Question

True or False

Answer 1

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