Answer:
1. x = ±9
2. 
3. 12 and -12.
4. Antoine is incorrect. There exists two solutions x=5 and x= -5.
Step-by-step explanation:
According to the questions,
Problem 1. 
i.e. 
i.e. x = ±9.
Problem 2. 
i.e. 
i.e. 
i.e.
Problem 3. [tex]f(x)=x^{2}-144[tex]
To find the roots, we take, [tex]x^{2}-144=0[tex] i.e. [tex]x^{2}=144[tex] i.e. x = ±12.
Thus, the options are 12 and -12.
Problem 4. We have [tex]f(x)=x^{2}+25[tex]
For the roots, we take, [tex]x^{2}+25=0[tex] i.e. [tex]x^{2}=25[tex] i.e. x = ±5.
Thus, Antoine is not correct and two solutions namely x=5 and x= -5 exists.
Answer:Tanya drives 11.4 miles farther.
Step-by-step explanation:
3.9+7.5=11.4 miles
Part A:
The first step of completing the square is writing the expression
as
which expands to
.
We have the first two terms exactly the same with the function we start with:
and
but we need to add/subtract from the last term, 49, to obtain 41.
So the second step is to subtract -8 from the expression
The function in completing the square form is
Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function
can either make U-shape or ∩-shape depends on the value of the constant
that goes with
. When
is (+), the curve is U-shape. When
(-), the curve is ∩-shape
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is
This function is shown in the diagram below
Answer: circumference: 22π area: 121π
Step-by-step explanation:
area of a circle is 
circumference is 
Answer:
<h2><u><em>
x = 2</em></u></h2>
Step-by-step explanation:
Find the value of x.
5+x=7
x = [?]
5 + x = 7
x = 7 - 5
<u><em>x = 2</em></u>
----------------check
5 + 2 = 7
7 = 7
the answer is good
