What is the value of x in the equation? 7 1 2 x + 3 2 3 = −13 a) −1 5 6 b) −2 1 6 c) −2 2 9 d) −2 5 9

C - 2 2/9

Step-by-step explanation:

7 1 /2 x + 3 2/ 3 = −13

Subtract 3 2/3 from each side

7 1 /2 x + 3 2/ 3 - 3 2/3 = −13 - 3 2/3

7 1/2x = -16 2/3

Change each mixed number to an improper fraction

7 1/2 = (2*7 +1)/2 = 15/2

16 2/3 = (3*16+2)/3 = 50/3

15/2 x = -50/3

Multiply each side by 2/15 to isolate x

2/15 * 15/2 x = -50/3 * 2/15

x = -100/45

Simplify

x = -20/9

Change back to a mixed number

9 goes into 20 2 times with 2 left over

x = -2 2/9

d

step-by-step explanation:

i used the pitagoras theoreme

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.