Directions: Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
In class, pairs of students were given numbers to work with. In each pair, one student found the greatest common factor and the
other student found the least common multiple.
Jess and Nate were given the numbers 8 and 12.
• Jess found that the greatest common factor is 4.
• Nate found that the least common multiple is 48.
One of these students made a mistake.
Which student made a mistake?
What number should the student have found instead?

Answers

Answer 1

Answer:

Nate made a mistake. The LCM is actually 24.

Step-by-step explanation:

So, Jess found the GCF of 8 and 12 is 4. Let's make sure first.

Method 1: List the factors of 8 and 12.

8: 1, 2, 4, 8

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

Method 2: Or find the prime factorization of 8 and 12

8: 2 * 2 * 2

12: 2 * 2 * 3

Both 8 and 12 share 2 2's.

Multiply 2 by 2 to get 4 as the GCF

4 is the greatest factor 8 and 12 share, so Jess is correct.

Nate found the LCM of 8 and 12 is 48. Let's make sure that's correct.

Method 1: List the multiples of 8 and 12.

8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

24 is the smallest number 8 and 12 have in common.

Method 2: Union of Primes

8: 2 * 2 * 2

12 : 2 * 2 * 3

Create a union of these primes.

Union: 2 * 2 * 2 * 3

4 * 2 * 3

8 * 3

24 = LCM

The LCM of 8 and 12 is 24, not 48, so Nate is incorrect. Thus, Nate made the mistake.


Related Questions

Maggie has 3 quarters, Elizabeth has 5 quarters, and Johnny has 7 quarters. If q represents $0.25, which of the following expressions represents how much money they have altogether?
15q
12q
0.25q
16q

Answers

Answer:

3 + 5 + 7 = 15

they have 15 quarters altogether so answer is 15q

6(-2x - 1) = -(13x+2) solve for x

Answers

Answer:

10

Step-by-step explanation:

-12x-12 = -13x-2

x= 10

Answer:

x=4

Step-by-step explanation:

-12x-6=-13x-2

+12x

-6=-x-2

+2

-4=-x/-1

x=4

4 (x-2) + 2 ( x + 1 )

Answers

Answer:

6−6 :)

Step-by-step explanation:

Can someone help its worth ✨15 points✨

Answers

Answer:

L is 132

3168 people voted for J

Step-by-step explanation:

tire rim has a diameter of 15 in. What is the circumference of the tire rim? Use 3.14 for Pi.
23.55 in.
46.10 in.
47.1 in.
94.2 in.

Answers

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Given}}} : [/tex]

Diameter ( d ) = 15 in Pi ( π ) = 3.14

[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

Circumference ( C )

[tex] \underline{ \underline{ \text{Solution}} }: [/tex]

[tex] \boxed{ \sf{Circumference \: of \: a \: circle ( C ) = \pi \: d}}[/tex]

⇢ [tex] \sf{3.14 \times 15}[/tex]

⇢ [tex] \sf{47.1 \: in.}[/tex]

[tex] \red{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \underline{ \tt{47.1 \: in.}}}}}}}[/tex]

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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Kayla wants to purchase some candy. All varieties of candy are $2.50. Kayla buys strawberry and mango candy. Write an expression that represents the total cost.



Plz help me

Answers

Answer:

2.50s + 2.50m

Step-by-step explanation:

s stands for strawberry

m stands for mango candy

each candy costs 2.50

hope this helps a bit!!!

If the bearing from A to B is 034 what is the beating from B to A?

Answers

Step-by-step explanation:

This is called a back bearing

when the given angle is less than 180, then the back bearing is= the given angle + 180

34+180=214°

The sum of 7.2 and a number is 10.
First, write an equation to describe the situation.
7.2 + 3 = 10
What is the number?
The number is

Answers

Answer:

7.2 + x = 10

Step-by-step explanation:

I did 7.2 + x = 10 Because there was suspose to be a number in between

that we do not know so you have to put 7.2 + x = 10

Then... For the next question (The same question but asking the number in between) The second Question you do 7.2 - 10 and you get 2.8

The equation to describe the situation when the  sum of 7.2 and a number is 10 is given so it is 7.2 + x = 10.

Calculation of an equation:

Since

The sum of 7.2 and a number is 10.

So here we assume the number be x

So,

7.2 + x = 10

x = 2.8

hence, The equation to describe the situation when the  sum of 7.2 and a number is 10 is given so it is 7.2 + x = 10.

Learn more about number here: https://brainly.com/question/15546484

Find the distance between the points A(10,-9) and B(8,7) round your answer to the nearest hundredth

Answers

Answer:

16.12 units

Step-by-step explanation:

These two points create a right triangle whose diagonal (hypotenuse) represents the desired distance.

Going from B(8, 7) to A(10, -9) involves two steps:  Moving 2 units to the right from B(8, 7) to A(10, -9), and moving 16 steps down from B(8, 7) to A(10, -9).

Thus, the horizontal side of the triangle in question has length 2 units and the vertical side 16 units.

The length of the diagonal (which is the desired distance) is then

|AB| = +√(2^2 + 16^2) = +√(4 + 256) = +√260

To the nearest hundredth, this is |AB| = 16.12 units

help please :) i'll mark brainliest!

Answers

Answer:

Everything except the 3rd one!

Step-by-step explanation:

8. Alex is buying a pair of new Nikes. Champs decided to apply a markdown of 35%. He found a coupon online for an additional 10% discount. What is the final cost after the markdown and then coupon is applied if the Nikes original cost is $130?

Answers

Answer:

175

Step-by-step explanation:

What is the constant of proportionality between y and x in the graph?

Answers

Answer:

y=3x

Step-by-step explanation:

y=kx, where k is constant

3y, 1x...so 3y = 1x

check: looking at the graph at 4.5y, 1.5x where y and x intersect...

4.5=3(1.5)

3 x 1.5 = 4.5

Simplify the ratio 20:50:100

Answers

Answer:

2:5:10

Step-by-step explanation:

how should i draw a)
please help its due soon :((

Answers

Answer:

I listed the coordinates below. Just place them on a graph and draw a line connecting the points.

Step-by-step explanation:

(-1,-8)

(0,-4)

(1,0)

(2,4)

(3,8)

Classify each triangle by its angle and by it sides

Answers

Answer:

right angles

Step-by-step explanation:

Work out the following and put them in there simplest form

[tex]\frac{3}{11}[/tex] ÷ [tex]\frac{3}{11}[/tex]

Answers

Answer:

1

Step-by-step explanation:

using the reciprocal rule

3/11÷3/11

thats the same as

3/11×11/3

3×11=33

11×3=33

33÷33=1

Solve with Quadratics

Answers

Answer:

x = 1 ± [tex]\sqrt{6}[/tex]

Step-by-step explanation:

Given

2x² - 4x = 10 ( divide through by 2 )

x² - 2x = 5

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 1)x + 1 = 5 + 1

(x - 1)² = 6 ( take the square root of both sides )

x - 1 = ± [tex]\sqrt{6}[/tex] ( add 1 to both sides )

x = 1 ± [tex]\sqrt{6}[/tex] ← exact solutions

Answer:

[tex]x \pm\sqrt6 +1[/tex]

Step-by-step explanation:

Hello!

Standard form of a quadratic: ax² + bx + c

Solve:

2x² - 4x = 102x² - 4x - 10 = 02(x² - 2x - 5) = 0x² - 2x - 5 = 0

Now, complete the square:

Take the b-value in our equation (-2)Divide it by 2 (-1)Square it (1)

Add and subtract that in our equation:

x² - 2x - 5 = 0x² - 2x + 1 - 5 - 1 = 0

Factor the perfect square trinomial:

(x - 1)² - 6 = 0(x - 1)² = 6[tex]\sqrt{(x-1)^2} = \sqrt{6}[/tex]x - 1 = ±√6x = ±√6 + 1

The solutions are [tex]x \pm\sqrt6 +1[/tex]

Please someone help me

Answers

pretty sure is 44km. At least i think so

-A triangle has sides with the measure of 11m, 11m, and 25m. State if this is a triangle
or not.
is it a triangle?

Answers

Answer:

Nope

Step-by-step explanation:

According to the Triangle Inequality Theorem, any 2 sides of the triangle must always be more than the third. Here, we can see that the theorem is violated because 11 + 11 < 25. Therefore, it is not a legitimate Triangle.

Your friend really wants to buy the newest coolest cell phone which will cost him $310 he gets a job detailing cars and suvs and plans to save all the money he earns if he gets paid $60 to detail a car and $85 to detail an suv which of the following inequalities can be used to determine how many of each he must detail in order to earn at least $310

Answers

Answer:

[tex]60c + 85s \geqslant 310[/tex]

Step-by-step explanation:

He needs to earn at least $310 so $60 per car is 60c and $85 per SUV is 85s. So the answer is the third option.

The required inequality:

60x + 85y >= 310

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, a person gets paid $60 to detail a car and $85 to detail an SUV.

Let's assume he needs to detail x number of cars and y number of SUVs to earn at least $310.

Then, the amount earned by detailing x cars and y SUVs can be expressed as:

60x + 85y

According to the problem statement, he wants to earn at least $310, so we can write the inequality:

60x + 85y >= 310

This is the required inequality to determine the number of cars and SUVs he needs to detail in order to earn at least $310.

Learn more about inequalities here:

https://brainly.com/question/30231190

#SPJ5

Jenny's frog made one jump of 2.34 meters. Christina's frog made jumps of 1.22 meters and 0.89 meters.

How much further did Jenny's frog jump in one jump than Christina's frog in two jumps combined?

Answers

Answer:

0.23

Step-by-step explanation:

The perimeter of a rectangular pool is 48 feet. Its length is 4 feet
more than its width.
Let the width of the pool be represented by x.
Which equation below can be used to describe the situation?
A x(x + 4) = 48
B 2x + 2(x + 4) = 48
С2x + 2x + 4 = 48
D 2x(x + 4) = 48

Answers

Answer:

B

Step-by-step explanation:

let's represent the width with x, if we represent the width with x then that makes the length x+4. Therefore the perimeter would be 2x+2(x+4)=48

Check
Match the fraction with the equivalent decimal or percentage.
3/20
38%
19/50
0.37
1/3
15%
37/100
33.3%
1/4
25%
Intro
Done

Answers

Answer:

See below

Step-by-step explanation:

Fraction Decimal

3/20. 15%

19/50. 38%

1/3. 33%

37/100. 37%

1/4. 25%

Answer:

3/20. 15%

19/50. 38%

1/3. 33%

37/100. 37%

1/4. 25%

Step-by-step explanation:

edge 2021

5w = -75
it’s for my math homework

Answers

Answer:

w=-15

Step-by-step explanation:

desmos graphing calculator. Just switch the w for x

Find the zero of the function:
y= 11x^2+25x-24

Answers

X=8/11,-3 is the answer to your question.

2. i. Mr. h. wants to save $80,000 for his son to go to
Stanford. How much money at 5% interest does he need
to invest if he has 10 years (compounded monthly)?
ii. How much money per month would he have to invest to
reach the same goal?

Answers

Step-by-step explanation:

$80,000×5×10/100= 40,000

 which ordered pairs match the table ? X 0,1, 2,1,3 Y 2,2,3,4,1

Answers

The answer have to be (A)

Write a system of equations
given the below information
then determine when their
companies will charge the same
amount. Bethany's company
charges a signup fee of $50 and
then $5 a month. Kami's
company doesn't charge a fee
but charges $10 a month.
Total Charge
28882383882
30
20
10
0

Answers

9514 1404 393

Answer:

y = 5x +50y = 10x10 months

Step-by-step explanation:

The equation for the charge (y) by Bethany's company for x months is ...

  y = 5x +50

The equation for the charge (y) by Kami's company for x months is ...

  y = 10x

The charges are equal when ...

  y = y

  5x +50 = 10x . . . . use the expressions for y

  50 = 5x . . . . . . . . subtract 5x

  10 = x . . . . . . . . . . divide by 5

The companies will charge the same for 10 months.

Pls this is my last question !!

Answers

Answer:

the 1st 2nd and last one

Step-by-step explanation:

Answer:

The first one, the third and the fourth one.

Will Mark Brainliest!!!

Please help! Thank you!!

What is the turning point of the graph of

f(x)=|x+2|−3?

A)(3, −2)

B)(−2, −3)

C)(−3, −2)

D)(−2, 3)

Answers

answer should be b hope it helps

Answer:

I'm pretty sure it's B -2 -3 :))))

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