Explain how to find the greatest number of identical arrangements that can be made with 54 roses and 42 tulips with no flowers left over.

Answers

Answer 1

Answer:

  GCF(54, 42) = 6 arrangements

Step-by-step explanation:

The number of such arrangements will be the greatest common factor (GCF) of the two numbers. You recall from your times tables that ...

  54 = 6×9

  42 = 6×7

The factors 9 and 7 have no factors in common, so 6 is the greatest common factor of 54 and 42.

  6 identical arrangements of 9 roses and 7 tulips can be made.

_____

Additional comment

When the numbers are small and found in your memorized times tables, finding the GCF is done by consulting your memory. Otherwise, it can be done by factoring, or by using Euclid's algorithm.

When the numbers are factored to primes, the GCF is the product of the prime factors the numbers have in common.

  54 = 2×3×3×3

  42 = 2×3×7

These factorizations have 2×3 = 6 in common.

__

Euclid's algorithm has you find the remainder from the division of the larger number by the smaller. When that remainder is not zero, it replaces the larger number, and the process repeats. When that remainder is zero, the divisor is the GCF.

  54/42 = 1 r 12

  42/12 = 3 r 6

  12/6 = 2 r 0 . . . . GCF = 6

This algorithm works on numbers of any size (including fractions and mixed numbers), so is especially useful when the factorization is not obvious.


Related Questions

Elena said the equation 9x+15=3x+15 has no solutions because 9x is greater than 3x. Do you agree with Elena? Explaining your reasoning.

Answers

Answer:

it does have a solution x=0

Step-by-step explanation:

9x+15=3x+15

6x+15=15

6x=0

x=0

Answer:

I agree.

Step-by-step explanation:

Here is my explantion:

[tex]9x+15=3x+15\\\\Simplify:\\9x=3x\\\\Subtract 3x from both sides\\9x-3x=3x-3x\\\\\\Simplify:\\6x=0\\\\Divide both sides by 6\\\frac{6x}{6} =\frac{0}{6}\\[/tex]

Is this answer right?

Answers

Answer:

that is the correct answer.

Step-by-step explanation:

The perimeter of the rectangle below is 68 cm. The perimeter of the triangle is 60 cm. Find the length of the hypotenuse of the triangle​

Answers

The right triangle is assumed to be inscribed in the rectangle, such that

hypotenuse is the diagonal of the rectangle.

The length of the hypotenuse of the triangle is 26 cm.

Reasons:

Let x and y represent the length of the sides of the rectangle

Whereby the base and height of the right triangle are the same as the

length and width of the rectangle, we have;

Perimeter of the rectangle = 2·x + 2·y = 68

Therefore;

[tex]\displaystyle x + y = \frac{68}{2} = 34[/tex]

x + y = 34

The base of the right triangle = x

The height of the right triangle = y

By Pythagoras's theorem, the length of the hypotenuse side = √(x² + y²)

Therefore; Perimeter of the right triangle = x + y + √(x² + y²) = 60

Which gives;

√(x² + y²) = 60 - (x + y) = 60 - 34 = 26

The length of the hypotenuse side, √(x² + y²) = 26 cm

Learn more about Pythagoras's theorem here:

https://brainly.com/question/8171420

cost $ 99.99 Markup rate 10 %
!!!!!!!10 POINTS TO WHO EVER ANSWER I WILL BE GIVING MORE ON THE NEXT QUESTION!!!!!!!

Answers

Answer: %0.00100010001

Step-by-step explanation:

How would you write 32 as a Roman numeral?

Answers

Answer:

XXXII

Step-by-step explanation:

The number 30 as a roman is XXX and the number 2 as a roman is ll. So the answer is XXXII

- Your welcome ;)

b)
Here is another number machine.
Input
Output
х
4x + 5

Answers

Answer:

collect like terms x=5-4=1

Find three consecutive whole numbers such that the sum of the squares of the numbers is equal to 434

Answers

Answer:

[tex]\left \{ {{x^2+y^2+z^2=434} \atop {x-y-z=0}} \right.[/tex]

Step-by-step explanation:

Can you help me please and thank you.

Answers

Answer:

The length is 40m

Step-by-step explanation:

Length = x

P = 2x + 2W

118 = 2x + 2(19)

118 = 2x + 38

118 - 38 = 2x

     80   = 2x

     80/2 = x

       40 = x   Length

y = amount of $ paid for the job

y  +  $48 = $200          total job for 3 -hours

 y  ÷   3                       amount paid per hour                    

please help me. i don't understand

Answers

Answer:

#9 the answer is 7

Step-by-step explanation:

so start with what you know. the sum of the angles in a triangle equal 180 degrees

so...

(x + 13) + (17x - 7) + 48 = 180

now just combine like terms

18x + 54 = 180

18x = 126

x = 7

The volume of a rectangular prism is (x^4 + 4x^3 + 3x^2 + 8x + 4), and the area of its base is (x^3 + 3x^2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? 4 O X+1- X4+4x2 + 3x? +8x+4 4 X+1+ X4-4x2 + 3x2 + 8x+4 x* O x+1-2-3x2 +8 © X+1 +

Answers

Answer:

If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by:

Given :

Volume of rectangular prism

Base Area of a rectangular prism =

 ---- (1)

Solution :

The volume of prism is the amount of space a prism occupies. It has two same faces and other faces that resemble a parallelogram.

Let the height of the prism be h.

Now, substitute the value of base area and volume of the rectangular prism in the given equation (1).

If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by:

Step-by-step explanation:

Dividing the volume by the base area, you find the height to be ...

The height of the prism is

If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by (x+1) - 4//(x³ + 3x²+8)

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The volume of prism is the amount of space a prism occupies. It has two same faces and other faces that resemble a parallelogram.

Let the height of the prism be h.

Now, substitute the value of base area and volume of the rectangular prism in the given equation (1).

x⁴ + 4x³ + 3x² + 8x + 4 = (x³ + 3x²+8)h

Divide both sides by  (x³ + 3x²+8)

h=(x⁴ + 4x³ + 3x² + 8x + 4)/(x³ + 3x²+8)

h=(x+1)((x³ + 3x²+8)-4)/(x³ + 3x²+8)

h=(x+1) - 4//(x³ + 3x²+8)

Hence, If the volume of a rectangular prism is the product of its base area and height, than the height of the prism is given by (x+1) - 4//(x³ + 3x²+8)

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ7

if anyone has mine.craft education edition, i just created a world and here the code

rail, llama, llama, cookie

:)))

Answers

Uh so like are llamas green

[tex]\sqrt{x} +1=3\\[/tex]

Answers

Answer:

x = 4

Step-by-step explanation:

√x + 1 = 3

√x = 3 - 1

√x = 2

(√x)² = (2)²

x = 4

If the Diameter is 10 of a circle then what is the radius.

Answers

Answer:

5

Reasoning

[tex]Diameter=2*radius[/tex]

Answer:

5

Step-by-step explanation:

the radius is always half of the diameter

Alexander and his friends are going into a restaurant. How much would it cost to buy 2 hotdogs and 40 chicken wings if each hotdog costs $4.00 and each chicken wing costs $0.50? How much would it cost to buy 22 hotdogs and 4040 chicken wings if each hotdog cost \$h$h and each chicken wing cost \$c?$c?

Answers

2 * 4
$8.00 - hot dogs

40 * 0.50
$20.00 - chicken wings

$28.00 total
4+4= $8 for 2 hotdogs
40 x by .50= $20 for the wings


22x4= $88 for 22 hotdogs
4040x.50= $2020 for 4040 wings

Help help help help help help help help help help

Answers

Answer:

-√32 < 59/11 < √30 < 5.49


In the base-ten number system, ten digits {0, 1, 2, 3, 4, 5, 7, 8, 9) are used for number
representations. The base-ten number 825 therefore means 8 x 102+2 x 10+5 x 1
Similarly, in the base-three number system, three digits {0, 1, 2) are used for number
representation. A base-three number 1212 means 1 x 3 +2 x 32 + 1 x 3+2 x 1. What
is the base-three representation of the base-ten number 35?

Answers

Answer:

..............I think its wrong .......

solve the system {2x+y=8 using substitution method.


{x-y=6 using elimination method


please answer my question ​

Answers

Answer:

y = -4/3

x = 14/3

Step-by-step explanation:

2x+y=8

x-y=6

First of all, we need the same coefficient, so we can make both of these 2x by multiplying the second one by 2.

2x+y=8

2x-2y=12

Then we need to subtract equation 1 from 2.

3y=-4

Solve normally

y = -1.33333 / -4/3

Substitute

x - (-4/3) = 6

x = 14/3

[tex]\large\huge\green{\sf{Answer:-}}[/tex]

[tex] \red {\mathbb{ \underline { \tt by \: elimination \: method \: s}}}[/tex]

2x+y=8________(i)x-y=6_________(ii)

from equation (i):-

[tex]2x - y = 8 \\ x = \frac{8 - y}{2} [/tex]

put value of x in eq (ii)

[tex]x - y = 6 \\ \frac{8 - y}{2} - y = 6 \\ \frac{8 - y - 2y}{2} = 6 \\ 8 - y - 2y = 12 \\ 8 - 3y = 12 \\ - 3y = 12 - 8 \\ - 3y = 4 \\ y = \frac{ - 4}{3} [/tex]

put value of y in eq (i)

[tex]2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} [/tex]

now,

By elimination method:-

[tex]2x + y = 8 \\ x - y = 6 \\ - - - - - - - \\ multiply \: eq \: (i) \: by \: 1 \\ and \: eq(ii) \: by \: 2 \\ \\ (2x + y = 8) \times 1\\ (x - y = 6) \times 2 \\ - - - - - - - \\2x + y = 8 \\ 2x - 2y = 12 \\ subtract \: these \\ 3y = - 4 \\ y = \frac{ - 4}{3} \\ [/tex]

put value of y in equation (i)

[tex]2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} [/tex]

Help! I give brainlest. Problem is in Image

Answers

Answer:

65

Step-by-step explanation:

let's place 9 in place of p and 4 in place of q. I will use a star in place of that symbol for the sake of my convenience having to look for it, apologies.

[tex]9 \star 4 = 9^2-4^2 = 81-16 = 65[/tex]

Answer:

65

Step-by-step explanation:

9^2-4^2=65

look at the image, i need help with b mostly and please also answer a so i can check my answer

Answers

Answer:

a) 10 per for 4 min means 150 per hour. so more hamburgers are sold per hour.

b) see attachment

3.53 divided by 51
24.2 divided by 42
9.13 divided by 23
79.2 divided by 39

Answers

Answer:

1. 0.0692156863

2. 0.5761904762

3. 0.3969565217

4. 2.030769231

Step-by-step explanation:

Round 4.01 to the nearest one decimal place.

Answers

The answer should be 4.00

Find the value of x and thank for answer

Answers

X = 70

90 + 90 = 180

360 - 180 = 180

180 divided by 2= 90

90 - 20 = 70°


Sketch the graph of each line by identifying the x-and y-intercepts.

Answers

Straight line at y=5
And goes all the way from -inf to +inf of the x-axis and doesn’t intersect with x-axis


Geometry work pls help ASAP

Answers

Answer:

3321

Step-by-step explanation:

What is the measure of _____?​

Answers

Answer:

95 degrees

Step-by-step explanation:

The sum of all the angles need to come to 360 degrees. We already have 2 90 degree angles, together 180 degrees. Subtract from 360 to get 180, so we know the other two angles together need to equal 180. x + x + 10 = 180

Add common terms, then subtract 10: 2x = 170

Divide by 2: x = 85

So angle F is 85 + 10, or 95 degrees.

He receives 35 rewards points just for signing up.
He earns 2.5 points for each visit to the movie theater.
He needs at least 55 points for a free movie ticket.

Write and solve an inequality which can be used to determine vv, the number of visits Omar can make to earn his first free movie ticket.

Answers

Answer:

8

Step-by-step explanation:

What is the slope of the line that passes through the points (9, 1) and (17, 2)
A: 8/15
B: 8/1
C: 1/8
D: 15/8

Answers

Answer:

C

Step-by-step explanation:

Slope of a line that goes trough the points (x1=9, y1=1) and (x2=17, y2=2)

m= (y2-y1)/(x2-x1) = (2-1) / (17-9) = 1/8

which ordered pair represents the coordinate of point h?
(0.6, - 1.4) (-1.4, 0.6) (-1.2 , 0.3) (0.3, - 1.2)

Answers

Answer:

-1.2 is the answer i think

a 4 foot statue has a shadow of 3 feet.next to the statue is a telephone pole with a shadow of 18 feet.what is the height of the telephone pole

Answers

Answer:

c 15.9 m

Step-by-step explanation:

you are welcome

Write an equation in
Slope - int form with the
given information
m=2, (3, 4)

Answers

Answer:

y=2x-2

Step-by-step explanation:

apply point

4=2(3)+n

4=6+n

n=-2

y=2x-2

Other Questions
HELPPP PLEASEEEE.. After Jackson was elected in 1828, what did he become a symbol of? If the perimeter of a square is 7 feet how many inches long is the square on each side? Beware the Ides of March!Identify the mood. Hello! I have a project where I invite 5 people to a dinner party to school. I want to invite a girl named Jaci Butler. Jaci Butler is her own agent in the singing industry. I found her address and want to send her a mail. Does this count as stalking? If you were Jaci butler, what would you think Im a stalker? If you were her, would you come? Choose the angles that are adjacent to For the oxidationreduction reaction equation2Sc+3Br22ScBr3indicate how many electrons are transferred in the formation of one formula unit of product. Main Idea or Topic: Document 1. The caption for this cartoon reads as follows: The duty of the hourto save her not only from Spain but from a worse fate. Add a second sentence that makes clear the meaning of this first one. Write a note to your English teacher. Something that you would like to tell her? 10 sentences or more sentences please answer fully/////////////// What did Jackson want to do if South Carolina followed through on a plan of secession? How does the first amendment protect religious freedom for american citizens? choose exactly two answers that are correct. PLEASEE HELPPP!!!!Hydrogen bonds can be found between molecules of which substance?1.) CH4 2.) H23.) C4H104.) NH3 One of the Temples in the Horyu-ji Area 2) What religion is this temple from? Can I please get help What is 2x-3 when x=5 Which of the following was true of hunters and gatherers please help me answer this question! handwashing with regular soap is effective because __________. A particle is constrained to move round a circle radius 382400km and makes a single revolution in 27.3 days. (i). Find the velocity in ms-1. (ii). Find its acceleration