitative

Number of adults over 18. = quantitative

Number of minors in the household = quantitative

Family role of respondent = not quantitative

Number of family members residing at the address = quantitative

Ethnicity = Not quantitative

Zip code = quantitative

a) name the transversal connecting 1 and 5
b) name the transversal connecting 7 and 14
c) name the transversal connecting 8 and 11
d) name the transversal connecting 7 and 15
e) name the transversal connecting 3 and 9

Answers

Answer:

a) Name the transversal connecting 1 and 5. Line r b) Name the transversal connecting 7 and 14. Line q c) Name the transversal connecting 8 and 11. Line s d) Name the transversal connecting 6 and 15. Line q e) Name the transversal connecting 3 and 9. Line p

Step-by-step explanation:

The angles pairs and the transversal connecting them are:

a. <1 and <5: transversal r.

b. <7 and <14: transversal q

c. <8 and <11: transversal s

<6 and <15: transversal q.

<3 and <9: transversal p.

Note the following about what a transversal is:

A transversal is a line that intercepts or cut-across two straight lines.

A transversal will connect two angles that lie in two other straight lines the transversal intercepts.

The two angles connected by a transversal can lie on opposite sides of a transversal or on same side along the transversal.

Let's determine the transversal connecting the following given angles:

<1 and <5, is connected by transversal r.

<7 and <14 is connected by transversal q

<8 and <11 is connected by transversal s

<6 and <15 is connected by transversal q

<3 and <9 is connected by transversal p

Therefore, the answers are:

a. <1 and <5: transversal r.

b. <7 and <14: transversal q

c. <8 and <11: transversal s

<6 and <15: transversal q.

<3 and <9: transversal p.

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a Clydesdale drinks about 120 gallons of water every 4 days. At this rate how many gallons of water does a Clydesdale drink in 28 days?

Answers

Answer:

A Clydesdale drinks 840 gallons of water in 28 days.

Step-by-step explanation:

120 gallons/4 days is 30 gallons every day. 30 gallons multiplied by 28 days is 840.

Yeah sorry I’mmmmm!!!

What is the quotient of 5.67 x 10^7 and 2.7 x 10^4 expressed in scientific notar

Answers

Answer:

2.1 * 10 ^3

Step-by-step explanation:

5.67  * 10 ^7 ÷2.7 x 10^4

Divide the numbers

5.67 / 2.7 =2.1

Divide the exponents

10^7 / 10 ^4

Remember when dividing power, we subtract the exponents

10 ^(7-4) = 10^3

Put this back together

2.1 * 10 ^3

Verify that this is in scientific notation

Since this is in scientific notation, we are done

Answer:

2.1x10 to the power of three

Step-by-step explanation:

\frac{5.67\times 10^7}{2.7\times 10^4}

2.7×10

4

5.67×10

7

Divide them.

\frac{5.67}{2.7}\times \frac{10^7}{10^4}

2.7

5.67

×

10

4

10

7

Divide numbers and 10's separeately.

2.1\times 10^3

2.1×10

3

Subtract exponents.

hello… please help What is a parabola in mathematics?​

Answers

A parabola in mathematics is basically plane curve which is mirror-symmetrical and is approximately U-shaped. A point and a line in a U shape.

Example below:

The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. Show your work

Answers

Pythagoras' theorem is a basic relationship between the three sides of a right triangle. The length of the entire walkway to the nearest hundredth of a yard is 50.24 yds.

What is Pythagoras theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

In order to calculate the length of the walkway, we need to calculate the value of b first. Therefore,  the value of b using the Pythagoras theorem can be written as,

[tex]D^2=12^2+b^2\\15^2=12^2+b^2\\225=144+b^2\\b^2= 81\\b=9[/tex]

As we  got the value of b, now the value of each of the four hypotenuses can be written as,

[tex]A = \sqrt{12^2+8^2} = \sqrt{208}=14.422\\\\B=\sqrt{6^2+8^2}=\sqrt{100} = 10\\\\C =\sqrt{6^2+9^2}=\sqrt{117} = 10.82\\\\D = 15[/tex]

Adding the value of all the hypotenuse to get the length of the walkway, therefore, the length will be,

[tex]Sum = A+B+C+D = 14.422+10+10.82+15 = 50.24[/tex]

Hence, the length of the entire walkway to the nearest hundredth of a yard is 50.24 yds.

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solve the equation x²+11=36

Answers

Answer:

x=5

Step-by-step explanation:

Equation:

x^2 + 11=36

1.Subtract 11 on both sides

x^2 = 25

2. Square root 25

x=5

true or faulse
-7(x^2-5x+3) is the same as -7x^2-35x-21

Answers

Answer:

sup

Step-by-step explanation:

jk it's true

Answer:

False

Step-by-step explanation:

-7(x^2-5x+3) is the same as -7x^2+35x-21 the original question had the wrong sign for the 35x, a negative times a negative is a positive.

how do I factor polynomials​

Answers

Break down every term into prime factors. ...
Look for factors that appear in every single term to determine the GCF. ...
Factor the GCF out from every term in front of parentheses, and leave the remnants inside the parentheses. ...
Multiply out to simplify each term.

and Slope
Which point-slope equation represents a line that passes through (3,-2) with a slope of - 4?
5
Oy-3=-=(x + 2)
Oy-2 = (x-3)
Oy+2=-(-3)
Oy+3 = (x + 2)

Answers

Answer: y+2=-4/5(x-3)

Step-by-step explanation:

The equation of the line passing through the point (3, -2) with a slope of - 4 is y = -4x+10

What is an equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is a slope of a line and a point passing by it, we need to find the equation of the line,

So, the general equation of the line is :-

y = mx + c

where, m is the slope, and the c is the y-intercept.

Put the value of the slope given, in the equation,

y = -4x+c

Now, for find the value of c, just put the values of the x and y from the point in the equation,

-2 = -4(3) + c

c = -2+12

c = 10

Now, we get the value of the c,

So, the equation is y = -4x+10

Hence, the equation of the line passing through the point (3, -2) with a slope of - 4 is y = -4x+10

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Triangle A″B″C″ is formed using the translation (x + 0, y + 2) and the dilation by a scale factor of 2 from the origin. Which equation explains the relationship between segment AC and segment A double prime C double prime? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3 segment AC over segment A double prime C double prime = 2 segment A double prime C double prime over segment AC = one half segment AC = segment A double prime C double prime over 2

Answers

Answer:

segment AC is equal to A''B'' over 2

Step-by-step explanation:

Given that,

Scale factor = 2

The coordinates of A is (-3,3)

The coordinates of B is (1,-3)

The coordinates of C is (-3,3)

We know that, the ratio of length of new segment to the length of segment of original figure is called scale factor.

So.

[tex]\dfrac{A''B''}{AC}=2\\\\\text{On cross multiplying,}\\\\AC=\dfrac{A''B''}{2}[/tex]

It means, segment AC is equal to A''B'' over 2 is the correct answer.

What single decimal multiplier would you use to decrease by 6% followed by a 19% increase?

Answers

Answer: 13% increase?

Step-by-step explanation: 19-6=13 which means it would be 1.13 the original amount?

Answer:

1.13

Step-by-step explanation:

A 6% decrease would be 0.94 and a 19% increase after that would be 1.13

what is the value of y

Answers

Answer:

100°

Step-by-step explanation:

180 - 80 = 100

The line is 180 so you take away what you already know (80) and then you have 100.

Answer:

180 degree (exterior angle ) please follow and like me

Someone please help me out !!!!!!!

Answers

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[tex](9x + 17) + (3x + 7) = 180[/tex]

[tex]12x + 24 = 180[/tex]

Subtract sides 24

[tex]12x + 24 - 24 = 180 - 24[/tex]

[tex]12x = 156[/tex]

Divide sides by 12

[tex] \frac{12}{12} x = \frac{156}{12} \\ [/tex]

[tex]x = 13[/tex]

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is 77.65488319 rational or irrational

Answers

Answer:

rationale

Step-by-step explanation:

step by step instructions

Answer:

Irrational

Step-by-step explanation:

The decimal doesn't terminate.

Write the equation of a line which passes through points (4,2) and (0, -2).

Answers

Answer:

y=x-2

Step-by-step explanation:

if you were to plot it onto a graph, the y intercept would be -2

A cargo plane weighed 400,000 pounds. A load of cargo was removed, and the plane weighed 348,963 pounds. Then, 15,358 more pounds of cargo were removed. How many total pounds of cargo were removed from the plane?​

Answers

Answer:

364,321

384963+15358=364321

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