find the least length of a rod which can be cut into exactly epual strips,each of either 36cm or 42cm in length​

Answers

Answer 1

Step-by-step explanation:

so, we need to find the smallest common multiple of 36 and 42.

that is the smallest number I can divide both by 36 and 42 without remain.

let's use the method of basic prime factors (we start with the smallest fitting prime number - 2 is a prime number too - and divide as often as possible, then continue with the next bigger prime number, until there is nothing left to divide) :

36 / 2 = 18

18 / 2 = 9

9 / 3 = 3

3 / 3 = 1 finished

therefore,

36 = 2×2×3×3

42 / 2 = 21

21 / 3 = 7

7 / 5 does not work

7 / 7 = 1 finished

therefore,

42 = 2×3×7

to find the smallest common multiple (SCM) we check the maximum length of each prime factor sequence.

and we see 2 times 2, 2 times 3 and 1 time 7.

so, the SCM = 2×2×3×3×7 = 252.

there is no smaller number that can be divided by both 36 and 42 without remain.

so, the rod must be at least 252 cm long to cut it into equally long pieces of either 36 cm (7 pieces) or 42 cm (6 pieces).


Related Questions

negative three over eight divided by five over nine..

Answers

Answer:

- 27/40

Step-by-step explanation:

Solve the system of equations using elimination.

6y−4x=20−4y+3x=−12


(4, 6)

(−4, 6)

(−4, −6)

Answers

Answer: A. (4,6)

Step-by-step explanation: 2(6y−4x = 20)                                                   3(−4y+3x = −12)                                                                                                     −8x+12y = 40                                                                                                     9x−12y = −36                                                                                                   -8x+9x                                                                                                                 +12y-12y                                                                                                               40-36                                                                                                                     x=4                                                                                                                   6y−4x = 20                                                                                                       6y−(4)(4) = 20                                                                                                   6y−16+16 = 20+16                                                                                                 6y/6 = 36/6                                                                                                           y = 6                                                                                                                       x = 4, and y = 6.

The solution for the given system of equations is (4, 6). Therefore, option A is correct answer.

The given system of equations are 6y-4x=20 and -4y+3x=-12.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here,

6y-4x=20 ----------(I) and -4y+3x=-12 ----------(II)

Multiply equation (I) by 3, we get

-12x+18y=60 ----------(III)

Multiply equation (II) by 4, we get

12x-16y=-48 ----------(IV)

Add equation (III) and (IV), that is

-12x+18y+(12x-16y)=60-48

⇒ 2y=12

⇒ y=6

So, 6y-4x=20

⇒ 36-4x=20

⇒ -4x=-16

⇒ x=4

The solution for the given system of equations is (4, 6). Therefore, option A is correct answer.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ2

A pet shelter 42 kittens for adoption at the beginning of the week by the end of the week there were 21 kittens left find the percent decrease

Answers

Answer:

50% decrease

Step-by-step explanation:

50% = half

half of 42 is 21

there are 21 left, so 21 (which is half or 50%) were adopted

Solve the equation √7x-6=x-2. Identify any extraneous solutions. Show your work

Answers

√7x-6=x-2
(√7x-6)^2=(x-2)^2
7x - 6 = x^2 - 4x + 4
x^2 - 11x + 10
(x - 1)(x - 10) = 0

x = 1 and x = 10

√7(1)-6 = 1-2 is false, so 1 is an extraneous solution

√7(10)-6 = 10-2 is true, so it is a solution.

find the solution to the following system by substitution
4x+y=40

Answers

There are many ways of doing it, but here is mine.

Step-by-step explanation:

x = 6, y = 16

So now you multiply six by four and you will get twenty four plus sixteen, if you add them then you will get forty.

need helps i will give brainliest

Answers

Answer:

2401

Step-by-step explanation:

two thousand four hundred and one

Step-by-step explanation:

First let's put your equation

[tex]7 {}^{4} [/tex]

This also be phrased as

[tex]7 \times 7 \times 7 \times 7[/tex]

Now let's start solving

[tex]49 \times 7 \times 7 [/tex]

Multiply again and we get

[tex]343 \times 7[/tex]

and finally when we multiply again

[tex]2401[/tex]

Have a good day :) !

what’s the gcf of 56 and 90

Answers

Answer:

2

Step-by-step explanation:

Answer:

2

[tex] \: \: \: \: \: \: \: [/tex]

A glass cube of side length 5cm has a mass of 306.25g.
Calculate the density of the glass in glcm3.
You must show you working’s

Answers

Answer:

2.45 g/cm3

Step-by-step explanation:

It's a cube, so all the side lengths are the same. It's volume is [tex](5cm)^3[/tex] = [tex]125 cm^3[/tex].

At this point, we apply the definition of density [tex]\rho = \frac mV[/tex] where m is the mass and V the volume.[tex]\rho = \frac{306.25g}{125 cm^3} = 2.45 g/cm^3[/tex]

Ari needs to mix 3 tablespoons of dish soap with 6 tablespoons of vinegar to make a cleaning solution. How many tablespoons of vinegar are needed for each tablespoon of dish soap?

Answers

Answer:1 tablespoon of dish soap to 2 tablespoons of vinegar

Step-by-step explanation:

Answer:

1 tablespoon of dat soap to 2 table spoons of dat vinegar.

Step-by-step explanation:

So imagine. If 3 tablespoons of dish soap is to 6 table spoons of vinegar then 3 goes into 6  twice. So, 1 tablespoon of dish soap  is it 2 table spoons of vinegar.

another way to look at it:

1tbs dish soap = 2tbs vinegar

2tbs dish soap  = 4tbs vinegar

3tbs dish soap = 6tbs vinegar

x³+2x²-15x, x²-7x+12 and 3x²-27 find h.c.f​

Answers

Answer:

[tex] {x}^{3} + 2 {x}^{2} - 15x \\ x( {x}^{2} + 2x - 15) \\ x( {x}^{2} + 5x - 3x - 15) \\ x(x(x + 5) - 3(x + 5) \\ x((x + 5)(x - 3)) \\ {x}^{2} -7x + - 12 \\ {x}^{2} - 4x + 3x - 12 \\ x(x - 4) + 3(x - 4) \\ (x - 4)(x + 3) \\ 3 {x}^{2} - 27 \\ 3( {x}^{2} - 9) \\ 3((x + 3)(x - 3)) \\ \\ the \: hcf \: = (x + 3)[/tex]

Jin schedules 496 hours for a project. He plans to work 8 hours each day. How many days will it take to complete the project?​

Answers

Answer:

62 days

Step-by-step explanation:

496/8 = 62

496/8=62

Hope this helps!

right now michael earns an annual salary of $46,023 he is Considering a job offer with an annual salary of $51,145 what is the difference in the monthly pay for these two jobs rounded to the nearest cent

Answers

Answer:  The job pays $32,400 per year, and the agency fee is equal to 45% of one month's pay.

Manuel ran his mile in 7.332 minutes. How fast is that to the nearest hundredth? Explain your answer.

Answers

Answer:

7300

Step-by-step explanation:

this is because 3 is in the hundreds column and is rounded down

because the number behind is 3 so it stays the same some it is 7300

Distance=1miTime=7.332minutes=7.332(60s)=439.92s[/tex]

[tex]\\ \sf\longmapsto Speed=\dfrac{1mi}{439.92s[/tex]

[tex]\\ \sf\longmapsto Speed=0.00227mi/s[/tex]

[tex]\\ \sf\longmapsto Speed=0.0023mi/s[/tex]

[tex]\\ \sf\longmapsto Speed=0.002mi/s[/tex]

explain each step please :)

Answers

Answer:

u need to use the quadratic formula

Step-by-step explanation:

I think this is about it

10 x f(7) +9 x g(-1)=

Answers

the answer is 78

Step-by-step explanation:

10×7+9x-1=78

Answer: The answer is -1

Step-by-step explanation:

How do you write 2,020 in scientific notation?

Answers

Answer:

a x 10b or 2.02 x 10³

Step-by-step explanation:

Have a great day!

Polly buys 6.8 yards of fabric for $28.90. What is the cost per yard?

Please help? :)​

Answers

Answer:

Polly has to pay $0.24 per yard of fabric.

Step-by-step explanation:

You simply have to divide the 6.8 yards by the $28.90 cost. The result is $0.235294118 dollars per yard, but since you can't have only half a cent, we will round it to the nearest hundredths and get $0.24 dollars.

(5x-3=3x+29 )what is the value of X?

Answers

Answer: x=16

Step-by-step explanation:

Move the variable to the left-hand side and change its sign

5 x - 3- 3 x =29

Move the constant to the right-hand side and change its sign

5 x - 3 x = 29 + 3

Collect like terms

2 x = 29+ 3

Add the numbers

2x= 32

Divide both sides by 2

and you get x=16

Step-by-step explanation:

5x - 3 = 3x + 29

5x - 3x = 29 + 3

2x = 32

x = 32/2 = 16

x = 16 ans

therefore, value of x is 16.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

Joshua gets a daily allowance of $30. Each day he spends 60% of it on lunch, 1/2 of the remainder on transport and saves the rest. Calculate the amount he saves each week.

Answers

Answer:

$8

Step-by-step explanation:

60% of 30 is 16.

1/2 of 16 is 8.

He has $8 left.

Rashad wants to buy a TV which is $235. He already has $35. If he saves $25 a week. For at least how many weeks he has to save money so that he can buy the TV?

Answers

8 weeks. 235-35 = 200 200/25 = 8

The standard diameter of a golf ball is 42. 67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0. 002 mm. Which function could represent this situation?.

Answers

The absolute value function that could represent this situation is:

[tex]|D - 42.67| = 0.002[/tex]

The absolute value function is defined by:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

It measures the distance of a point x to the origin.

The diameter should be of 42.67 mm with an allowance of 0.002 mm. Thus, the absolute value of the difference between the diameter and of 42.67 should be of 0.002, that is:

[tex]|D - 42.67| = 0.002[/tex]

A similar problem is given at https://brainly.com/question/24514895


Solve for x

x/4=4/10

Give your answer as an improper fraction in its simplest form.

Answers

Answer:

1.6

hope this helps you!!!!!!!

Step-by-step explanation:

the answer which I have solved is in the image if you have any query then please ask...

x²+5x+6, x²+x-6 and x²-9 find hcf​

Answers

Answer:

[tex]x {}^{2} + 5x + 6 \\ {x}^{2} + 3x + 2x + 6 \\ x(x + 3) + 2(x + 3) \\ (x + 3) (x + 2)\\ \\ ( {x}^{2} + x - 6) \\ {x}^{2} + 3x - 2x - 6 \\ x(x + 3) - 2(x + 3) \\ (x - 2)(x + 3) \\ \\ {x}^{2} - 9 \\ (x - 3)(x + 3) \\ \\ the \: hcf \: = (x + 3)[/tex]

A triangle has an area of 160 square inches and the base of the triangle is 40 inches. What is the height of the triangle?

Answers

Answer:

answer-8 Inches.

Step-by-step explanation:

Area of triangle=160 square inches

Base of triangle=40 inches

area of triangle=1/2*base*height

160=1/2×40×height

160 =20×height

160/20=height

height=80 inches.

y = x - 15 when x is 2.65

Answers

Answer:

y = -12.35

Step-by-step explanation:

Plug in 2.65 for x giving you y = 2.65 - 15

find the length of segment AB

Answers

Answer:

96

Step-by-step explanation:

Answer:

96

hope this helps you!!

Use properties to evaluate (-25) HIS O A. – 15 5 O B. 5 C. - OC. 15 O D. 1​

Answers

Answer:

-15/4

Step-by-step explanation:

Answer: Its - 15/4 or 05/12 but the person above me is correct

Step-by-step explanation:

IF ANYONE IS A GENIUS AT MATH PLZ HELP AND ANSWER MY LATEST QUESTION!! I RLLY NEED HELP, IM LITERALLY GONNA CRY!!! IF YOU CAN'T FIND IT, BELOW IS AN IMAGE OF THE MATH SCENARIOS THAT I NEED HELP WITH!!! PLZ EXPLAIN EACH AND EVERY PART.

Answers

Answer:

Step-by-step explanation:

im not a genius at math, but i will give it a shot

scenario 3:

let m= cost per minute for WDE, let b= flat fee for WDE

42.5=50m+b

65=100m+b

subtract the two equations

65-42.5=50m

m= .45 (this is the cost per minute on WDE wireless)

plug in m=.45 into the first equation

42.5=50(.45)+b

b= 20 (this is the fixed monthly fee for WDE wireless)

HTR offers .25 per minute, whereas WDE offers .45 a minute which means that HTR has the cheaper per minute rate

htr has the equation .25x+30

WDE has the equation .45x+30

set them equal to each other and solve for x .25x+30=.45x+20

x= 50 minutes

Scenario 4:

Same deal as last question, let m=cost/movie, b=flat fee

41.25=5m+b

57.5=10m+b

subtract the two equations and solve for m

57.5-41.25=10m-5m+b-b

m= 3.25 (slope)

b=25  (y intercept)

y=3.25x+25

y=3.25(125)+25  = 431.25

3.25x+25=2.75x+35

.5x= 10

x= 20

HELP QUICKKK I NEED THIS FOR SCHOLL ASAP

Answers

Answer:

20, 30, 35, 45, 15

Step-by-step explanation:

Just got to multiply all numbers by 5 little guy

find the highest common factor of 9, 12 and 15​

Answers

Hello there! :)

The highest common factor of 9, 12, and 15 is 3.

To find the HCF (also called the GCF) of two or more numbers, we list their factors:

9: 1, 3, 9

12: 1, 2, 3, 4, 6, 12

15: 1, 3, 5, 15

Can you see that 3 is their GCF?

Hope this helps!

~Just a determined gal

#CarryOnLearning

[tex]MysteriousNature[/tex]

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