√4 + √16 = 2 + 4 = 6 <--- rational
√5 + √36 = √5 + 6 <--- irrational
√9 + √24 = 3 + √24 <--- irrational
2 * √4 = 2 * 2 = 4 <--- rational
√49 * √81 = 7 * 9 = 63 <---rational
3√12 = 3√(4 * 3) = (3 * 2)√3 = 6√3 <---irrational
Hope this helps ^-^
Answer:
C
Step-by-step explanation:
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
Sallys statement is always true
for example:
-6 + 2 = -4
but if I turn it around
2 - 6 = -4
same answer
-6 -6 = -12
swap around -6 - 6 = 12
same answer
again -3 + 6 = 3
and 6 - 3 = 3
