(HELP QUICKLY PLEASE) Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $97.50. Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. Determine the price of each bag of popcorn and the price of each drink.

Each bag of popcorn costs $____
and each drink costs $_____

Answer:

125, 216, 343, 512

Step-by-step explanation:

The next number in the sequence 1, 8, 27, 64 is 125.

This sequence follows the pattern of starting with the number 1, then finding the cube of each subsequent integer (the cube of a number is found by multiplying the number by itself twice, so the cube of 2 is 222=8). Therefore, the next number in the sequence would be 555=125.

Answer: 25 degrees

Step-by-step explanation:

2x + 10 + 30 = 90

2x = 50

x = 25 degrees

The perimeter of the given polygon is about 16.4 units.

We want to find the perimeter of the polygon whose vertices are (-3, 2), (2, 2) and (-1, -3).

The perimeter will be equal to the sum of the distances between the vertices, and remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:

d = √( (x₂ - x₁)² + (y₂ - y₁)²)

The distances are:

between (-3, 2) and (2, 2)

d = √( (-3 - 2)² + (2 - 2)²) = 5

between (-1, -3) and (2, 2)

d = √( (-1 - 2)² + (-3 - 2)²)

d = √( 9 + 25) = 6

between (-1, -3) and (-3, 2)

d = √( (-1 + 3)² + (-3 - 2)²)

d = √29 = 5.4

Then the perimeter is:

5.4 + 6 + 5 = 16.4

Learn more about perimeter at:

https://brainly.com/question/24571594

#SPJ1

The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)

The list of options represents the given parameter

All ordered pairs are relations but not all ordered pair are functions

For an ordered pair to be a function, the following must be true:

The y values on the ordered pair must have  different x values

Using the above as a guide,

This means that the ordered pair in option (b) represents a function

Hence, the ordered pair that is a function is (b)

To learn more about ordered pairs refers to;

https://brainly.com/question/29358259

#SPJ1

K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

If you have an angle and its opposite side, you may calculate the hypotenuse by dividing the length of the opposing side by sin().

To find the length of the side next to the angle, you can also divide the length by tan().

Let the hypotenuse be AC=x

Now given AB=Kx

In △ABC

sin45 ∘ = AC / AB

1/2 = kx/x

K= 1/2

K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

I am so glad you were able to do it! Congrats on 100%

Step-by-step explanation:

That's great you got 100%!!!

Answer:

Todd spent 75, Matt spent 50 and Jeff spent 150

Step-by-step explanation:

Matt = y - 25

Jeff = 3(y - 25)

Todd = y

y - 25 + 3y - 75 + y = 275

5y - 100 = 275

5y = 275 + 100

5y = 375

y = 375/5

y = 75.......Todd therefore spent 75 dollars!!

I think it gets easy from here

Point B on line AB, which is tangent to circle O, has a length of 12 units. The circle is intersected by the line AO from point A to the circle's centre at point C, and the line segment AC has a length of 8 units.

If you know the circumference C, you can calculate the radius of a circle using the formula r = C / (2 * ). If you know a circle's diameter, d, you can calculate its radius using the formula r = d / 2. The line AB crosses the circle at the precise locations P and Q. Here, the line AB is known as the secant of the circle.

Due to the fact that the endpoints of the line segment P Q are on the circle's circumference, it is known as the circle's chord.The two-headed arrow over AB designates a line that passes through points A and B. The name of a line that crosses two distinct points A and B is written as "line AB" or as.

To learn more about radius refer to :

https://brainly.com/question/1550587

#SPJ1

[tex] \frac{3x + 9}{6} = x - 3 \\ [/tex]

[tex]3x + 9 = 6(x - 3)[/tex]

[tex]3x + 9 = 6x - 18[/tex]

[tex]6x - 3x = 9 + 18[/tex]

[tex]3x = 27[/tex]

[tex]x = \frac{27}{3} \\ [/tex]

answer: [tex]x = 9[/tex]

final answer:y= - 1/97 - 6

to find slope, just do the opposite reciprocal of the given slope

to find y-intercept just substitute the given point in y=mx+b

hope this helps!

According to estimates, there were 7,060,268,214 people on Earth as of August 16, 2012. Rounding to the nearest hundred million, 7,060,268,214 equals 7,100,000,000.

Find the digit that is 100,000,000 places away first. The next step is to check if the number that comes after the hundred million place is 5 or higher. Next, multiply the result by 100 million to the nearest billion. 200,000,000 is the reply. 4,000,000 or 5,000,000 may be the million closest to you.

Take a glance at the number in the right-hand column, the hundred thousands, to determine the nearest million. 5 appears in the column for "hundred thousands." It is standard practise to round up numbers that are five or more. This means that you should look at the digit in the ten thousand spot to round numbers out to the nearest hundred thousand. 1,000,000 is added as a rounding error.

To learn more about Population refer to :

https://brainly.com/question/13670638

#SPJ1

Step-by-step explanation:

remember,

x^-n = 1/x^n

any negative exponent of 1.3 means we have to consider it as 1/1.3 with the positive exponent.

so, if the given temperature (x) is negative, 1.3 has a positive exponent and gets bigger and bigger the lower (smaller) x gets.

if the given temperature (x) is positive, 1.3 has a negative exponent and gets smaller and smaller the higher (bigger) x gets.

the domain is the interval or set of all valid x-values.

there is no need for any restriction for x.

so, the domain is all real numbers.

the question is : up to what temperature will there be heating ?

at 5°C ? yes, sure.

at 10°C ? yes, sure.

at 15°C ? some people still need heating.

at 20°C ? most likely not.

but f(20) = $0.042094266... ≈ $0.04

so, still a tiny little bit of heating is happening for the function, but in reality most likely not at all.

the information about such a limit is missing in the question. so, again no limit for x.

f(-8) means that x = -8.

f(-8) = 8(1.3)^--8 = 8(1.3)⁸ = 8×8.15730721 =

= 65.25845768

when the low outside temperature is -8°C, it would cost $65.26 to heat the building.

I don't know the answer options to the last part, but the interpretation certainly is in the context of the problem.

Negative numbers doesn't have real square roots since a square is either positive or 0.

Negative Square Roots Simplifying an expression involving the square root of a negative quantity is done by simplifying the quantity as if it was positive, and placing an i in front as a coefficient.

for example:-

The square root of -9 is 3i. But if you are talking about real numbers, then there would be no solution.

Square root

The square root of a number is defined as the value, which gives the number when it is multiplied by itself.

The √ symbol that is used to denote square root or nth roots.

Learn more about square root here: -

https://brainly.com/question/29286039

#SPJ4

Answer:its b

Step-by-step explanation:yall dume

A number that goes into a greater number with no remainders is called a factor.

A factor is an integer that divides into a greater number without any remainders.

For example, the number 6 is a factor of 18 because when 18 is divided by 6, the answer is 3 with no remainders. Similarly, the number 3 is a factor of 12 because when 12 is divided by 3, the answer is 4 with no remainders.

Factors are important in mathematics because they can be used to solve equations and determine the greatest common divisor (GCD) of two or more numbers. Factors can also be used to determine prime numbers and their multiples.

To learn more about factor, click here:

https://brainly.com/question/14209188

#SPJ4

12 rows had been completed before Elena started working.

What is meant by rows ?

To learn more about rows refer to

https://brainly.com/question/29311084

#SPJ1

Trial Balance as of December 31, 20X1:

Account Debit Credit

Cash: 179,000

Equipment: 69,000

Accounts Receivable: 11,100

Accounts Payable: 69,000

Supplies: 35,000

Scott Hamilton, Capital: 179,000

Fee Income: 29,200

Telephone Expense: 590

Scott Hamilton, Drawing: 3,900

Salaries Expense: 9,900

Total: 368,190 368,190

Income Statement for the month ended December 31, 20X1:

Revenue: 29,200

Expenses:

Equipment: 69,000

Supplies: 35,000

Telephone Expense: 590

Salaries Expense: 9,900

Total Expenses: 114,490

Net Income: (85,290)

To learn more about account statements:

https://brainly.com/question/15525383

#SPJ4

Let's first review the Sin function before talking about Sin 0. Therefore Sin 0 value is 0.

The Sine, Cosine, and Tangent functions in trigonometry are used to determine the angles and length of a right-angled triangle, respectively.

The relationship between the angle, perpendicular side, and hypotenuse side is defined by the sine function.

Alternatively, you can use sin theta, which is equal to the right-angled triangle's perpendicular to hypotenuse ratio. Sin theta is the angle produced between the hypotenuse and adjacent side.

Definition Of Sin In Relation To Sin 0.

Sin 0 denotes that (x,y) is where the value of the x coordinate is 1, and the value of the y coordinate is 0. (1,0). In this case, the hypotenuse has a value of 1, and the opposing side or perpendicular has a value of 0.

As a result, if we set the numbers in the sin ratio for = 0, the perpendicular side to be 1, and the hypotenuse to be 0, we obtain,

Sin 0 = 0/1

Sin 0 = 0

To know more about hypotenuse ratio visit:

https://brainly.com/question/24164512

#SPJ4

One graph will pass through the origin and the second graph will meet the x-axis at 3, -1.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given two function

For  y=2x²:

Since the value of x = 0, the value of y is 0.

thus this graph will pass through the origin and will only have 1 solution.

For  y = x²-2x-3:

At y = 0

x²-2x-3 = 0

x = 3, -1

Therefore, This graph will pass through the x-axis at 3, -1.

Learn more about function here:

https://brainly.com/question/21145944

#SPJ1

Answer:

From the top of a 12 foot ladder, the angle of depression to the far side of a sidewalk is , while the angle of depression to the near side of the sidewalk

Step-by-step explanation:

Answer:

He plans to kayak a total of 6.4 miles. Damon kayaks at an average speed of 1.6 miles per hour. How many hours will it take Damon to kayak the 6.4 miles? It will take Damon 4 ‾ hours to kayak 6.4 miles.

[tex]{3 }^{p} = \frac{1}{9} [/tex]

[tex]{3 }^{p} = 9 {}^{ - 1} [/tex]

[tex]{3 }^{p} = (3 {}^{2} ) {}^{ - 1} [/tex]

[tex]{3 }^{p} = 3 {}^{} {}^{ - 2} [/tex]

[tex]p = - 2[/tex]

The log₂(7) is irrational, because if we assume that it is rational, we can reach a contradiction.

Assume that log₂(7) is rational. This means that it can be written as the ratio of two integers, a/b, where a and b are integers and b is not equal to zero.

Then, using the definition of a logarithm, we have: 2^(a/b) = 7

Multiply both sides by b, we have: 2^a = 7b

Now we have a problem, because 7b is not necessarily a power of 2. This means that our assumption that log₂(7) is rational leads to a contradiction, and therefore log₂(7) must be irrational.

To know more on logarithmic function

https://brainly.com/question/16017369

#SPJ4

In the production range of 2 to 3 combs, the opportunity cost of producing one more comb is d) 0.14 brushes.

To learn more about production range refer to:

https://brainly.com/question/21439279

#SPJ1

The given statement that " Ricardo has an equally likely chance of spinning an odd number as spinning a number less than 4" is True.

When rolling a fair dice, the probability of getting an odd number is:

= Number of odd numbers / Number of sides on die

Number of odd numbers = 1, 3, 5

Probability of odd number:

= 3 / 6

= 1 / 2

Probability of number less than 4 :

= 3 / 6

= 1 / 2

Ricardo therefore has  an equally likely chance.

Find out more on probability at https://brainly.com/question/12645719

#SPJ1

Options for this question are:

(b) √29 is between 5 and 6. You can approximate it by finding the perfect squares that are closest to 29: 25 (5^2) and 36 (6^2). √29 is between 5 and 6 since 5^2 < 29 < 6^2

(c) √54 is between 7 and 8. You can approximate it by finding the perfect squares that are closest to 54: 49 (7^2) and 64 (8^2). √54 is between 7 and 8 since 7^2 < 54 < 8^2.

Answer:

  y = 900(0.91^t)

Step-by-step explanation:

You want a function that describes the value of a $900 sound system that decreases in value by 9% per year.

When the amount of change is proportional to the amount, the amount is described by an exponential function:

  y = ab^x

where 'a' is the initial value, and 'b' is the "growth factor."

Here, the change is expressed as a "growth rate" of -9% per year. The growth factor is 1 added to the growth rate:

  b = 1 +(-9%) = 1 -0.09 = 0.91

The initial value is given as ...

  a = 900

So the function you want is ...

  y = 900(0.91^t)

__

Additional comment

The independent variable in this case is time, and the problem statement tells you to use 't' to represent it. The decay rate is given as a percentage per year, so the units of t will be years.

A system of three linear equations in two variables that satisfies the given situation can be x + y = 5, 2x + y = 5, and x + 2y = 5

To satisfy the given situation for a system of three linear equations, write any linear equation as the first equation. Let's say

x + y = 5

For the second equation, multiply the x term of the first equation by any factor, keeping the y term and the constant unchanged.

2x + y = 5

The last equation could be written using the second equation wherein the constant of the variable x and y are interchanged.

x + 2y = 5

Any two of the equations in this system have exactly one solution, because they have a unique solution when we solve them individually. However, when we try to solve the entire system by using all three equations, we find that the system has no solution.

This can be easily seen by solving the system by substitution, elimination, or graphical method.

It is also possible to use different equations but with the same criteria, the key is that at least one of the equations should be the negation or a multiple of another equation.

The problem seems incomplete/unreadable, it must have been...

"Write a system of three linear equations in two variables so that any two of the equations have exactly one solution, but the entire system of equations has no solution."

Learn more about system of linear equations here: https://brainly.com/question/13729904

#SPJ4

To make a true equation, check your math to make sure that the values on each side of the equals sign are the same.

step1

(a) a +v = b-(v+5)

1+5=6 not equal a+ v=5

To check if a given value is a solution to an equation:

Evaluate the left-hand side expression at the given value to get a number

Evaluate the right-hand side expression at the given value to get a number.

See if the numbers match.

If you add the same number to both sides of an inequality, the inequality remains true.

To learn more about inequalities refers to;

brainly.com/question/29321548

#SPJ1

Correct question:

What criteria must meet to say that a+v=b-(v+5) is true?