Mathematics College

Given 64 / 108, what common factor would reduce this fraction to its lowest terms?

Answers

Answer 1

Answer:

Common factor of 4
Simplest terms is 16/27

Step-by-step explanation:

Let's find the factors of both numbers

64:

1, 2, 4, 8, 16, 32, 64

108:

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The greatest common factor is 4

The fraction in simplest terms would be [tex]\frac{64}{108}*\frac{4}{4} = \frac{16}{27} \text{ cross reduce}[/tex]

-Chetan K

Related Questions

1. Think of two things that you can measure. Give one that requires high precision, or a low level of uncertainty. Give another that can have lower precision, or a higher level of uncertainty.

2. Explain why you made your choices. Why does one measurement need to be more precise than the other

Answers

1. We can measure the following two things:

(i) a person's height

(ii) the velocity required to reach Mars.

2. Everything involving a rocket launch needs to be extremely precise; otherwise, it could result in tragedy. However, anything involving a person's height won't result in disaster.

This can be solved using the concept of precision and uncertainty concept.

What is precision and uncertainty?

The accuracy of a material or substance is the distance or degree to which two or more measurements are near to one another. Every time a measurement is performed, a new result is obtained that falls within the uncertainty interval that surrounds the measured value.

1. We don't need to be very precise because we can measure a person's height with a modest degree of accuracy. The person hearing would get a notion of their height if we said, "That individual is roughly 5 feet tall."

On the other hand, if we estimate the rocket speed to Mars incorrectly, it would lead to tragedy in the future, hence we require great precision. In order to ensure that we strike the necessary objective in space, we apply intricate mathematics.

2. Like we stated in problem 1, everything involving space travel needs extreme accuracy. The spaceship might crash and calamity could ensue if our estimates are incorrect. Engineers utilized the incorrect settings in the one instance where anything went wrong, causing the Mars lander to smash into the planet rather than securely land there.

Due to the enormous expense of these space exploration missions, it is imperative to obtain as many exact and accurate values as possible. Now, details like a person's height don't necessarily need to be accurate because we can just guesstimate a person's height depending on who we're speaking to.

To know more about precision refer to:

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Evaluate −4|x+2| when x=−5.

−28

−12

12

28

Answers

Answer:

Step-by-step explanation:

Find the inverse of the matrix [6, 7] [-6, 7] if it exists

Answers

For any square matrix A, if it is invertible, its inverse is given by

[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A)[/tex]

where adj(A) is the so-called adjugate matrix, which is the transpose of the cofactor matrix of A. If you don't know what that is, that's not terribly important. What is important is that the inverse does not exist if the determinant, det(A), is zero.

We have

[tex]A=\begin{bmatrix}6&7\\-6&7\end{bmatrix} \implies \det(A) = 6\times7-7\times(-6)=84 \neq 0[/tex]

so the inverse does indeed exist. (And we eliminate D as an answer.)

From the given choices, it's quite clear that C must the correct answer, since we know det(A) = 84, and we can easily confirm that

[tex]\begin{bmatrix}7&-7\\6&6\end{bmatrix} \begin{bmatrix}6&7\\-6&7\end{bmatrix} = \begin{bmatrix}84&0\\0&84\end{bmatrix}[/tex]

so that multiplying by 1/84 recovers the identity matrix.

We are given with a square matrix and we are asked to find it's inverse if it exists . So , let's recall some important points first :-

Inverse can only be found of square matrices.

If [tex]{\bf A}[/tex] is a square matrix than , it's inverse is denoted by [tex]{\bf A^{-1}}[/tex] , and is given by [tex]{\bf{A^{-1}=\dfrac{1}{adj(A)}det(A)}}[/tex] , where adj(A) is the adjoint of the matrix A and det(A) is the determinant of the matrix A

Inverse of a matrix exist if A is non-singular

Non-Singular means that det(A) ≠ 0

Adjoint of a matrix is the matrix of transpose of cofactors

Transpose of a matrix is founded by exchanging it's rows by columns and columns by rows and is denoted by [tex]{\bf{A^{T}}}[/tex]

Now , in this question let's assume that [tex]{\sf A=\begin{bmatrix}6 & 7 \\ -6 & 7\end{bmatrix}}[/tex]

Now , Calculating det(A) :-

[tex]{:\implies \quad \sf det(A)=\begin{vmatrix}6 & 7 \\ -6 & 7 \end{vmatrix}}[/tex]

[tex]{:\implies \quad \sf det(A)=42-(-42)}[/tex]

[tex]{:\implies \quad \sf det(A)=42+42}[/tex]

[tex]{:\implies \quad \sf det(A)=84}[/tex]

As , det(A) ≠ 0 . So , [tex]{\bf A^{-1}}[/tex] exists . Now , we need to find the matrix of cofactors first , but let's find cofactors first , so here ;

[tex]{\blacktriangleright \sf C_{11}=7,\: C_{12}=6,\: C_{21}=-7,\: C_{22}=6}[/tex]

Now , let's assume that matrix of cofactors is C , so putting the cofactors as elements of the matrix , C will be ;

[tex]{:\implies \quad \sf C=\begin{bmatrix}7 & 6 \\ -7 & 6\end{bmatrix}}[/tex]

Now , adj(A) will be found by interchanging it's rows by columns and vice versa.

[tex]{:\implies \quad \sf adj(A)=\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex]

Now as [tex]{\sf A^{-1}}[/tex] is given by [tex]{\bf{A^{-1}=\dfrac{1}{adj(A)}det(A)}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{A^{-1}=\dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}}}[/tex]

Hence , Option C) [tex]{\sf \dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex] is correct :D

Help! I can't figure this out!

Answers

Answer:

57/6 60/6 22/6 26/6

Step-by-step explanation:

So the answers for the blanks are 57, 60, 22, 26.

Let me know if I am incorrect.

a case of toothpicks has 5,400 toothpicks, there are 9 boxes of toothpicks in the case.how many toothpicks are in each box?

( awnser this untill tmr and u will get 200 points!)

Answers

Answer:

divide it, 5400 divided by 9 is 600.

if you have 5,400 picks, there are 600 picks in each box.

An 8-year-old boy is half his sister's age. When the boy is 12, how old will his sister be?

Answers

Answer:

20 years

Step-by-step explanation:

when the boy is 8 and half his sisters age his sister is 16

four years later the boy will be twelve, so if his sister was 16 four years later she will be 20

Answer:

20 years old

Step-by-step explanation:

Let n represent the age of the boy's sister then...

[tex]8=\frac{1}{2}n[/tex]

Multiply both sides by 2

[tex]n=16[/tex]

When the boy is 12, it will be 4 years from when he is 8 therefore...

16 + 4 = 20 years old

If you were in charge of the money, how would you recommend your friends spend it? Explain why you chose the solution you did. Why do you think it's the most fair? (3 points: 1 point for stating your recommendation and 2 points for explaining your reasoning)

Answers

Prioritize meeting basic needs and invest in education and skill development, while supporting community projects for a fair distribution of funds.

Prioritize basic needs: I would recommend ensuring that everyone's basic needs are met first, such as food, shelter, and healthcare. This promotes fairness by addressing essential requirements for survival and well-being.

Invest in education and skill development: Allocating funds towards education and skill development programs can empower individuals to improve their future prospects and contribute to society. It promotes fairness by providing equal opportunities for personal growth and advancement.

Support community projects: Encouraging investments in community projects, infrastructure development, and social initiatives can benefit a broader range of people. It promotes fairness by aiming to uplift the community as a whole, rather than focusing solely on individual interests.

By following these principles, the recommended approach for spending money can ensure fairness by addressing basic needs, fostering personal development, and benefiting the community at large. Ultimately, the specific allocation of funds would depend on the context, priorities, and values of the individuals involved.

Learn more about projects: here:

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Paul had 84 fliers to post around town. Last week, he posted 1/4 of them. This week, he posted 4/7 of the remaining fliers. How many fliers has he still not posted?

Answers

27 fliers

1/4 of 84 is 21
84-21=63
4/7 of 63 is 36
63-36=27

What are the domain and range of the function?
f(x) = -5/5x^3

Answers

Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

Hope that helps!

Use the distributive property to write an expression that is equivalent to each expression. If you get stuck, consider drawing boxes to help organize your work.
9(4x−3y−23)
-2(-6x+3y−1)
15(20y−4x−13)
8(-x−12)
-8(-x−34y+72)

Answers

Answer:

a) 36x-27y-207

b)12x-6y+2

c)300y-60x-195

d)-8x-96

d)8x+272y-576

Step-by-step explanation:

In all of these equations, you multiply the numbers on the outside of the parentheses to all of the terms inside the parentheses to get each of your different answers.

Hope this helps and please award brainliest if possible!

Someone please help me!

Answers

Answer:

[tex]y= -\frac{8}{7} x - 7[/tex]

Step-by-step explanation:

Hope this helps! :)

(x + 4)2 – 3(x + 4) – 3 = 0 Select the solution(s) of the original equation.

Answers

Answer:

x=−7

Step-by-step explanation:

(x+4)(2)−3(x+4)−3=0

(x)(2)+(4)(2)+(−3)(x)+(−3)(4)+−3=0(Distribute)

2x+8+−3x+−12+−3=0

(2x+−3x)+(8+−12+−3)=0(Combine Like Terms)

−x+−7=0

Here is a rhombus.
Diagram not drawn to scale
80°
A straight line joining the midpoints of two of its sides is drawn.

Answers

Answer:

130 degrees

Step-by-step explanation:

The right top triangle is isosceles, so the supplementary angle of angle α is (180 - 80)/2 = 50 degrees.

Therefore, α = 180 - 50 = 130 degrees.

Classify the segment in each part below.
Only use the information given in the figure.
Do not assume measures are equal unless the markings indicate they are.
If necessary, you may learn what the markings on a figure indicate.

Answers

Answer:

See below

Step-by-step explanation:

(a)

IO is the perpendicular bisector of FH

(b)

ZV is the angle bisector of Z

Check IO bisects the FH at 90°.

So it's a perpendicular bisector of FH

Its altitude

So the options are

Perpendicular bisector.Angle bisectorAltitude

Help math math ASAP

Answers

Answer:

y = 2x - 3

Step-by-step explanation:

y - 9 = 2 ( x - 6 )

y - 9 = 2x - 12

Hi! I can help you with a smile! :)

Perpendicular lines have slopes that are opposite reciprocals.In order to find the opposite reciprocal of a number, flop it over, and change its sign:-1/2-22 (slope of the line that's perpendicular to the given line)Use Point-Slope:y-y1=m(x-x1)y-9=2(x-6)y-9=2x-12y=2x-12+9y=2x-3

Answer:

y=2x-3

Hope it helps!

~Nature~

Enjoy your day!

Three workers are digging a ditch. They take turns working, and every one of them works for as long as it would take the other two to dig half of the ditch. They finished digging the ditch working in this manner. How many times faster would the three workers have finished digging the ditch if they had all been working at the same time?

Answers

The work would be finished 2.25 times faster if they had been doing the work at the same time.

Rate of doing work

Assumption;

Provided each one of the workers works for an hour which is equivalent to the time it takes to finish half of the ditch.

In essence, the total time required to finish the ditch by 2 workers is; 2 hours.

Hence, for 3 workers working simultaneously, the time required is 1hour 20 minutes. = 80 minutes

However, since they took 1 hour turns on the job, it follows that; The total time used is;

Total time = 3 × 1hr = 3 hours = 180 hours

Hence they could have finished the work in;

R = 180/80 times faster = 2.25 times faster.

Answers

Step-by-step explanation:

f'(x)=-2sin(x)+2cos(2x)=0

as cos(2x)=2sin(x)cos(x),

-2sin(x)+4cos(x)sin(x)=0

sin(x)-2cos(x)sin(x)=0

(sin(x))(1-2cos(x))=0

-> x = 0, pi/3

testing these values along with the end points of the interval,

f(0)=2

f(pi/3)=1+(0.5sqrt(3))

f(pi/2)=0

so the min is 0 and the max is 2.

HELPP MEEE WITH MY HOMEWORK PLEASEEEE

Answers

Answer:

Letter a is 6:38 and letter b is 2:17

Hope this helps!

Answer:

A: 6:38 B: 3:17

Explanation:

A: when you count the big dots the small line is 6 so it is 6 o clock and when you look at the big line it it 38 so 38 minutes. The answer is 6:38.

B: when you count the big dots the small line is 3 so it is 3 o clock and when you look at the big line it it 17 so 17 minutes. The answer is 3:17

Hope it helps!

y = 4.45 = 1.4
y=

Please help (ASAP‼️)

Answers

Answer:

y=6.23 hope this Helps!

Step-by-step explanation:

The sum of 75 and 45 is divided by 5 and the difference of quotient and 10 is multiplied by 2. (Ans: 28) (Hint:- Make mathematical expressions, then simplify) (Please solve my question)

Answers

Answer:

Step-by-step explanation:

(((75+45) ÷5) - 10 )2 -> first add 75 and 45

((120 ÷ 5) - 10)2 -> Divide 120 by 5

(24 - 10)2 -> Subtract 24 by 10

(14)2 - > 28

Ans: 28

-2(x + 7) simplified expression, please do it I don't understand it for some reason and I'm gonna fail my test which is 50% of my grade :(

Answers

Answer:

-2 (x+7)

-2x-14

hope it helps you

have a great day :)

Which of the following triangles are possible to draw? halppppp for 25 points

A triangle with angle measures of 100°, 40°, and 45°.
A triangle with angle measures of 55°, 35°, and 80°.
A triangle with angle measures of 30°, 60°, and 90°.
A triangle with angle measures of 25°, 65°, and 90°.
A triangle with angle measures of 20°, 50°, and 105°.

Answers

The triangles which are possible to draw are
angles measures 30° ,60° and 90°
angles measures of 25°, 65° and 90°
The triangles must add up to 180° for it to be drawn

A circle has an area of 12.251 x pi cm^2
Calculate:
a its diameter
b its circumference

Answers

Answer:

A) 3.94

B) 12.40

Step-by-step explanation:

Refer to the work image. You also need the radius to calculate A and B.

Use the figure to solve the inequality

Answers

Answer:

c hope this hrlpe

Step-by-step explanation:

Please help me I really need this

Answers

Answer:

Step-by-step explanation:

8C5 = 56

Answer:

8C5 = 56

Step-by-step explanation:

The formula for nCk is ...

nCk = n!/(k!(n-k)!)

Then the value of 8C5 is ...

8!/(5!(8-5)!) = 8·7·6/(3·2·1) = 8·7

8C5 = 56

_____

Additional comment

The larger of the denominator factorials will cancel most of the factors of the numerator. The remaining denominator factors can be factored from the remaining numerator values to simplify the problem of doing the math by hand. Most graphing calculators and all spreadsheets can compute this function for you.

[tex]\dfrac{8!}{5!\cdot3!}=\dfrac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(5\cdot4\cdot3\cdot2\cdot1)(3\cdot2\cdot1)}=\dfrac{8\cdot7\cdot6}{3\cdot2\cdot1}=\dfrac{8\cdot7\cdot6}{6}=8\cdot7[/tex]

Convert 24 feet to inches.

Answers

Answer:

288 inches

Step-by-step explanation:

24x12 = 288

each foot has 12 inches

Help please I am lost

Answers

The answer is -447

= 9(3).f(3) + 3f' (3).g(3) + 3g' (3).f(3)
= 13x9 + 3x/ - 11 )x13 + 3x/ - 5 )×9
= 117 + ( - 429 ) + (- 135 )
= 117 - 135 - 429
= - 18 - 429
= -447

I hope this helped! Please give brainliest and I hope you like the explanation!

in order for students to have a club at school they need a minimum of 26 students. If there are 19
students signed up for the club, how many more students does the club need?
What are the solutions? Select the correct choice below and fill in the answer box to complete your
choice

Answers

Answer:

7 more students.

Basic subtraction:

needed students: minimum required students - students signed up

needed students: 26 - 19

needed students: 7 students, the club needs.

Solution:

We know that the inequality form is x ≥ 26. If we subtract the number of students required by the number of students joined, we will obtain the required students to start the club.

=> Required students - Students joined = Students remained to join=> 26 - 19 = Students remained to join=> 7 students

Hence, the club needs 7 more students to have a club.

5(x+4) simplify by distribtuion

Answers

= 5x + 20

Because you first multiply 5 with x
=5x
Then you multiple 4 with 5
=20

Answer:

5x + 20

Step-by-step explanation:

5(x+4)

5(x) + 5(4)

5x + 20

Hope this helps!

tori has to place one more x on the line plot for the eighth month then the total length in hours of all the calls for the eighth month will be 6 hours what is the length in hours of tori's phone calls for just eight months.
Talks 1hr month 9
Talks 1 1/2 hrs 10 and. 11th month
Ta;ks. 3/4 hr 12th month

Answers

Line plots are used to express variables using markers

The total phone call for eight months is [tex]10\frac 34[/tex] hours

How to determine the total phone calls

From the line plot, we have the following summation

[tex]Total = 1hr + 1\frac 12 hr * 2 + \frac 34 hr[/tex]

When the total hours of phone call for the 8th month is added, the summation equation becomes

[tex]Total = 1hr + 1\frac 12 hr * 2+ \frac 34 hr + 6 hr[/tex]

Add the expressions

[tex]Total = 10\frac 34[/tex]

Hence, the total phone call for eight months is [tex]10\frac 34[/tex] hours