Mean=21.5 (addition of all numbers, divided by total number=129/6)
Median=22.5 (middle number, since there are two add them both and divide)
Mode=24 (most occurring number)
If I understand the second part of the question you would have #3 as your choice.
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:
Lixins monthly sales = $18,000
Step-by-step explanation:
Let x be the total sales.
Given:
Basic salary = $500
Commission on sales = 4% = 0.04
Monthly income = $1220
We need to find her sales for the month.
Solution:
First we write the equation for given situation:
Therefore, Lixins monthly sales are $18,000.
A rectangular backyard garden has a width that is 4 feet wider that its length
let the Length of the garden is 'l'
Width is 4 more than the length so width is l + 4
Area of rectangle = length * width
= l * (l+4)
= 
Degree is the exponent so the area of the garden has a degree of 2
Answer is 2
Answer:
7
Step-by-step explanation:
