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 a drink, to the nearest cent.


​

Answer:

$51200

Step-by-step explanation:

Simply do this: 2¹⁰ × 50. You are doing this because you are doubling it for each year that goes by.

I am joyous to assist you anytime.

The smallest number that's in the domain of f ° g is x = 0.

The function f(x) = √(9x) represents the square root of 9x.

The function g(x) = x + 7 represents adding 7 to x. To find the smallest number that is in the domain of f ° g, we need to determine the values of x that satisfy both f(x) and g(x).

We can start by looking at the domain of g(x), which includes all real numbers. So any value of x will work for g(x).

Next, we need to consider the domain of f(x). Since taking the square root of a negative number is not defined in the real number system, we must ensure that 9x is positive or zero.

So we set 9x ≥ 0 and solve for x: x ≥ 0. This means any non-negative value of x will work for f(x).

Now, to find the smallest number in the domain of f ° g, we need to find the intersection of the domains of f(x) and g(x).

Since any value of x will work for g(x) and only non-negative values of x will work for f(x), the smallest number that satisfies both functions is x = 0.

Answer:

[tex]\large\boxed{\left(-\dfrac{1}{2},\ -1\right)}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)\\\\================================\\\\A(1,\ -3),\ B(-2,\ 1)\\\\\text{Substitute:}\\\\x=\dfrac{1+(-2)}{2}=\dfrac{-1}{2}=-\dfrac{1}{2}\\\\y=\dfrac{-3+1}{2}=\dfrac{-2}{2}=-1[/tex]

Answer:

[tex](\frac{-1}{2} ,-1)[/tex]

Step-by-step explanation:

line segment AB has endpoints A(1,-3) and B(-2,1).

To find the midpoint of AB we use formula

[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

A(1,-3) is (x1,y1) , B(-2,1) is (x2,y2)

Plug in the values in the formula

[tex](\frac{1-2}{2} ,\frac{-3+1}{2} )[/tex]

[tex](\frac{-1}{2} ,\frac{-2}{2} )[/tex]

[tex](\frac{-1}{2} ,-1)[/tex]

System of equations helps us to compare two real-life problems. The system of equations will have no solution.

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

As the systems of two-equations are given, therefore, the two equations are:

Now, if we plot the two-equation on the graph, we will find that the lines of the two equations are parallel. therefore, the system of equations will have no real solution or will have no solution.

Hence, the system of equations will have no solution.

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Answer:

moderate negative

Step-by-step explanation:

a perfect would be a rate, I believe.

The statement which best describes the association between variables X and variable Y is:

          moderate negative association

Since  by looking at the scatter plot we see that the Y-value is decreasing with the increasing x-value i.e. the two variables are in inverse proportion.

Hence, the two variables has a negative association.

Also, when we will draw a line of best fit we will observe that not all the data points will lie on the trend line but they will be closely related to the line of best fit.

Hence, the relationship is moderate.

             Hence the answer is:

           Moderate negative association.

Answer:

The volume of the prism is [tex]1,299\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the prism is equal to

[tex]V=BL[/tex]

where

B is the area of the triangular base

L is the length of the prism

we have

[tex]L=30\ in[/tex]

Find the area of the base B

The area of a equilateral triangle is equal to

[tex]B=\frac{1}{2}(10)^{2} sin(60\°)[/tex]

[tex]B=25\sqrt{3}\ in^{2}[/tex]

substitute

[tex]V=(25\sqrt{3})(30)=1,299\ in^{3}[/tex]

The volume of the traingular prism is 1,280.85 in³.

The volume of the prism is determined using the following formulas as show below;

V = Bh

where;

Base area is calculated as follows;

[tex]A = \frac{a^2\sqrt{3} }{4} \\\\A = \frac{10^2 \times \sqrt{3} }{4} \\\\A = 25\sqrt{3} \ in^2[/tex]

[tex]L^2 = (\frac{a}{2} )^2 + h^2\\\\h^2 = L^2 - (\frac{a}{2} )^2\\\\h^2 = 30^2 - (\frac{10}{2} )^2\\\\h^2 = 875\\\\h = \sqrt{875} \\\\h = 29.58 \ in[/tex]

V = 25√3 x 29.58

V = 1,280.85 in³

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Answer:

3) 3a - 2 + 3 = -2

   3a            = -2 + 2 - 3 = -3

   a              = -3/3 = -1

4) m/-6 - 18 - 4 = -16

   m/-6             = -16 + 18 + 4 = 6

   m                  = 6 · (-6) = -36

5) x/-2 - 4 + 22 = -28

   x/-2              = -28 + 4 - 22 = -46

   x                   = -46 · (-2) = 92

6) -13 = 5 + 20m - 2m

   -13 = 5 + 18m

   -18 = 18m

   m  = -18/18 = -1

7) -2(2p - 1) = -14

   -4p + 2   = -14

   -4p          = -14 - 2 = -16

   p              = -16/(-4) = 4

8) -1(8x + 20) = 12

   -8x - 20      = 12

   -8x              = 12 + 20 = 32

   x                  = 32/(-8) = -4

9) -49 = 7(2x + 3)

   -49 = 14x + 21

   -14x = 49 + 21 = 70

   x                     = 70/-14 = -5

10) 3(8h - 4) + 17 = -19

     24h - 12 + 17 = -19

     24h               = -19 + 12 - 17 = -24

     h                   = -24/24 = -1

Answer:

2

Step-by-step explanation:

7 divided by 4 equals 1.75 then round to nearest tenth you get 2.

the answer is 1.8 because 1.75 is getting rounded by the 7 place which is the tenths place

Answer:

the 1st one in the 2nd row

Step-by-step explanation:

Final answer:

To determine the number of one-point and two-point shots made by a basketball team that scored 92 points from 55 shots, set up a system of equations. Solve the system to find that the team made 18 one-point shots and 37 two-point shots.

Explanation:

Finding the Number of One-Point and Two-Point Shots

Let's define x as the number of one-point shots and y as the number of two-point shots. We then have the following system of equations based on the information provided:

x + y = 55 (Total number of successful shots)

1x + 2y = 92 (Total points scored)

To solve for x and y, we can use either substitution or elimination methods.

Using substitution:

Solve the first equation for x: x = 55 - y.

The team made 18 one-point shots and 37 two-point shots.

Answer:

The measure of angle KLM is 62°

Step-by-step explanation:

* Lets revise the properties of the rhombus

- The rhombus has 4 equal sides in length

- Every two opposite angles are equal in measure

- The two diagonals bisect each other

- The two diagonals perpendicular to each other

- The two diagonals bisect the vertices angles

* Lets solve the problem

∵ JKLM is a rhombus

∴ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus

∵ JL and KM are diagonals in the rhombus and intersect each

   other at N

∴ JL bisects ∠MJK

∴ m∠KJL = m∠MJN

∵ m∠KJL = (2x + 5)°

∵ m∠MJN = (3x - 8)°

∴ 2x + 5 = 3x - 8 ⇒ subtract 2x from both sides

∴ 5 = x - 8 ⇒ add 8 to both sides

∴ 13 = x

∴ The value of x = 13

∵ m∠KJL = (2x + 5)° ⇒ substitute the value of x

∴ m∠KJL = 2(13) + 5 = 26 + 5 = 31°

∵ m∠KJL = 1/2 m∠MJK

∴ m∠MJK = 2 m∠KJL

∴ m∠ MJK = 2 × 31° = 62°

∵ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus

∴ m∠KLM = 62°

Answer:

Let's solve your system by substitution.

x=5;y=−7

Step: Solve x=5 for x:

x=5

Step: Substitute 5 for x in y=−7:

y=−7

y=−7

Answer:

x=5 and y=−7

x=3;y=2x−1

Step: Solve x=3 for x:

x=3

Step: Substitute 3 for x in y=2x−1:

y=2x−1

y=(2)(3)−1

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

Let's solve your system by substitution.

y=6x+3;y=5x+4

Step: Solve y=6x+3 for y:

y=6x+3

Step: Substitute 6x+3 for y in y=5x+4:

y=5x+4

6x+3=5x+4

6x+3+−5x=5x+4+−5x(Add -5x to both sides)

x+3=4

x+3+−3=4+−3(Add -3 to both sides)

x=1

Step: Substitute 1 for x in y=6x+3:

y=6x+3

y=(6)(1)+3

y=9(Simplify both sides of the equation)

Answer:

x=1 and y=9

2x+3y=2;y=x−6

Step: Solve y=x−6 for y:

y=x−6

Step: Substitute x−6 for y in 2x+3y=2:

2x+3y=2

2x+3(x−6)=2

5x−18=2(Simplify both sides of the equation)

5x−18+18=2+18(Add 18 to both sides)

5x=20

divide both sides by 5

5x/5 and 20/5

x=4

Step: Substitute 4 for x in y=x−6:

y=x−6

y=4−6

y=−2(Simplify both sides of the equation)

Answer:

x=4 and y=−2

Answer:

Question 1: b Question 2: yes

Step-by-step explanation:

The variable must go with 7+1/3 calculate time for all the levels. Then add 5+1/6. It must be less than or equal to because you want to play all 6 levels. You can play all 6 when you plug in 6 as the variable. It is less than 60

Answer:

BC = 11

Step-by-step explanation:

Substitute x = 5 into the expression for BC

BC  = 2x + 1 = (2 × 5) + 1 = 10 + 1 = 11

11 is the answer good luck

In order to t² - t -2 = 0 become into this (t - 2)(t + 1) = 0, we have to know that a  polynomial of the form ax² + bx + c = 0 can be factored as a(x + r1)(x + r2) = 0, where r1 and r2 are the roots of the equation ax² + bx + c = 0 and we can find them using the Quadratic Formula.

Let's solve the equation step-by-step.

t² - t -2 = 0 has the form at² + bt + c = 0, so can be factored as a(t + r1)(t + r2) = 0. With a = 1, b = -1, and c = -2

Step 1. Use the Quadratic Formula to find the roots r1 and r2.

t =  −b ± √b²−4ac/2a

t = -(-1) ± √(-1)²−4(1)(-2)/2(1)

t = 1 ± √1+8/2

t = 1 ± √9/2 where r1 = 1 + √9/2 and r2 = 1 - √9/2

Step 2. Calculate the roots r1 and r2

r1 = 1 + √9/2 = 2

r2 = 1 - √9/2 = -1

Step 3. Write the factored equation a(t + r1)(t + r2) = 0, with a = 1 and the values of r1 and r2 with opposite signs.

1(t - 2)(t + 1) = 0

(t - 2)(t + 1) = 0

Answer:

Check 318 was not cashed or deposited.

Step-by-step explanation:

If you look at the check numbers, check number 318 was not used. Therefore that is why Larry's balance is different from the banks balance.

Answer:

Step-by-step explanation:

Option D. check 318 was not cashed or deposited.

Answer: 8/9

Hope it helped!

Answer:

8/9

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 72 and 81 is 9

72 ÷ 9

81 ÷ 9

= 8/9

Answer: x < -1

Remember:

Answer: D, or x<-1

Step-by-step explanation:

The arrow on the number line indicates the direction in which the set of numbers represented is going. In this case, the arrow is pointing in the negative direction from -1; so we know that it will be either x < -1 or x ≤ -1

The circle represents whether the set of points is inclusive or exclusive. This is an exclusive case, which means that the point x = -1 is not included in the set of points.

That's how we know the inequality represented by the graph is x < -1

Answer:

Sample Response: Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.

Step-by-step explanation:

i did it.

Answer:

Sample Response: Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.

Step-by-step explanation:

make sure to inlcued

- area of rectangle

- half the diameter for the radius

- half the area of the circle

- subtract the area of the half circle from the area of the rectangle

Answer:

The equation is equal to 78°-x=56°

The decrease in temperature is 22°

Step-by-step explanation:

Let

x-----> the decrease in temperature

we know that

The equation that represent this situation is equal to

78°-x=56°

Solve for x

x=78°-56°

x=22°

Answer:

The required equation is [tex]78^\circ F-t=56^\circ F[/tex]

The decrease in temperature is 22°F.

Step-by-step explanation:

Given : The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.

To find : Write and solve an equation to  find the decrease in temperature ?

Solution :

We have given that temperature is dropped i.e. there is decrease in teh temperature.

Let the decrease in the temperature be 't'.

According to question,

The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.

i.e. the required equation is [tex]78^\circ F-t=56^\circ F[/tex]

Solve,

[tex]t=78^\circ F-56^\circ F[/tex]

[tex]t=22^\circ F[/tex]

The decrease in temperature is 22°F.

Answer:

Third option: 28

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In the right triangle shown in the figure, you can identify:

[tex]\alpha=30\°\\opposite=14\\hypotenuse=x[/tex]

Then, you need to substitute the corresponding values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:

 [tex]sin(30\°)=\frac{14}{x}[/tex]

Now, you can solve for "x":

[tex]xsin(30\°)=14\\\\x=\frac{14}{sin(30\°)}\\\\x=28[/tex]

Answer:

The value of x is 28 units

Step-by-step explanation:

Given a right angled triangle with one side 14 units and one angle 30°

we have to find the value of x

By trigonometric ratios

[tex]\sin \theta=\frac{Perpendicular}{Hypotenuse}[/tex]

[tex]\sin 30^{\circ}=\frac{14}{x}[/tex]

[tex]\frac{1}{2}=\frac{14}{x}[/tex]

[tex]x=14\times 2=28 units[/tex]

Hence, the value of x is 28 units.

Option C is correct

Answer:

Step-by-step explanation:

The square of the sum of the first five positive integers:

(1 + 2 + 3 + 4 + 5)² = 15² = 225

The sum of the first positive perfect square:

1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55

225 - 55 = 200

The positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170. This is obtained by taking the sum of first five numbers, squaring the sum and subtracting the sum of first five perfect squares.

The sum of first five positive integers = 1+2+3+4+5 = 15

Square of the sum of the first five positive integers = 15² = 225

The sum of the first five positive perfect squares =1²+2²+3²+4²+5²

                                                                                 =1+4+9+16+25

                                                                                 =55

The positive differenece = 225-55=170

Hence the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170.

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Answer:

They paid $2.85 for each burger and $1.8 for each order of fries

Step-by-step explanation:

It will be solved simultaneously,

let x represent burger and y represent fries

John's order gives the first equation

3x + 2y = 12.15   ........(1)

Emily's order gives the second equation

4x + 3y = 16.80 ..........(2)

multiply equation (1) by 3 and equation (2) by 2 so as to eliminate y

9x + 6y = 36.45 ....... (3)

8x + 6y = 33.6 ........... (4)

subtract equation (4) from (3)

9x - 8x + 6y -6y = 36.45 - 33.6

x = 2.85

substitute x= 2.85 in equation (1)

3(2.85) + 2y = 12. 15

8.55 + 2y = 12.15

2y = 12.15 -8.55

2y = 3.6

y = 1.8

Answer:

Cost of burger = $2.85 and Cost of fries =   $ 1.80.

Step-by-step explanation:

Given  : john order 3 burgers and 2 fries for $12.15. Emily bought 4 burgers and 3 fries for $16.80.

To find : How much did the pay for each burger and order of fries.

Solution : We have given 3 burgers and 2 fries for $12.15.

Let the cost of 1 burger = x .

Let the cost of 1 Fries = y .

3 x + 2 y = $12.15 ------(1)

4 x + 3 y =  $16.80-----(2)

On multiplying (i) by 4 and (ii) by 3 and subtracting the equation .

12x + 8y = $48 .60

(-)12x +(-) 9y = (-)$50 .40

_____________

0 -y = -$ 1.80

y =  $ 1.80.

3x + 2(1.80) = $12.15 .

3x + 3.60 = 12.15

3x = 12.15 -  3.60

3x = 8.55

On dividing both sides by 3.

x = $2 .85

Therefore, Cost of burger = $2.85 and Cost of fries =   $ 1.80.

Answer:

c

Step-by-step explanation:

Both the events are equally likely so neither can be more likely.

The correct answer is: C Neither. Both events are equally likely.

Given that the probability of it snowing in Eastern Canada tomorrow is 0.4 and that of in Western Canada is 2/5,

We need to determine which of the given events is more likely,

To determine which event is more likely, we compare the probabilities provided for each event:

The probability of it snowing in Eastern Canada tomorrow is 0.4.

The probability of it snowing in Western Canada tomorrow is 2/5, which is equivalent to 0.4.

Since both probabilities are equal (0.4), we can conclude that both events, A (It snows in Eastern Canada tomorrow) and B (It snows in Western Canada tomorrow), are equally likely.

Therefore, the correct answer is: C Neither. Both events are equally likely.

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Answer:

24ft^3

Step-by-step explanation:

Hope it helped you!

Answer:

24 ft.

Step-by-step explanation:

Someone please show a quicker way! (Done inefficiently in my head.)

((1.5 x1.2) + (((1.2 x .5)/2) x 2)) x 10 = 24

Answer:

Step-by-step explanation:

B or C depending on how many bags you have

A reasonable tip for an airport skycap is generally $2 per bag, reflecting both the service provided and the quantity of luggage.

The question asks about the appropriate tip amount for an airport skycap. A common guideline for tipping skycaps is $2 per bag, which is considered to be a reasonable amount. Tipping $5 per bag may be considered generous in many cases, and a flat rate of $2 in total could be seen as insufficient unless you only have one bag. The tip should reflect the quality of service provided and the number of bags. The provided information regarding airline costs and opportunity costs of time at airports is not directly related to tipping skycaps but does highlight the broader context of airport expenses and the value of time for air travelers.

The balance of a $4000 loan at a 3% annual interest rate compounded monthly after three payments of $200 each is $3428.58.

To find the balance after the third payment of a $4000 loan, compounded monthly at an annual interest rate of 3%, we must first determine the monthly interest rate. The annual rate of 3% means a monthly rate of 0.25% (3%/12 months). Next, we'll apply the loan payment process three times to calculate the remaining balance.

The balance after the third payment is $3428.58.

Answer:

h(1)= 1

h(4)=5

Step-by-step explanation:

Given

h(x)= x^3 for 1≤x≤3

and

h(x)=5 x>3

Now finding h(1), i.e when x=1

x=1 lies in the range 1≤x≤3 hence putting value x=1 in x^3

h(1)= 1^3

     = 1

Now finding h(4), i.e when x=4

x=1 lies in the range x<3 hence putting value x=4 in h(x)=5

h(4)= 5 !

Answer:

8

Step-by-step explanation:

Answer: 8

Step-by-step explanation: