Solve 7/8c-3(1/8c-7)=-6

c = -54

Step-by-step explanation:

Solve for c:

(7 c)/8 - 3 (c/8 - 7) = -6

Put each term in c/8 - 7 over the common denominator 8: c/8 - 7 = c/8 - 56/8:

(7 c)/8 - 3 c/8 - 56/8 = -6

c/8 - 56/8 = (c - 56)/8:

(7 c)/8 - 3(c - 56)/8 = -6

(7 c)/8 - (3 (c - 56))/8 = (7 c - 3 (c - 56))/8:

(7 c - 3 (c - 56))/8 = -6

-3 (c - 56) = 168 - 3 c:

(7 c + 168 - 3 c)/8 = -6

7 c - 3 c = 4 c:

(4 c + 168)/8 = -6

Multiply both sides of (4 c + 168)/8 = -6 by 8:

(8 (4 c + 168))/8 = -6×8

(8 (4 c + 168))/8 = 8/8×(4 c + 168) = 4 c + 168:

4 c + 168 = -6×8

8 (-6) = -48:

4 c + 168 = -48

Subtract 168 from both sides:

4 c + (168 - 168) = -168 - 48

168 - 168 = 0:

4 c = -168 - 48

-168 - 48 = -216:

4 c = -216

Divide both sides of 4 c = -216 by 4:

(4 c)/4 = (-216)/4

4/4 = 1:

c = (-216)/4

The gcd of -216 and 4 is 4, so (-216)/4 = (4 (-54))/(4×1) = 4/4×-54 = -54:

c = -54

2

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.