'justify your answer using complete sentences' means re-write your answer in a complete sentence. In other words, say your answer in a full and clear sentence.
Answer:
x = - 5, x = - 3
Step-by-step explanation:
Given
x² + 15 = - 8x ( add 8x to both sides )
x² + 8x + 15 = 0 ← in standard form
Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)
The factors are 5 and 3, since
5 × 3 = 15 and 5 + 3= 8, thus
(x + 5)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 3 = 0 ⇒ x = - 3
Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft.
Area of rectangle will be:
A=length*width
A=x(50-x)
A=50x-x^2
at maximum area, dA/dx=0
thus
dA/dx=50-2x=0
solving for x we get
2x=50
x=25
thus for maximum area length=25 ft
the size of the width will be
50-x=50-25=25 ft
thus the maximum area will be:
25*25=625 sq. feet
The formal name for the property
of equality that
allows one to add the same quantity to both sides
of an equation.
This is one
of the most commonly used properties for solving equations.
The formula tells us that if a = b, then a + c = b + c. The letters a and b stand for two separate numbers, our two twins, and the letter c
stands for what we give to each twin to keep them matching. So, for
example, if we add 1 to the left side of the equation, we must also add 1
to the right side of the equation. By doing this, we keep the equation,
the twins, the same.
Answer: correct choice is B.
