X=hours master worked
y=hours apprentice worked
62x+40y=492
if master worked 3hours more than apprntice
x=3+y
sub 3+y for x
62(3+y)+40y=492
expand
186+62y+49y=492
186+102y=492
minus 186 both sides
102y=306
divide both sides by 102
y=3
sub back
x=3+y
x=3+3
x=6
master electrician worked 6 hours
6*62=372
master electrician earned $372
Answer:
cos x ≠ 0 ⇔ x ≠
; k ∈ N

<=> cos²x + sin²x = 1
⇔ 1 = 1
=> x = { R \ (pi/2 + k.pi); k ∈ N}
Step-by-step explanation:
The zero product property tells us that if the product of two or more factors is zero, then each one of these factors CAN be zero.
For more context let's look at the first equation in the problem that we can apply this to:

Through zero property we know that the factor

can be equal to zero as well as

. This is because, even if only one of them is zero, the product will immediately be zero.
The zero product property is best applied to
factorable quadratic equations in this case.
Another factorable equation would be

since we can factor out

and end up with

. Now we'll end up with two factors,

and

, which we can apply the zero product property to.
The rest of the options are not factorable thus the zero product property won't apply to them.
The discriminant is b^2 -4ac
a = 1
b = -2
c = 4
discriminant = 4 -4 * 1 * 4 =
4 -16 =
-12
I get MINUS 12 as the answer but that isn't one of the choices.