Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that 7 cups of water and 3 liters of water filled 9.8 pints. Later, they find that if they start with 5 liters of water and remove 9 cups of water, they end up with 6 pints of water. Model the given two situations as a system of linear equations. Based on your equations, determine the relationship between;

●cups and liters,
●cups and pints,
●and pints and liters.

Show all your work and submit your work along with the resulting relationships.

Answers

Answer 1
7 cups + 3 litres = 9.8 pints 
[tex]7c+3l=9.8p[/tex] ⇒ Equation 1

5 litres - 9 cups = 6 pints
[tex]5l-9c=6p[/tex] ⇒ Equation 2

Relationship between cups and litres
Rearranging equation 1 to make pints the subject
[tex]7c+3l=9.8p[/tex]
[tex]p= \frac{7c+3l}{9.8} [/tex] ⇒ substitute this into Equation 2

[tex]5l-9c= \frac{7c+3l}{9.8} [/tex]
[tex]49l-88.2c=7c+3l[/tex]
[tex]49l-3l=7c+88.2c[/tex]
[tex]46l=95.2c[/tex]
[tex]l=2.1c[/tex]

Hence, 1 litre = 2.1 cups

Relationship between cups and pints
Rearrange equation 1 to make litres the subject
[tex]7c+3l=9.8p[/tex]
[tex]3l=9.8p-7c[/tex]
[tex]l= \frac{9.8p-7c}{3} [/tex] ⇒ Substituting this into Equation 2

[tex]5( \frac{9.8p-7c}{3})-9c=6p [/tex]
[tex] \frac{49p-35c}{3}-9c=6p [/tex]
[tex] \frac{49}{3}p- \frac{35}{3}c-9c=6p [/tex]
[tex] \frac{49p}{3}-6p= \frac{35}{3}+9c [/tex]
[tex] \frac{31}{3}p= \frac{62}{3}c [/tex]
[tex]p=2c[/tex]

Hence, 1 pint = 2 cups

Relationship between pints and litres
Rearranging equation 1 to make cup the subject

[tex]7c=9.8p-3l[/tex]
[tex]c= \frac{9.8p-3l}{7} [/tex] ⇒ subsitute this into equation 2

[tex]5l-9( \frac{9.8p-3l}{7})=6p [/tex]
[tex]5l- \frac{63}{5}p+ \frac{27}{7}l=6p [/tex]
[tex]5l+ \frac{27}{7}l=6p+ \frac{63}{5}p [/tex]
[tex] \frac{62}{7}l= \frac{93}{5}p [/tex]
[tex]l=2.1p[/tex]

Hence, 1 litre = 2.1 pints


Answer 2

Here's work you can copy and paste:

7 cups + 3 liters = 9.8 pints

7c+3l=9.8p

5 liters - 9 cups = 6 pints

5l+9c=6p

Cups and Liters

7c+3l=9.8p

p= 7c+3l/9.8 (put in equation 2)

5l-9c= 7c+3l/9.8

49l-88.2c=7c+3l

49l-3l=7c-88.2c

46l=45.2c

1Liter = 2.1 Cups

Cups and Pints

7c+3l=9.8p

3l=9.8p-7c

l=9.8p-7c/3 (put in equation 2)

5(9.8p-7c/3)-9c=6p

(49p-35c/3)-9c=6p

49/3p-35/3c-9c=6p

49/3p-6p=35/3c+9c

31/3p=62/3c

1 Pint = 2 Cups

Pints and Liters

7c=9.8p-3l

c=9.8p-3l/7 (put in equation 2)

5l-9(9.8p-3l/7)=6p

5l-63/5p+27/7l=6p

5l+27/7l=6p+63/5p

62/7l=93/5p

​1 Liter = 2.1 Pints


Related Questions

Simplify. Rewrite the expression in the form of 5^n. What is 5^-5\5^8.

Answers

[tex] \cfrac{5^{-5}}{5^8} =5^{-5-8}=5^{-13}[/tex]
remember that [tex] \frac{x^m}{x^n}=x^{m-n} [/tex]

so
[tex] \frac{5^{-5}}{5^8}=5^{-5-8}=5^{-13} [/tex]

NEED HELP FAST!
3.
The coordinate grid shows the graph of four equations:



Which set of equations has (5, 0) as its solution? (5 points)


A and B

C and D

B and D

A and D

Answers

the answer is currently A so yep thats the answer ok

Answer:

the answer is a and bbecause they both cross at (5,0)

An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). The equation of the ellipse is in the form below. What is the value of b in the equation? (Enter a positive number.)

Answers

I just did this, the answer is 12 :) hope that helps!

Answer: 12

Step-by-step explanation:

The weight of an African elephant is 6x10^6 grams; the weight of a tiger is 3x10^5 grams. How many times heavier is the elephant than the tiger?

Answers

so that means
elephant= x times tiger

6 times 10^6=x times 3 times 10^5
divide both sides by (3 times 10^5)
remember that (x^m)/(x^n)=x^(m-n)
so
(6 times 10^6)/(3 times 10^5)=x
(6/3) times (10^6)/(10^5)=x
2 times 10^1=x
2 times 10=x

that would be 2 times 10^1 or 20 times
The answer would be 20 times longer.

The four people at Carla's birthday will get one-quarter (one fourth) of the cake each. Carla puts 16 candies on the cake so that each person gets the same number on their piece of cake. How many candies will each person get on their piece of cake?

Question 4 options:

4


8


12


16

Answers

You would do 16 divided by 4 to get your answer. The answer is 4.
I agree. The answer is definitely four!

You need to cut a 9 foot piece of plywood into 12 inch sections. Every cut also removes 1/8 inch. How many 12 inch sections can you get out of the 9 foot piece of plywood?

Answers

you can get 9 because in one foot there is 12 inches and there in 9 feet 

Could 3.2, 10.7, and 5.5 be the side lengths of a triangle?

Answers

no because the 2 shorter sides has to be more than the longer side
No, for any triangle with sides a,b, and c, a+b>c

Here 3.2+5.5=8.7

And 8.7<10.7, so this could not be a triangle.

What is the 1st term when −5z2 + 7z4 + 11z − 8z3 is arranged in descending order

Answers

descending order...largest to smallest
the largest one is the one with the biggest exponent
so the first term is : 7z^4

Answer:

7z^4

Step-by-step explanation:

Look at the exponent power. The largest exponent goes first, the second largest goes second (etc.). The number/variable with no exponent will always go last.

Help with 69 and 70 plzzz

Answers

3665 is not divisible by nine, as 3665/9 is 407.2222222.

5 boxes + 9 boxes = 14 boxes. 193 CDs + 108 CDs = 301 CDs. 301/14 = 21.5. This means that they do not divide evenly among the boxes.

TL;DR:

No

No
69.) No it's not because the rule for 9 is that you need to add the digits together which would equal to 20

70.) Melissa cant but Jennifer can because, you can divide 108 by 9 evenly but not 193 and 5

A packet of sour worms contains four strawberry, four lime, two black currant, two orange sour, and three green apples worms. What is the probability that Dustin will choose a green apple sour worm, P(green apple)?

Answers

When you add all the worms in the bag together, you have a total of 15 worms. There are three green apple flavored sour worms. the ratio of green apple to the total is 3/15. To simplify this ratio further, divide by the common factor of 3. You will get 1/5. The probability that Dustin will pick a green apple worm is 1/5. To convert to percentage , simply divide one by 5. you will get .2, which in percent is 20%. The probability that Dustin will pick a green Apple worm is 1/5 or 20%.
3/15, or 1/5, or 20%

At the beach 29% of people have red towels and 18% have white towels if the rest have blue ,what percentage of the people at the beach have blue towels

Answers

the anwser is 53%....
To find the percentage of the people with blue towels, we must complete this equation:

✯1 - (0.29 + 0.18) = 0.53
✯ 0.53 = 53%
✯Thus your answer: 53% of people on the beach have blue towels.

Evaluate the following expression (a + b)^0

Answers

Answer:

So, [tex](a + b)^0=1[/tex]

Step-by-step explanation:

[tex](a + b)^0[/tex]

To evaluete this expression we apply exponential property

[tex]x^0=1[/tex]

IF any expression has exponent 0 then the value is 1 always

for example, [tex]3^0 =1[/tex]

[tex]5^0=1[/tex]

[tex](x+2)^0=1[/tex] because exponent is 0

So, [tex](a + b)^0=1[/tex]

Answer:

1

Step-by-step explanation:

i just made a B in this class

The polnomial y=x^2-2x+1 has a repeated factor? True or false

Answers

The answer is False because if you notice none of the factors are like terms or repeat.

jim says that the output of the floor function is the number before the decimal point in the input. For what domain is Jim’s statement correct? Justify your answer.

Answers

Jim’s statement is correct for all numbers greater than or equal to 0 and negative integers. It does not work for negative non-integer numbers.

Step-by-step explanation:

Given :

The output of the floor function is the number before the decimal point.

Solution :

Jim’s statement is correct for all numbers greater than or equal to 0 and negative integers. It does not work for negative non-integer numbers.

For example, the floor of –5.5 is –6, the floor of -4.5 is -5 (the number before the decimal point).

For more information, refer the link given below

https://brainly.com/question/13666156?referrer=searchResults

The floor function outputs the number before the decimal point for non-negative real numbers.

Jim's statement is correct for non-negative real numbers.

The floor function rounds down to the nearest integer, which is always the number before the decimal point.

For example, if the input is 3.8, the output will be 3.

If the input is -2.5, the output will be -3.

Can someone help me in graphing

Answers

I like to write a table:

X | Y = 5/4x-2
____

0 | -2

4 | -1

Two pints enough for a line!

Same with the other one (it's parallel and one unit below)

Mr. and Mrs. McClurrie are debating on whether or not to remove a tall tree in their front yard. Mr. McClurrie is concerned that the tree could fall during a storm and land on their home. Mrs. McClurrie disagrees. She thinks the tree poses no danger to their home and wants to keep the tree because of the wonderful shade it provides. They decide to estimate the height of the tree using special right triangles.

They stood 25 feet from the base of the tree to create a 30° angle from the ground to the top of the tree.

If their home is 20 feet from the base of the tree, could the McClurrie's wait a few more years before cutting down the tree or does it pose a risk now?

Answers

Check the picture.

Let A be the point where Mr. and Mrs. McClurrie are standing, let B be the base of the tree and C the top of the tree. Let H be the point representing the house.

ABC is a right triangle, with m(BAC)=30°.

so by special triangles, if the length of the hypotenuse is  2x, the length of BC is x, since it is the side opposite to the 30° angle.

by the pythagorean theorem :

[tex](AC)^{2}= (AB)^{2}+(BC)^{2} [/tex]
[tex](2x)^{2}= (25)^{2}+(x)^{2} [/tex]
[tex]4x^{2}= (25)^{2}+x^{2}[/tex]
[tex]3x^{2}= (25)^{2}[/tex]
[tex]x= \sqrt{ \frac{(25)^{2} }{3}}= \frac{25}{ \sqrt{3} }= \frac{25 \sqrt{3} }{3} [/tex]
[tex]\frac{25 \sqrt{3} }{3}=25* \frac{ \sqrt{3} }{3}=25*0.577= 14.43[/tex] (feet)

so even if the tree falls, it falls more than 5 feet away from the house.

Answer: they can wait a few more years.

Jaime has 6 cups of milk. Each batch of cookies she is making will require 3/4 of a cup of milk. How many batches of cookies can Jaime make with milk she has?

Answers

6 / (3/4) =
6 * 4/3 =
24/3 =
8 batches of cookies can be made with 6 cups of milk

Answer:

8

Step-by-step explanation:

What is the equation of the line in slope-intercept form that is perpendicular to the line y = x – 2 and passes through the point (–12, 10)? y = x – 6 y = x + 6 y = x + 26 y = x + 10

Answers

The slope of the given line   y = x – 2   is 1.  Therefore, the slope of a line perpendicular to  y = x – 2   is -1/1, or just -1.

In point-slope form, the equation of the new line is 

y-10 = -1(x-[-12]), or            y-1 = -(x+12)          or   y-1 = -x - 12, or
                                                                                 y = -x - 11.

Answer:

y =-4/3 x – 6

Step-by-step explanation:

2.8 in expanded form

Answers

2+.8 is the answer hope this helps

I WILL GIVE BRAINLIEST please answer correctly

Answers

it would be 7 out of 10 bars multiplied by 8 out of ten bars for the other one it would be a full 10 bars the 7 out of ten bars multiplied by 8 out of ten bars

What can be concluded from observing a 45-degree angle translated across the y-axis three times ?

Answers

 Just reflecting a figure does not change it's size

Paul Steve robin and Ryan all play different instruments. Their instruments are guitar, bass

Answers

Yeah did u even finish the question or what?

103,727,495 in word form and expanded form

Answers

One hundred and three million, seven hundred and twenty seven thousand four hundred and ninety five

Word form: one hundred three million, seven hundred twenty-seven thousand, four hundred ninety-five

Expanded form: 100,000,000+3,000,000+700,000+20,000+7,000+400+90+5

HOPE I HELPED YOU!

NEED DONE NOW!!!!!!
Three highways connect the centers of three towns and form a triangle. A cell phone company wants to place a new cell tower so that it is the same distance from the centers of the three towns. How can the company find where to place the tower? Explain.Three highways connect the centers of three towns and form a triangle. A cell phone company wants to place a new cell tower so that it is the same distance from the centers of the three towns. How can the company find where to place the tower? Explain.

Answers

The company can find where to place the tower by determining the point of concurrency of these three (3) towns.

What is a triangle?

A triangle refers to a two-dimensional shape that is typically made up of three (3) sides, three (3) vertices and three (3) angles. This ultimately implies that, a polygon that has three (3) lengths of sides is a triangle.

What is a point of concurrency?

A point of concurrency can be defined as a single point that is shared by three (3) or more lines, segments, rays, or planes. Thus, a triangle is considered to be concurrent when at least three (3) lines intersect at a single point.

Based on geometry, the point (circumcenter) that is equidistant from the vertices of the triangular tower would be equal in distance from each of the centers of these three (3) towns.

Generally, the circumcenter of a triangle can easily be determined by constructing the point of concurrency of the perpendicular bisectors of a triangle.

In conclusion, the company can find where to place the tower by determining the point of concurrency of these three (3) towns, so that they all have the same distance from the centers.

Read more on point of concurrency here: https://brainly.com/question/11844452

Answer:

For the tower to be the same distance from each of the centers, the company must find the point that is equidistant from the vertices of the triangle. This is the circumcenter of the triangle and can be found by constructing the point of concurrency of the perpendicular bisectors of the triangle.

The tower needs to be equidistant from the vertices of the triangle.

The tower should be placed at the circumcenter of the triangle.

To find the circumcenter, find the intersection point of the three perpendicular bisectors of the triangle.

Step-by-step explanation:

Which of the following is equal to 5 4/9

Answers

These are simple, just multiply your numerator by 5. So 4 * 5/9 = 20/9 = 2.22.


Which following? Let me give you choice. Just multiply the whole number (5) by the denominator (9), you will get 45. Lastly add the 45 to the numerator (4). Which is 49/9.

(08.01)Which of the following questions is a statistical question?

a How many professional sport leagues are there?
b Where do the professional sport leagues play?
c How many hours of professional training took place over the weekend?
d How many hours do you spend each week training for a sports league?

Answers

The answer would be d. because it is the only one that asks a question that has an individual answer.

Match the solution set of each of the following inequalities with its graph.

Answers

The following inequalities with its graph are:

For graph 1: x≤-2,

For graph 2: x≥2,

For graph 3: x≥2,  

For graph 4: -2<x

For graph 5: x<2

Inequality is defined as a relationship between two expressions or values that are not equal to each other.

A number line is a representation of real numbers in the form of a graduated straight line.

The solution for the first graph is x less than or equal to -2.

1. x≤-2

The solution to the second graph is x higher than or equal to 2

x≥2

In the third graph, the solution x is greater than or equal to 2

x≥2

The solution x in the fourth graph is greater than -2.

x>-2 or -2<x

The solution x in the fifth graph is smaller than 2.

x-2<0

x<2

As a result, the inequalities for the respective graphs are x-2, x2, x2, -2x, and x2.

The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 4 inches less than 5 times the perimeter. Find the length and width of the rectangle.

Answers

Solution:
Let the width of the rectsngle (b) be x
and the length of the rectangle (l) =x+4
Area of the rectangle (A)=?
Perimeter of the rectangle (P)=?
Now,
P= 2 (l+b)
= 2 (x+4+x)
= 2 (2x+4)
= 4x+8
And,
A= l×b
= x(x+4)
= x^2+4x
According to the question,
A=5P-4
or, x^2+4x =5 (4x+8)-4
or, x^2 +4x =20x+40-4
or, x^2 = 20x-4x+36
or, x^2 = 16x+36
or, x^2-16x-36 = 0
or, x^2-(18-2)x-36 = 0
or, x^2-18x+2x-36 = 0
or, x (x-18)+2 (x-18) = 0
or, (x-18) (x+2) = 0

Either, Or,
x-18 = 0 x+2 = 0
so, x = 18 so, x = -2

Taking the value of x = 18 ( Because the length is always positive)
Length = x+4 = 18+4 = 22 cm
Width = x = 18 cm

How many whole numbers between 99 and 999 contain exactly one 0?

Answers

the correct answer is 162
There are 900 numbers that contain one 0.

A $129.50 stereo is discounted 40%. The next month, the sale price is discounted 60%. is the stereo now "free"? If not, what is the sale price?

Answers

discounted 40% means u pay 60%
0.60(129.50) = 77.70....1st discounted price

discounted 60% means u r paying 40%
0.40(77.70) = 31.08 <=== sale price
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