(The one you have checked so far is not correct, the product of a rational and irrational number is irrational)
The sum of a and b is never rational
b^2 is sometimes rational
^ Those two I know are correct
I forget if A^2 is always rational is correct or not
I hope this helps at all
8x - ¹/₃y = 16
8x - ¹/₃(0) = 16
8x - 0 = 16
8x = 16
8 8
x = 2
X-Intercept: (2, 0)
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = = 10
Answer:
B) (-3, 5) and (1, 5)
Step-by-step explanation:
<span>Write the quadratic function in the form:
f(x) = a(x-h)</span>²<span> + k
Given Function:
f(x) = 3x</span>²<span> + 18x + 28
Using the completing square method:
</span> f(x) = 3(x² + 6x + 28/3)
f(x) = 3(x² + 6x + (3)² - (3)² + 28/3)
f(x) = 3[(x+3)² - (3)² + 28/3]
f(x) = 3[(x+3)² - 9 + 28/3]
f(x) = 3[(x+3)² - 27/3 + 28/3]
f(x) = 3[(x+3)² - 1/3]
f(x) = 3(x+3)² - 1
Therefore,
The vertex is (h,k) = (-3,-1)