A display has 666 packs of marbles with a total mass of 629\,\text{g}629g629, start text, g, end text. The packaging of each pack has a mass of \dfrac{2}{3}\,\text{g} 3
2

gstart fraction, 2, divided by, 3, end fraction, start text, g, end text and each marble has a mass of 4\dfrac{1}{2}\,\text{g}4
2
1

g4, start fraction, 1, divided by, 2, end fraction, start text, g, end text.
Which equation can we use to determine mmm, the number of marbles per pack?
Choose 1
Choose 1

(Choice A)
A
6\cdot 4\dfrac{1}{2}m+\dfrac{2}{3}=6296⋅4
2
1

m+
3
2

=6296, dot, 4, start fraction, 1, divided by, 2, end fraction, m, plus, start fraction, 2, divided by, 3, end fraction, equals, 629

(Choice B)
B
6m\left(4\dfrac{1}{2}+\dfrac{2}{3}\ right)=6296m(4
2
1

+
3
2

)=6296, m, left parenthesis, 4, start fraction, 1, divided by, 2, end fraction, plus, start fraction, 2, divided by, 3, end fraction, right parenthesis, equals, 629

(Choice C)
C
6m+4\dfrac{1}{2}+\dfrac{2}{3}=6296m +4
2
1

+
3
2

=6296, m, plus, 4, start fraction, 1, divided by, 2, end fraction, plus, start fraction, 2, divided by, 3, end fraction, equals, 629

(Choice D)
D
6\left(4\dfrac{1}{2}m+\dfrac{2}{3}\ right)=6296(4
2
1

m+
3
2

)=629

45

step-by-step explanation:

to find a percentage, add a decimal in front and multiply it by the other number.

.25 times 180= 45

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6

answer: none of these answers are correct only the second half is

step-by-step explanation:

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.