Use the drop-down menus to identify the GCF of each pair of numbers.

The GCF of 12 and 16 is

The GCF of 15 and 60 is

The GCF of 24 and 30 is

The GCF of 18 and 72 is​

Answer:

Depends on how many spoonfuls they use per sundae. If they use one spoonful they made 32 sundaes, if they use 2 spoonfuls they made 16 sundaes.

Answer:

Step-by-step explanation:

5.

[tex]12,\:30\\\\\mathrm{Prime\:factorization\:of\:}12:\quad 2\times\:2\times\:3\\\mathrm{Prime\:factorization\:of\:}30:\quad 2\times\:3\times\:5\\\\=2\times\:2\times\:3\times\:5\\\\=60[/tex]

6.

[tex]6,\:10\\\\\mathrm{Prime\:factorization\:of\:}6:\quad 2\times\:3\\\mathrm{Prime\:factorization\:of\:}10:\quad 2\times \:5\\\\=2\times \:3\times \:5\\\\=30[/tex]

7.

[tex]16,\:24\\\\\mathrm{Prime\:factorization\:of\:}16:\quad 2\times \:2\times\:2\times\:2\\\mathrm{Prime\:factorization\:of\:}24:\quad 2\times\:2\times\:2\times\:3\\\\=2\times\:2\times\:2\times\:2\times\:3\\\\=48[/tex]

8.

[tex]14,21\\\\\mathrm{Prime\:factorization\:of\:}14:\quad 2\times\:7\\\mathrm{Prime\:factorization\:of\:}21:\quad 3\times\:7\\\\=2\times\:7\times\:3\\\\=42[/tex]

9.

[tex]9,15\\\\\mathrm{Prime\:factorization\:of\:}9:\quad 3\times\:3\\\mathrm{Prime\:factorization\:of\:}15:\quad 3\times\:5\\\\=3\times\:3\times\:5\\\\=45[/tex]

10.

[tex]5,\:11\\\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Prime\:factorization\:of\:}11:\quad 11\\\\=5\times \:11\\\\=55[/tex]

(- 1 - 2√3)²

applicating (a - b)² = a² + b² - 2ab

a = - 1

b = 2√3

so:

(- 1 - 2√3)² =

(- 1)² + (2√3)² - 2(- 1)(2√3) =

1 + (2² * √3²) + 2(2√3) =

1 + (4 * 3) + 4√3

1 + 12 + 4√3 = 13 + 4√3

Answer:

Domain: [-4, 4]

Range: [-3, 5]

Function? No

Step-by-step explanation:

Domain is all x-values that can be inputted in the graph that returns an output.

Range is all y-values that are outputted when x is inputted.

A function has to pass the Vertical Line Test.

[tex]-2x\left(-12\right)=24x[/tex]

Answer:

24x

Step-by-step explanation:

Parenthesis implies multiplication, and when a negative and a negative are multiplied, the answer becomes positive. Adding on the x, the answer to this equation if 24x.

Step-by-step explanation:

Hey there!!

During evaluating the expression, you must follow,

Here,

[tex]i). \: b + {c}^{2} [/tex]

[tex] = 30 + {6}^{2} [/tex]

= 30+36

= 66.

ii). b-4c

= 30 - 4×6

= 30 - 24

= 6

Hope it helps...

Answer: 1.12099824328 or estimated is 1

Answer:

let angle AOB and angle COD be x

the it would be

x+x+110=180

2x+110=180

2x=180-110

2x=70

x=70/2

x=35 degree.

hope it will help you.

Answer:

Snacks are distributed in a school.

There are only 36 apples and 44 bananas for the students, but there are 72 orange juices and 28 tangerine juices. The distribution would be 4/5, it would take 20 fruits so that the snack per student be the same.

Step-by-step explanation:

A fraction is a whole number that expresses a certain number of portions that are taken from a whole divided into parts.

It is represented by a bar that separates the first part (numerator) from the second (denominator).

The numerator represents the number of parts taken and the denominator represents the entire element.

For example, 3 eaten parts of a 4-piece cake.

3/4 of the cake was eaten.

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the value of y when x= 18 we must first find the relationship between them

The statement

y varies directly as x is written as

[tex]y \: \: \alpha \: \: kx[/tex]

where k is the constant of proportionality

when y = 37

x = 5

Substitute the values into the above formula and solve for k

That's

37 = 5k

Divide both sides by 5

So the formula for the variation is

When x = 18

y = 7.4(18)

We have the answer as

Hope this helps you

Answer:

Hey there!

-6-(-12)

-6+12

6

Hope this helps :)

Answer:

[tex]6[/tex]

Step-by-step explanation:

[tex]-6-(-12)[/tex]

[tex]-6+12[/tex]

Since 12 - 6 is equal to 6, -6 + 12 would be 6.

[tex]=6[/tex]

Now you have your answer!

Hope this helps!

Answer:

14 is 4

15 is check your self

in Google

Answer:

-5

Step-by-step explanation:

-3 - 2 = -5

Answer:

1144.18 e-12 chips

Step-by-step explanation:

Conversation rate of nanometers

1 nanometers =1* 10^-12 km

35 nanometers= 35 *10^-12

Radius of earth= 6371 km

Circumference of earth = 2πr

Circumference= 2*22/7*6371

Circumference=40046.29 km

The number of chips to be used to circle the earth

= 40046.29/35 *10^-12

=1144.18 *10^-12

= 1144.18 e-12 chips

Answer:

[tex]\boxed{\bold 4.651 \times {10}^{5}}}[/tex]

Step-by-step explanation:

[tex]400000 + 60000 + 5000 + 100 \\ = 465100[/tex]

Now write it in standard form.

[tex]465100 \\ = 4.651 \times {10}^{5} [/tex]

hope this helps you.

will give the brainliest!

follow~Hi1315~

Answer:

142

Step-by-step explanation:

Step-by-step explanation:

70 - -72

= 70+ 72

= 142

I think this should be the answer

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected number of outcome/Total outcome

Since a pair of die with six faces is rolled, the total number of outcome will be 6^2 = 36

Expected outcome is the sum of dice greater than 10. The only time we can get a sum of the dice grater than 10 is when the following are rolled; (5,6), (6, 5) and (6, 6). The sum of the numbers will give us 11 ans 12 respectively which are values greater than 10.

The expected outcomes = 3 outcomes

The probability that the sum of my dice is greater than 10 = 3/36

Hence the probability that the sum of my dice is greater than 10 is 1/12

Answer:

14 [tex]\frac{5}{48}[/tex]

Step-by-step explanation:

rectangular volume = length * height * width

1354 = (20+4) * 4 * width

1354 = 24 * 4 *w

1354 = 96w

14.1 = w

Answer:

10

Step-by-step explanation:

Solving $4x=3y$ for $x$ gives $x = \frac{3}{4}y$. Substituting this into the desired expression gives\begin{align*}\frac{2x+y}{3x-2y} &= \frac{2\left(\frac34\right)y + y}{3\left(\frac34y\right) - 2y}\\

&=

\frac{\frac32y + y}{\frac94y - 2y} = \frac{\frac52y}{\frac{y}{4}} \\

&=\frac{5}{2}\cdot 4 = \boxed{10}.\end{align*}

Answer:

10

Step-by-step explanation:

Substitution and simplification

Answer:

R (t) = 60 - 60 cos (6t)

Step-by-step explanation:

Given that:

R(t) = acos (bt) + d

at t= 0

R(0) = 0

0 = acos (0) + d

a + d = 0 ----- (1)

After [tex]\dfrac{\pi}{12}[/tex] seconds it reaches a height of 60 cm from the ground.

i.e

[tex]R ( \dfrac{\pi}{12}) = 60[/tex]

[tex]60 = acos (\dfrac{b \pi}{12}) +d --- (2)[/tex]

Recall from the question that:

At t = 0, R(0) = 0 which is the minimum

as such it is only  when a is  negative can acos (bt ) + d can get to minimum at t= 0

Similarly; 60 × 2 = maximum

R'(t) = -ab sin (bt) =0

bt = k π

here;

k  is the integer

making t the subject of the formula, we have:

[tex]t = \dfrac{k \pi}{b}[/tex]

replacing the derived equation of k into R(t) = acos (bt) + d

[tex]R (\dfrac{k \pi}{b}) = d+a cos (k \pi)[/tex] [tex]= \left \{ {{a+d \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.[/tex]

Since we known a < 0 (negative)

then d-a will be maximum

d-a = 60  × 2

d-a = 120 ----- (3)

Relating to equation (1) and (3)

a = -60 and d = 60

∴ R(t) = 60 - 60 cos (bt)

Similarly;

For [tex]R ( \dfrac{\pi}{12})[/tex]

[tex]R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60[/tex]

where ;

[tex]cos (\dfrac{\pi b}{12}) =0[/tex]

Then b = 6

∴

R (t) = 60 - 60 cos (6t)

Answer:

x = ± sqrt(k)

x = ± 8 by the square root property

Step-by-step explanation:

x^2 = k

K is a real number

Take the square root of each side

sqrt(x^2) = ± sqrt(k)

x = ± sqrt(k)

Letting k = 64

x = ± sqrt(64)

x = ± 8 by the square root property

Answer:

x = ± √k

x = ± √8 by the square root property

Step-by-step explanation:

x² = k

where k is a real number

square root of each side

√x² = ± √k

x = ± √k

let k = 64

x = ± √64

therefore

x = ± 8 by the square root property

Answer:

[tex]8n[/tex]

Step-by-step explanation:

The answer would be [tex]8n[/tex] because [tex]8*n[/tex] = [tex]8n[/tex]

Answer:

[tex]42\pi -78[/tex]

Step-by-step explanation:

Attached below is the detailed solution of the volume of the solid in the first octant bounded by the cylinders r = 2 r = 5  z = 8-x-y

The volume of the solid in the first octant bounded by the cylinders r = 2 r = 5,  z = 8-x-y  : [tex]42\pi -78[/tex]

Answer:

I think it's     (16/81)

Step-by-step explanation:

Answer:

the sum would be located 2 notches to the right from 0.

Step-by-step explanation:

since the notches are already split up into 5, you just count 2 notches to the left (since its negative) and then count 4 notches to the right and then you land on your sum :) btw I like your profile picture

Answer:

x + 13

Step-by-step explanation:

5x + 2(3 - 2x) +7

Distribute the 2 into (3 - 2x)

5x + 6 - 4x + 7

Combine like terms

x + 13

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.

The given expression 5x+2(3−2x)+7 can be simplified as shown below.

5x + 2(3−2x) + 7

Open the parenthesis,

= 5x + 6 − 4x + 7

Bring the like terms together,

= 5x − 4x + 7 + 6

Add the like terms,

= x + 13

Hence, The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.

Learn more about PEMDAS here:

https://brainly.com/question/36185

#SPJ2