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Explanation:
Let x and y be two positive whole numbers. They may or may not be equal.
The first bag has the ratio of red to blue as 3:5, which scales up to 3x:5x after multiplying both parts by x. We have 3x red and 5x blue.
The second bag has the ratio 3:2 which scales up to 3y:2y. This bag has 3y red and 2y blue.
We can make a handy table to keep track of all the expressions
[tex]\begin{array}{|c|c|c|}\cline{1-3}\text{ } & \text{Red} & \text{Blue}\\ \cline{1-3}\text{bag 1} & 3x & 5x\\ \cline{1-3}\text{bag 2} & 3y & 2y\\ \cline{1-3}\end{array}[/tex]
Based on that, we can then say:
The two red quantities add to R = 3x+3yThe two blue quantities add to B = 5x+2yEffectively, I added down along each column of that table.
Divide the two expressions for R and B to lead to the fraction 11/9, which is directly from the ratio 11:9
So,
(total red)/(total blue) = 11/9
R/B = 11/9
(3x+3y)/(5x+2y) = 11/9
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Let's cross multiply and then solve for y
(3x+3y)/(5x+2y) = 11/9
9(3x+3y) = 11(5x+2y)
27x+27y = 55x+22y
27y-22y = 55x-27x
5y = 28x
y = 28x/5
y = (28/5)x
y = 5.6x
We'll keep this in mind for later.
---------------------
Now let:
F = amount of marbles in the first bagS = amount of marbles in the second bagRecall that we had 3x red and 5x blue for the first bag. That means we have 3x+5x = 8x marbles in the first bag. Therefore, F = 8x.
Also, we had 3y red and 2y blue for the second bag.
So we have S = 3y+2y = 5y
Then we can apply further substitution to say
S = 5y
S = 5(5.6x) .... plug in y = 5.6x
S = 28x
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In short,
F = 8xS = 28xfor some positive whole number x. We don't have enough info to pin down what x is exactly; however, it doesn't really matter. This is because the x variable will cancel when dividing F over S
F/S = (8x)/(28x) = 8/28 = 2/7
The fraction 2/7 leads directly to the final answer of the ratio 2:7
In other words, the ratio 8x:28x simplifies fully to 2:7 after dividing both parts by 4x.
The ratio between the total marbles of the first bag and the second bag is 2:7.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x marbles in the first bag.
red marbles = 3x
blue marbles = 5x
y marbles in the second bag.
red marbles = 3y
blue marbles = 2y
Now,
Total red marbles in both bags.
3x + 3y = 11 _____(1)
3x = 11 - 3y
x = (11 - 3y) / 3
Total blue marbles in both bags.
5x + 2y = 9 ______(2)
From (1) and (2) we get,
Multiply 2 in (1).
6x + 6y = 22
6y = 22 - 6x _____(3)
Multiply 3 in (2)
15x + 6y = 27 ______(4)
Putting (3) in (4)
15x + 22 - 6x = 27
9x = 27 - 22
9x = 5
x = 5/9
Now,
x = 5/9 in (3)
6y = 22 - 6(5/9)
6y = 22 - 10/3
6y = (66 - 10)/3
y = 56/18
y = 28/9
Now,
First bag.
Red marbles = 3x = 3 x 5/9 = 5/3
Blue marbles = 5x = 5 x 5/9 = 25/9
Total marbles = 5/3 + 25/9 = (15 + 25)/9 = 40/9
Second bag.
Red marbles = 3y = 3 x 28/9 = 28/3
Blue marbles = 2y = 2 x 28/9 = 56/9
Total marbles = 28/3 + 56/9 = (84 + 56)/9 = 140/9
Now,
The ratio between the total marbles of the first bag and the second bag.
= 40 :140
= 4:14
= 2:7
Thus,
The ratio is 2:7.
Learn more about equations here:
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Please help me with this
Answer:
h,c
Step-by-step explanation:
Work out 247 as a percentage of 380.
Answer:
65%
Step-by-step explanation:
You can use the equation " is over of " to solve this. 247/380 * ?/100. After simplifying, you get 24700/380 which equals 65%.
Brainliest would be appreaciated! :-)
I think the answer is 65%. Hope that helps.
If f(x) = 2x – 5, then what is the value of f(2) + f(5)
Answer:
4
Step-by-step explanation:
first to solve right get brainlest
If AABC ~ ADEF, then which of the following must be true? Check all that apply.
Answer:
#1 and #3
Step-by-step explanation:
Simple Geometry Question 100 Points
How do you use coordinates to find the area of polygons?
Answer:
By finding the product of a point's x coordinate times the next point's y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon.
Step-by-step explanation:
Melanie has 10 packets of 20 biscuits. She puts 3/10 of them on a plate to serve. How many biscuits are being served?
From the problem statement Melanie has 10 packets of 20 biscuits
60 biscuits
Solution
Let us find 3/10 of 10 packets
= 3 packets
In one packet there are 20 biscuits,
Hence in 3 packets there will be
20*3 = 60 biscuits
From the solution above Melanie served 60 biscuits in the plate
Learn more about fraction here:
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10,000 candy canes was divided into 50 boxes. How many candy canes were in each box?
Answer:
200
Step-by-step explanation:
Answers ASAP THANKS!!!
Solve for the x
[tex]\frac{36}{x}[/tex] = -9
[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]
[tex]:\implies\sf{ \frac{36}{x} = - 9} \\ \\ :\implies\sf{ \frac{36}{ 9} = -x} \\ \\ :\implies\sf{4 = -x} \\ \\ :\implies\sf{x = -4}[/tex]
There are 32 vanilla cupcakes and 40 chocolate cupcakes at a bakery. All of the cupcakes must be placed in boxes with the same number of vanilla cupcakes and the same number of chocolate cupcakes in each box.
Answer:
5 to 4
Step-by-step explanation:
when it's asking for a ratio it's basically division
chocolate/vanilla = 40/32 = 5/4
5/4 is the same as 5:4 or 5 to 4
22 of the 30 students in Evan's grade have a pet. What is the ratio of the number of students who do not have a pet to the number of students who have a pet?
Answer:
8 to 22
Step-by-step explanation:
if there are 22 people that have a pet whens there is 30 students in total, you have to do, 30-22, and 30-22=8 meaning there are 8 students who don't have pets.
And if already says 22 students have pets, therefore the answer is
8 to 22
8:22
Suppose the relationship between x and y is proportional. When x is 7 , y is . 147 Identify the constant of proportionality of y to x.
Answer:
its 21
Step-by-step explanation:
can anybody help me with this?
Answer:
a) 3.6 × 10²
Time = distance / speed
So time = 1.08 × 10⁸ / 3 × 10⁸
= 1.08 × 10¹¹ / 3 × 10⁸ ( converted 10⁸ km to meter )
= 1.08 × 10³ / 3
= 0.36 × 10³
. = 3.6 × 10²
Time = 3.6 × 10²
What does 100+100-200+90+20=
Answer:
110
Step-by-step explanation:
Which of the following is equal to
(x - 3)(2x + 4x - 1)?
A 2x3 - 2x2 - 11x + 3
B 2x3 -- 2x2 - 13x + 3
Answer: [tex]2x^3-2x^2-13x+3[/tex]
======================================================
Work Shown:
I'm assuming you meant to say [tex](x - 3)(2x^2 + 4x - 1)[/tex]
Let [tex]y = x-3[/tex]
So,
[tex](x - 3)(2x^2 + 4x - 1)\\\\y(2x^2 + 4x - 1)\\\\y2x^2 + y4x - y\\\\2x^2(y) + 4x(y) - (y)\\\\2x^2(x-3) + 4x(x-3) - (x-3)\\\\2x^3-6x^2 + 4x^2-12x - x+3\\\\2x^3-2x^2-13x+3\\\\[/tex]
The basic idea is to use the distribution rule (line 3 and line 6) and then combine like terms.
slopes of a quadrilateral please hurry before a bot attacks me ive been attacked all day. Multippe choice.
Answer: 3rd one got it right on mine
Step-by-step explanation:
A taxicab charges $3.00 per person
plus $1.25 per mile. What is the
greatest distance one passenger
could travel with a budget of
$28.00?
Answer:
I believe the answer would be 20 miles max for one passenger.
Step-by-step explanation:
This is because if you create an equation out of this, knowing that only one passenger will be riding, you will get:
$3.00+$1.25x=$28 ($3 added too $1.25 times the number of miles (x) which equals the total amount you have ($28)).
x being the number of miles (so we need to calculate for x)
$3 + $1.25x = $28
-subtract 3 on both sides-
$1.25x=$28-$3
$1.25x=$25
-divide by 1.25 on both sides-
x=$25/$1.25
x=20 miles
Not sure if all calculations are correct, but I hope this helps :)!
HELP PLEASE IS IMPORTANT!
Solve the equation by using the Quadratic Formula.
2x 92-5
See attachment for answer and math work.
The difference between eight times a number and three is equal to negative nineteen. What is the number?
-2
2
-3
3
Answer:
-2
Step-by-step explanation:
3 - 19 = 8(x)
-16 = 8(x)
-16/8 = x
x = -2
Answer:
I believe that it is -2
Step-by-step explanation
I had this math question too
My friend needs your help
Answer:
I can't make a graph, but you would start by putting a point at -1 on the Y axis, then plot the rest of the points by going up 4, and over 7 from the original point you plotted
Step-by-step explanation:
I hope you can make sense of that
(34.23 x 2.3) + 432.15
Answer:
The answer is 510.879
Step-by-step explanation:
Multiply parentheses first:
34.23×2.3=78.729
Add to 432.15
=510.879
If 333 + 555 = 999 And 123 + 456 = 488 And 505 + 213 = 809 Then 344 + 732 = ???
Answer:
1076
Step-by-step explanation:
I just need points lol
there are 1200 students in a school. if 2/5 are girl what is the number and percentage of boys? find it
Step-by-step explanation:
Hope it will help you...
10)
There are 14 black pens out of 25 pens. What percent of the pens are black?
Answer:
Step-by-step explanation:
14 dived by 25 is 56%
angle A and angle B are supplementary angles. If m∠=(4x - 30) degree and m∠B =(4x-14) degree, then find the measure of ∠A
Answer:
<A = 26°
Step-by-step explanation:
4x - 30 + 4x - 14 = 180
Supplementary angles sum together to make 180
=> 4x + 4x = 16x
=> -30-14 = -44
16x = 180+44
16x = 224
x = 224/16
x = 14°
4(14) - 30 = 26°
If x=2, y=4, m= -1, and n=3 find the value of :
X^m+n * y^n-m/ x^m-n * y^n+m
Answer:
The value is [tex]\frac{1}{16384}[/tex]
Step-by-step explanation:
Here we need to find
[tex]\frac{x^{m+n}\cdot y^{n-m}}{x^{m-n}\cdot y^{n+m}}=x^{m+n-(m-n)}\cdot y^{n-m-(n+m)}\\\\=x^{2n}\cdot y^{-2m}\\\\=2^{2\cdot-1}\cdot 4^{-2\cdot3}\\\\=\frac{1}{2^2\times4^6} \\\\=\frac{1}{16384}[/tex]
The price tag on the remote-controlled helicopter said $79. If Jimmy buys the
helicopter, he'll also have to pay 8% sales tax. How much does the helicopter cost with
tar?
Step-by-step explanation:
79×0.08 = 6.32 (tax)
79(price) + 6.32(tax) = 85.32
What's the formula for the area of a triangle?
Answer:
A=hb/2
To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2. Find the area of a triangle where height = 5 cm and width = 8 cm. A triangle is always half the area of a rectangle with the same height and width.
Hey there!
“ What's the formula for the area of a triangle?”
The area of triangle formula is:
A = hbB/2
Whereas “hb” is your “height base” & “b” is your “base”
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Side note:
You can look at the question for an example of what the area of a triangle is
Which of the sets of ordered pairs represents a function?
A = {(3, −5), (4, 6), (3, 9), (2, 7)}
B = {(2, 4), (−1, 4), (5, 4), (4, 4)}
a
Both A and B
b
Only B
c
Only A
d
Neither A nor B
Answer:
B
Step-by-step explanation:
A does not represent a function because the x-value of 3 appears twice, and by the defenition of a function, the x-value cannot appear twice for it to be considered a function. B could be a function because the x-values are not repeated.
Therefore the answer is B, only B is a function.