X² - 8x = -10
to have a complete square, we must have this format:
a² + 2ab + b²
a² = x²
2ab = -8x ⇒ 2(x)(-4)
b² = -4² = 16
x² - 8x + 16 = -10 + 16
x² - 8x + 16 = +6
(x-4)² - 6 = 0
Both sides must have an additional value of 16.
A) h(x) = g(x) + 30
The term g(x) represents the cost of the cable service minus the startup fee. Also, B, C, and D choices do not represent $30 as a one-time startup fee, so they are immediately wrong answers.
Good luck!
Answer:
A. x=2, y = 7.
B. (2, 7).
Step-by-step explanation:
A. You can eliminate y by subtracting the equations:
y = 8x - 9
y = 4x - 1 Subtract:
0 = 4x - 8
4x = 8
x = 8/4 = 2.
Now substitute for x in the first equation:
y = 8(2) - 9 = 7.
Check in the second equation:
y = 4x - 1
7 = 4(2) - 1 = 7. Check is OK.
B. On the graph they will intersect at the point (2, 7).
They will intersect here because the values x=2 and y=7 satisfy both the 2 equations.
The expression given is ambiguous according to the standard rules of math (PEMDAS) due to the lack of appropriate parentheses and probably the exponentiation symbol ^.
From the context, I assume it to mean
(3^(1/3)) / (3^(1/3)) = 1
Since 3^(1/3) is the cube-root of 3, and is thus irrational.
However, the quotient is exactly 1, which is a rational number.
The example is therefore a counter-example for the statement that "set of irrational numbers is closed under division", or stated differently,
"<span>the set of irrational numbers is not closed under division"</span>
