Zach Casper's DEV Project

Problem 1

Step 1: Set the equation equal to "y"

Step 2: Substitute "y" for "x", set the equation equal to "x"

Step 3: Times both sides of the equation by 33y+4

Step 4: Subtract 33xy+4 to both side. While adding 9 to both sides as well

Step 5: Factor out the "y" to make 32-33x and divide it to both sides

Final answer should be y=4x+9 / -33x+32

Problem 2

Step 1: take x^6 and divide it by x to get x^5

Distribute x^5 to x+5 

Subtract x^6+5x^5 by itself

Drop down -10x^4-50x^3

Step 2: divide -10x^4 by x to get -10x^3

Distribute -10x^3 to x+5

Subtract -10x^4-50x^3 by itself

Drop down -50x^2-275x

Step 3: divide -50x^2 by x to get -50x

Distribute -50x to x+5

Subtract -50x^2-275x by -50x^2-250x

Drop down -25x-125

Step 4: divide -25x by x to get -25

Distribute -25 to x+5

Subtract -25x-125 by itself

Drop down 0

The final answer will be x^5-10x^3-50x-25

Problem 3

Step 1: subtract 10 by both sides

Step 2: factor out 3 of the equation

Divide -3 by 2 and square it

Step 3: multiply 9/4 by 3 to get 27/4 and add that to -10

Step 4: add -13/4 to both sides

Final equation will be f(x)= 3(x-3/2)^2+13/4

The domain is all real numbers 

The range is [13/4, infinity)

The vertex is (3/2, 13/4)

Problem 4

Step 1: Put the numbers that corespond with each letter

Step 2: simplify the equation

Step 3: divide 6x by 18x and divide 12 by 12

Step 4: distribute 9x to 1/3x+1

Step 5: factor out the 3 and divide the "b" value by 2 and square it to get 9/4

Step 6: multiply 9/4 by 3 and add that to the other side of the equation

Step 7: subtract 27/4 from both sides

The final equation will be 3(x+3/2)^2-27/4

The Domain will be all real numbers

The Range is [-27/4, infinity) 

The Vertex will be (-3/2, -27/4)