Answer:
x = -3 + 2 i or x = -3 - 2 i
Step-by-step explanation:
Solve for x:
x^2 + 6 x + 13 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 13 from both sides:
x^2 + 6 x = -13
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 9 to both sides:
x^2 + 6 x + 9 = -4
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x + 3)^2 = -4
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x + 3 = 2 i or x + 3 = -2 i
Hint: | Look at the first equation: Solve for x.
Subtract 3 from both sides:
x = -3 + 2 i or x + 3 = -2 i
Hint: | Look at the second equation: Solve for x.
Subtract 3 from both sides:
Answer: x = -3 + 2 i or x = -3 - 2 i
Three rational numbers between
1/3 and 1/5 are 4/15, 3/10, and 7/30
Given:The two numbers are 1/3 and 1/5
To find:The rational number between two numbers
Solution:Now, to find the rational number, add the numbers and divide their sum by 2.
(i) First rational number between
1/3, 1/5 = 1/3+1/5=8/5
Divide 18/5 by 2------> 8/15 x 1/2= 8/30= 4/15
The series becomes, 1/3, 4/15, 1/5
(ii) Second rational number
= 4/15+1/5 = 7/15
Divide
7/15 by 2 ------> 7/15 x 1/2 = 7/30
Hope this helps!
Basic amount that Edgar Anderson earns per week = $300
Sales of Mr. Anderson for one week = $2500
Percentage of commission on sales above $1000 = 15%
Then
Amount of commission
earned for the week = [2500 - 1000] * (15/100) dollars
= 1500 * (15/100) dollars
= 15 * 15 dollars
= 225 dollars
Then
Gross pay of Edgar Anderson for the week = (300 + 225) dollars
= 525 dollars
So the gross pay of Edgar Anderson for the week is $525.
Option D: The distance between the two points is 13 units
Explanation:
It is given that the two points are 
and 
We need to determine the distance between the two points.
It is also given that the distance between the two points can be determined using the formula,
Substituting the points and for the coordinates 
and 
Thus, we get,
Simplifying, we have,
Adding the terms, we get,
Squaring the terms, we have,
Adding the terms, we get,
Simplifying and rounding off the value to the nearest tenth, we have,
Hence, the distance between the two points is 13 units.
Therefore, Option D is the correct answer.
Answer:
B. 
Step-by-step explanation:
Let l represent length of rectangle and w represent width of rectangle.
We have been given four formulas for the perimeter of rectangle. We are asked to choose the formula that displays a common student error for finding the perimeter.
We know that perimeter of a polygon is sum of all sides of the polygon. We also know that rectangle is polygon having two sets of equal sides.
The perimeter, P, of rectangle will be sum of its all sides that is:
Combine like terms:
Factor out 2:
Upon looking at our given choices, we can see that formula represented by option B displays a common student error for finding the perimeter.
