Step-by-step explanation:
Q1)
for x = 2, y = 1
-8x³y⁴/7 = -64/7
-8×2³×1⁴/7 = -8×8×1/7 = -64/7
true
Q2)
x/4 + x/6 - x/2 = 3/4
is x = -9 ?
bringing everything to 1/12 ...
3x/12 + 2x/12 - 6x/12 = 3×3/12
-x/12 = 9/12
-x = 9
x = -9
true
Q3)
can
1 - 2ab - (a² + b²) = 1 - 2ab - a² - b² be factored as
(1 + a - b)(1 + a + b)
let's multiply
(1 + a - b)(1 + a + b) =
= 1 + a + b + a + a² + ab - b - ab - b² =
= 1 + 2a + a² - b²
this is NOT the same as
1 - 2ab - a² - b²
false
Q4)
The horizontal distance of a point from the y-axis is called abscissa or x coordinate of the point.
3 is the y coordinate of (2, 3) and not the x coordinate.
false
Q5)
(7, 9) and (9, 7)
the x coordinates are different, and the y coordinate are different. so, they are definitely NOT the same point.
this would be like saying 5 hours and 3 minutes is the same as 3 hours and 5 minutes.
false
Q6)
now, this is tricky. there are 4 perfect cubes between 1 and 100 :
1×1×1 = 1
2×2×2 = 8
3×3×3 = 27
4×4×4 = 64
did your teacher mean "exactly 3 perfect cubes" ? because, since there are 4, there are also 3, of course (and 2, and 1).
and did "between 1 and 100" mean including the numbers 1 and 100, or excluding the numbers 1 and 100 ?
so, if excluding 1 and 100, then it is true.
if including 1 and 100 and asking for exactly 3, then it is false.
if including 1 and 100 and truly only asking for 3, then it is true.
Q7)
12³ = 12×12×12 = 144×12 = 1728
true
Q8)
(a+1)(a-1)(a²+1) = (a⁴ -1) ?
let's multiply
(a² + a - a - 1)(a² + 1) = (a²-1)(a²+1) = a⁴ - a² + a² - 1 = a⁴-1
true
Q9)
the areas of the 2 squares are
25a² and 25b²
the sum is
25a² + 25b² = 25(a² + b²)
but
25(a+b)(a-b) = 25(a² - b²)
this is NOT the same.
false
Q10)
abc + bca + cba
a monomial is, roughly speaking, a polynomial which has only one term.
but the given expression has 3 terms.
false
is the mean, that we already found at point 1), and N=4. Substituting data, we have:
