Answer:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
(−11,−5/4)
Equation Form:
x=−11,y=−5/4
Answer:
(a) There are two complex roots
Step-by-step explanation:
The discriminant of a quadratic function describes the nature of its roots:
- <u>negative</u>: two complex roots
- <u>zero</u>: one real root (multiplicity 2)
- <u>positive</u>: two distinct real roots.
__
Your discriminant of -8 is <em>negative</em>, so it indicates ...
There are two complex roots
_____
<em>Additional comment</em>
We generally study polynomials with <em>real coefficients</em>. These will never have an odd number of complex roots. Their complex roots always come in conjugate pairs.
One fifth of a number n is equal -7 as an equation would look like this:
1/5 n = -7 / * 5 (both sides)
n = -35
So if number n equals -35, then it's true that 1/5n equals -7.
It is equivalent to 4/6 so yeah yay.
Answer:
Prove set equality by showing that for any element
,
if and only if
.
Example:
.
.
.
.
.
Step-by-step explanation:
Proof for
for any element
:
Assume that
. Thus,
and
.
Since
, either
or
(or both.)
- If
, then combined with
,
. - Similarly, if
, then combined with
,
.
Thus, either
or
(or both.)
Therefore,
as required.
Proof for
:
Assume that
. Thus, either
or
(or both.)
- If
, then
and
. Notice that
since the contrapositive of that statement,
, is true. Therefore,
and thus
. - Otherwise, if
, then
and
. Similarly,
implies
. Therefore,
.
Either way,
.
Therefore,
implies
, as required.