Two solutions were found :
1. x=4
2. x= -4
Step by step solution: Step 1 :
Equation at the end of step 1 :
(((x3) + 22x2) - 16x) - 64 = 0
Equation at the end of step 1 :
(((x3) + 22x2) - 16x) - 64 = 0 :
Step 2 :
Checking for a perfect cube :
2.1 x3+4x2-16x-64 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3+4x2-16x-64
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3+4x2
Group 2: -16x-64
Pull out from each group separately :
Group 1: (x+4) • (x2)
Group 2: (x+4) • (-16)
-------------------
Add up the two groups :
(x+4) • (x2-16)
Which is the desired factorization
Trying to factor as a Difference of Squares :
2.3 Factoring: x2-16
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (x + 4) • (x - 4)
Multiplying Exponential Expressions :
2.4 Multiply (x + 4) by (x + 4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+4) and the exponents are :
1 , as (x+4) is the same number as (x+4)1
and 1 , as (x+4) is the same number as (x+4)1
The product is therefore, (x+4)(1+1) = (x+4)2
Equation at the end of step 2 :
(x + 4)2 • (x - 4) = 0
Step 3 :
Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
3.2 Solve : (x+4)2 = 0
(x+4) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation :
3.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
Two solutions were found :
x = 4
x = -4
(Sorry the question is too long, but I hope you understand the question)
Answer:
90
Step-by-step explanation:
The total number of "ratio units" is 9+6 = 15, so each one must stand for 225/15 = 15 people. Then 6·15 = 90 people were snowboarders who bought season passes.
The answer you are looking for could either be 16 or 40. To solve the equation, you would follow the steps of PEMDAS. Since the 2 above the equation is an exponent, you'd first solve there.
Fill in "a" and "b", the equation will now say 2^2 * 3 + 4 = ?. Assuming that the exponent is meant to go with the 2 alone, 2 * 2 = 4. This leaves the equation to say 4 * 3 + 4 = ? Multiply 3 and 4 to get 12, then add 4 to get 16.
OR
Fill in "a" and "b". This time, we're assuming that the exponent is going with 2 * 3 (originally 2a). Multiply 2 and 3 to get 6, then square 6 to get 36. Finally, add 4 to 36 to get 40.
I'm not quite sure where the exponent was meant to go, but I hope this helps!
