Answer:
Step-by-step explanation:
a) 4x¹⁰ = 2² * x¹⁰
64x² = 2⁶ *x²
GCF = 2² * x² = 4x²
b) 4x¹⁰ - 64x² = 4x²*(x⁸ - 16)
=4x² *[ (x⁴)² - 4²]
= 4x² * (x⁴ + 4) (x⁴ - 4)
= 4x² * (x⁴ + 4)* [(x²)²- 2²]
=4x² * (x⁴ + 4) * (x² + 2)(x² - 2)
F(x)=3x²-6x+13
a=3, b=-6, c=13
the x coordinate of the vertex is x=-b/(2a), so x=-(-6)/(2*3)=1
when x=1, y=3(1)²-6(1)+13=10
the vertex is at (1,10)
answers are in bold.
The absolute value function |<em>x</em>| always returns a non-negative number. It takes any number <em>x</em> and returns <em>x</em> if it's already non-negative, or -<em>x</em> if it is negative in order to make it positive.

For the equation
-3 + 4 |2<em>x</em> - 5| = 14
rearrange terms to get
|2<em>x</em> - 5| = 17/4
Now,
• if 2<em>x</em> - 5 ≥ 0, then |2<em>x</em> - 5| = 2<em>x</em> - 5. Then
2<em>x</em> - 5 = 17/4
• and if instead 2<em>x</em> - 5 < 0, then |2<em>x</em> - 5| = -(2<em>x</em> - 5), so that
-(2<em>x</em> - 5) = 17/4, or
2<em>x</em> - 5 = -17/4
In the first case,
2<em>x</em> - 5 = 17/4
2<em>x</em> = 17/4 + 5 = 37/4
<em>x</em> = 37/8
In the second case,
2<em>x</em> - 5 = -17/4
2<em>x</em> = -17/4 + 5 = 3/4
<em>x</em> = 3/8
Answer:
15%
Step-by-step explanation:
300 / 3 = 100
45 / 3 = 15
15 of 100 is 15%