The correct question is
<span>
Penelope determined the solutions of the quadratic function by completing the square.f(x) = 4x² + 8x + 1
–1 = 4x² + 8x
–1 = 4(x² + 2x)
–1 + 1 = 4(x² + 2x + 1)
0 = 4(x + 2)²
0 = (x + 2)²
0 = x + 2
–2 = x
What error did Penelope make in her work?
we have that
</span>f(x) = 4x² + 8x + 1
to find the solutions of the quadratic function
let
f(x)=0
4x² + 8x + 1=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(4x² + 8x)=-1
Factor the
leading coefficient
4*(x² + 2x)=-1
Complete the square Remember to balance the equation
by adding the same constants to each side.
4*(x² + 2x+1)=-1+4 --------> ( added 4 to both sides)
Rewrite as perfect squares
4*(x+1)²=3
(x+1)²=3/4--------> (+/-)[x+1]=√3/2
(+)[x+1]=√3/2---> x1=(√3/2)-1----> x1=(√3-2)/2
(-)[x+1]=√3/2----> x2=(-2-√3)/2
therefore
the answer is
<span>
Penelope should have added 4 to both sides instead of adding 1.</span>
1/5...
This question should be relatively easy for a high schooler...
Answer:
Step-by-step explanation:
Start box
180 = 89+42+x
180-89-42=x
49 = x
2nd box
180 = 84+58+x
180-84-58=x
38 = x
3rd box
180=74+2x
180-74=2x
106/2 = x
53 = x
4th box
180=102+2x
180-102=2x
78/2 = x
39 = x
4th box
180 = 73+81 +x
180-73-81=x
26 = x
5th box
180=2*54+x
180 - 2*54 = x
72 = x
6th box
180=62-2x
180-62=2x
118=2x
118/2=x
59 = x
7th box
180 = 2*68 + x
180-2*68=x
44 = x
Answer:
x²-y² = 40
Step-by-step explanation:
Factorising x²-y²:
x²-y² = (x+y)(x-y)
This is due to the property that states:
a²+b² = (a+b)(a-b)
Substituting the given values into the above equation:
x²-y² = (10)(4)
= 40
Hence, x²-y² = 40
<em>Hope this helps and be sure to have a wonderful time ahead at Brainly! :D</em>
