A company sells three types of gift baskets. The basic basket has two movie passes and one package of microwave popcorn, and costs $15.50. The medium basket has two movie passes, two packages of microwave popcorn, and one DVD, and costs $37. The super basket has four movie passes, three packages of microwave popcorn, and two DVDs, and costs $72.50.



Create a system of equations and solve using matrices to find the price of each basket item.

Answers

Answer 1

The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.

Let x represent the cost of each movie, y represent the cost each microwave and z represent the cost of each DVD.

For the basic:

2x + y = 15.50    (1)

For medium:

2x + 2y + z = 37    (2)

For super:

4x + 3y + 2z = 72.50  (3)

[tex]\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right] \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}15.5&37&72.5\end{array}\right] \\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] =\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right]^{-1}\left[\begin{array}{c}15.5&37&72.5\end{array}\right]\\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}7&1.5&20\end{array}\right] =[/tex]

The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.

Find out more at: https://brainly.com/question/21105092


Related Questions

Write the expression using exponents.

3 × 3 × 3 × 3

A. 33
B. 34
C. 43
D. 35

Answers

Answer:

B

Step-by-step explanation:

18 ounces. of iced tea costs 2.99. How much will 30 ounces. cost

Answers

Answer:

About $4.98

Step-by-step explanation:

The cost of 30 ounces of iced tea will be $4.98.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

18 ounces. of iced tea costs 2.99. Then the ratio of cost to weight is calculated as,

⇒ $2.99 / 18

⇒ $0.166 per ounce

Then the cost of 30 will be calculated as,

⇒ $0.166 x 30

⇒ $4.98

The cost of 30 ounces of iced tea will be $4.98.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

There are 60 students eating lunch in the cafeteria five-tenths of them brought lunches from home. How many students brought lunches from home?

Answers

Five-tenths is equal to a half and half of 60 is 30 so the answer would be 30 students!:)

Answer: 30   Hope this helps please mark brainliest! Thanks!

Step-by-step explanation:

Five tenths=5/10=50%=1/2

So basically it's 30 out of 60 students brought lunch from home.

So the answer is 30!

Find the area of the composite figure made up of a square and a semicircle. Use 3.14 as an approximate for pi and give your nearest square inch. Enter only the number.

Answers

Answer:

200.52 in^2

Step-by-step explanation:

to find the area of a circle, you square 6 and multiply it by pi in this case 3.14.

that gives you 113.04 but because this is only a half circle, it is 56.52 in^2.

Next, you need to find the rectangle. multiply 12(length) by 12(Width) to get 144 add 144 to 56.52 to get 200.52.

Hope this helped if it did please give me brainliest it helps me a lot. :)

Hope this helped!

need helps plsssssssssssssss

Answers

Answer:

64

Step-by-step explanation:

4^3 is just 4*4*4

so 4*4=16

and 16*4=64

TADAAAAAAAAAA

Answer
The value of 4^3 is 64




………………

Juan wants to buy a house for $162,800. The rate of down payment is 20% of the cost of the house. What is the down payment? i assume $3,256,00

Juan wants to buy a house for $162,800. The rate of down payment is 20% of the cost of the house. What will the mortgage be?

Answers

Answer:

I think its gonna be 162.860

Christine's parents gave her $70 to spend at the Topsfield Fair. She spent $10 on flowers and needs to buy vases. Each antique flower vase at the fair costs $3.
Which represents the number of antique flower vases Christine can buy?
at least 20 vases
O at the most 20 vases
O exactly 20 vases
O at the most l vase

Answers

Answer:

97

Step-by-step explanation:

Write a proof. fill in statements and reasons for the blank sides, 10 points for each question.

Answers

Step-by-step explanation:

Statements / reasons:

Statement 1 >> RS ≅ UT            Reason 1 >> Given

Statement 2 >> RT ≅ US           Reason 2 >> Given

Statement 3 >> TS ≅ TS            Reason 3 >> Common side

Statement 4 >> ΔRST≅ΔUTS    Reason 4 >> SSS theorem

Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?

Juan made a lower rate of pay because he made less money.

Lisa made a better rate of pay because she made more money.

Lisa said she made a better rate of pay because her rate was $14 an hour.

Juan said he made a better rate of pay because he was paid $14.80 an hour.

Answers

Answer:

Juan said he made a better rate of pay because he was paid $14.80 an hour.

Step-by-step explanation:

Juan made more because he makes $14.80 an hour, whereas Lisa makes only $14 an hour.

Enjoy your day! :D

Select all the equations that are true when x = 6.
6x = 12
17 – x = 11
x ÷ 2 = 3
19 ÷ 3 = x
5 + x = 11

Answers

Answer:

everything but the 4th are true

Step-by-step explanation:

fax

Answer:

B,C,E

Step-by-step explanation:

Select the equation of a line in slope-intercept form that passes through (-2, 2) and is perpendicular to the graph of y=1/2 x-2.

Answers

Answer:

y=-2x-2

Step-by-step explanation:

since the line is perpendicular to y=1/2x - 2, the slop is -1/(1/2)=-2. so we have y=-2x+b. now plug in the point given: 2= -2(-2)+b, 2=4+b, b=-2, y=-2x-2

xin hãy giúp ekmmm plllllllllllllllllllllllllllllllllllllll!

Answers

57485743i753i457394574930

Find the inverse (pre-calc)

Answers

Answer:

f^(-1)(x) = e^(x/3)

Step-by-step explanation:

1.  Replace 'f(x)' by 'y:'  y = 3ln x

2. Interchange x and y:  x = 3ln y => x/3 = ln y

3. Solve for y:  

   e^(x/3) = y

4.  Replace this 'y' with 'f^(-1)(x)'

    Then f^(-1)(x) = e^(x/3)

For this exponential function, what is the output value (y), when the input value (x) is O? y = 5. 2x ​

Answers

Answer:

(0,. 5 )

Step-by-step explanation:

Substitute the input x = 0 into the function for output y

y = 5 × [tex]2^{0}[/tex] = 5 × 1 = 5 [ note [tex]a^{0}[/tex] = 1 ]

for a brainlist pls answer
Find the intercepts of the given equation. To earn full credit, show your work using a method explained in the Orientation.

Answers

Answer:

[tex]x=-2y+10[/tex]

Step-by-step explanation:

Step 1: Flip the equation.

Step 2: Add -5 to both sides.

Step 3: Divide both sides by (-1)/2.

Solve the equation. Enter your answer in the box. V27​

Answers

The correct answer is 3
3


step by step explanation: when it has the little 3, it means what number would need to be divided by itself to equal the number


hope this helps

Need helpppp pleaseeeee

Answers

Umm...

What is your question??? You have no question in the question box or attachments.

help with this question please!

Answers

Gotta subtract the triangle from the semi circle

Triangle: 1/2 base • height
= 1/2 (6) • 3
= 9

Then find the semi circle
(pi r^2)/2
= (3.14 • 3^2)/2
= 14.13

14.13 - 9 = 5.13 mm^2

i fractions what is 2 x 5/8 i need heeeeeeeeeeeeeelp

Answers

Answer:

1 . 25 or 5/4 as a fraction

Step-by-step explanation: Hope this helps mark me branliest plssss;)

Answer:

2*5/8 = 5/8 + 5/8

So the answer is 1 and 1/4 :)

You call two car rental companies to find out their rental prices Company A charges $75 plus $.30 per mile and Company B charges $80 plus $.25 per mile. If you are traveling 150 miles, which company gives you the better deal?

Answers

Company A= 75+•30x150=120
Company B= 80+•25x150=117.50
Altogether company A gives the better deal at $117.50

Pls answer all 4 questions AND HURRY!!!!

Answers

Answer:

5pts

Step-by-step explanation:

Charlie is making chocolate cake for his birthday party. He found a recipe that needs 2 cups of cocoa powder for every 3 cups of sugu. Al of his friends

are coming, so he uses 6 cups of cocoa powder in his cake,

How many cups of sugar should Charlie uso?

Answers

Step-by-step explanation:

the mix follows the ratio 2/3 (cups of cocoa to sugar).

2 × x = 6 cups

x = 6/2 = 3

so, the cocoa cups number is multiplied by the factor 3, and we need to multiply also the sugar cup number with the same factor to keep the ratio value unchanged :

so, we need 3×3 = 9 cups of sugar.

What is the area of this figure?

Answers

Given :-

A figure is given to us .

To Find :-

The area of the figure .

Solution :-

As we can see that the given figure is made up of a parallelogram and a ∆ . As we know that the opposite sides of a parallelogram are equal . So that the base of the ∆ would be 9cm . Now ,

[tex]\longrightarrow[/tex] Area = ar(||gm ) + ar(∆)

[tex]\longrightarrow[/tex] Area = (9*5 + 1/2*8*9)cm²

[tex]\longrightarrow[/tex] Area =( 45 + 45 ) cm²

[tex]\longrightarrow[/tex] Area = 90cm²

Hence the area of the given figure is 90cm² .

The basic Sl unit for measuring mass is the liter. True False​

Answers

Step-by-step explanation:

False

The SI unit of mass is Kilogram ( Kg)

for each of the solutions of the equations find two consecutive integers between which the solution is located.

x²=3

Answers

Using squares of integers numbers, it is found that the solution of the equation is located between the integers x = 1 and x = 2.

The equation given is:

[tex]x^2 = 3[/tex]

The solution of the equation given is:

[tex]x = \sqrt{3}[/tex]

The squares of the integers numbers until the square root of 3 are:

[tex]1^2 = 1[/tex]

[tex]2^2 = 4[/tex]

Since [tex]1 < 3 < 4[/tex], the square root of 3, which is the solution to the equation, is located between the integers x = 1 and x = 2.

A similar problem is given at https://brainly.com/question/3729492

which quadrilaterals always have diagonals that bisect opposite angles

Answers

The answer to you question is it’s a rhombus. I hope this has helped you.


[tex]\Large\mathtt\color{red}{H}\color{orange}{E}\color{yellow}{L}\color{lime}{P}\color{green}{M}\color{cyan}{E}\color{aquamarine}{!}[/tex]



[tex]\Large\mathtt\color{cyan}{╭──━━━═══════━━━──╮}╭──━━━═══════━━━──╮[/tex]

5400 ÷ 300000

[tex]\Large\mathtt\color{cyan}{╰──━━━═══════━━━──╯}╰──━━━═══════━━━──╯[/tex]




[tex]\Large\blue{\boxed{\tt{\colorbox{cyan}{WITH}}}}[/tex]
[tex]\Large\blue{\boxed{\tt{\colorbox{cyan}{SOLUTION}}}}​[/tex]









[tex]\tt\colorbox{blue}{\boxed{\colorbox{red}{ \color{pink}{ \rm{ NONSENSE = REPORT }}}}}[/tex]

​​ ​​​

Answers

Step-by-step explanation:

[tex] \\ {5400} \div 300000[/tex]

[tex] \\ = \frac{5400}{300000} [/tex]

[tex] \\ = \frac{ \cancel{5400}}{ \cancel{300000}} [/tex]

[tex] \\ = \frac{9}{500} [/tex]

[tex] \\ = 0.018[/tex]

Is z = 11 a solution to the inequality below?

4z - 4 < 43

yes or no

Answers

Plug it in like any normal algebra

4(11) - 4 < 43

44 - 4 < 43

40 < 43

The statement is correct.

Z = 11 is a solution.  

GOLDEN RULE FOR INEQUALITIES

WHENEVER SOLVING AN INEQUALITY TREAT IT LIKE REGULAR ALGEBRA, but whenever you MULTIPLY or DIVIDE both sides of an inequality by a NEGATIVE NUMBER, you must flip the inequality symbol.

At a picnic, 12 people shared 4 large sandwiche
equally. How much of a sandwich did each
person get to eat?

Answers

Answer:

1/3

Step-by-step explanation:

Answer:

each person ate 1/3 of a sandwich

Step-by-step explanation:

a wind up robot can travel 20m on a single wind. how many times will it need to wind to cover a distance of half a mile?

Answers

40 winds. To be exact 40.2336 winds. But that’s not really possible so I would say 41 winds.
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