4. Find the sum of (0.75x - 12y) and (-5 + 6y - 0.5x)

Show each step of your work.

5. Which expression(s) is/are equivalent to 8-2(5x-3). Show your work to justify your decision.

a. 6(5x-3)

b. 8-10x+6

c. 8-(10x-6)

d. 8-10x-6

e. -10x+14

6. In math class, students are attempting to simplify the expression written on the board: 7 - 2 (3 - 8x)

Three students make an attempt at a first step:

Len writes: 5 (3 - 8x)

Monty writes: 7 - 2 (-5x)

Nailany writes: 7 - 6 - 16x

Do you agree with any of the students? Explain your reasoning for each one.

yo i only got number 4 for you but here it goes: 0.70x+18y-5

Step-by-step explanation:

(0.75x  -  12y) + (-5  +  6y  -  0.5x)

regroup to the variables : (0.70x-0.5x) + (12y+ 6y-5)

put it together: (0.70x)+(18y-5)

you cant add unlike terms so you remove the parenthesies and your done.

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.

soo this can be solve by using the formula:

f = p( 1 + i)^ n

where f is the future profit

p is the initial profit

i is the percent increase

n is the number of years

a . f = 30000 ( 1.05)^n

b. f = 30000 ( 1.05)^15

f = $62,368