Answer:The solutions are:x = -5
x = -6
Explanation:To get the solution, we can either use a graphical method or an algebraic method.
1- graphical method:The solution of the equation would be the values of the x-intercept.
Graphing the equation (check attached image), we would find that the solutions are: -6 and -5
2- algebraic method:The general formula of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
x² + 11x + 30 = 0
By comparison:
a = 1
b = 11
c = 30
To get the roots, we will substitute in the quadratic formula (attached in the images)
Doing this, we will find that:
either x =

= -5
or x =

= -6
Hope this helps :)
Answer:
Step-by-step explanation:
Area of rectangle = Length × Width
The given rectangle has a length if x meters
The width of the triangle is (x-3) meters
The area of the rectangle is given as 10 square meters.
Area if rectangle = x(x-3) = 10
Multiplying each term in the parentheses,
x^2 -3x = 10
x^2 -3x -10 = 0
This is a quadratic equation
We will look for two numbers such that when they are multiplied, it will give us -10x^2 and when they are added, it will give -3x. It becomes
x^2 + 2x - 5x -10 = 0
x(x+2)-5(x+2) =0
( x + 2)(x-5) = 0
x = -2 or x = 5
The length of the rectangle cannot be negative so the length is 5 meters
Widith = x+3 = 5-3 = 2 meters
420 miles/ 12 gallons= 35 miles per gallon
Final answer: 35 miles per gallon
35 divided by 12 is 2
So D is the answer
Answer:
10 + 6C
Step-by-step explanation:
C = the number of CDs Alyssa has
Alyssa has C CDs
Fran has five more than three times as many CDs as Alyssa.
Fran has 5 + (3 * C)
Fran has (5 + 3C) CDs
Jessica has twice as many CDs as Fran
Jessica has 2 * (5 + 3C) CDs
Jessica has 10 + 6C CDs