Solving Expressions - Algebra 2

We can express each plant's growth as a function of years in the following equations:

Rose height after x years =

Tulip height after x years =

Since we are looking for the year when the two plants are of equal height, we set these expressions for height equal to each other, and solve for x:

Combining like terms by subtracting 2x from both sides and subtracting 5 from both sides gives us:

The plants will reach the same height after 6 years of growth.

First, you substitute for :

Next, use PEMDAS (Parentheses, Exponents, Multiplication, Dividion, Addition, and Subtraction) to preform the algebraic operations in the correct order. When we apply this rule to simplify we get the following:

First, substitute 2 for z:.

Then, simplify: .

Next, you must isolate y by moving all other numbers and variables to the other side of the equation: , which gives you .

And simplify: .

Here, we then take the square root of both sides: .

Simplfy: , because both and .

First, substitute 1 for z, 2 for x and 3 for y: and simplify: .

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction), we simplify the multiplication: .

Then add and subtract from left to right: .

After you plug in all of your given values the expression is as followed;

Since the numerator is zero, therefore, the entire fraction equals zero.

When you plug in your given values the expression should read as followed;

First, you subsitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, you substitute for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for , for , and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for , for , and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for , for , and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,