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Mathematics

1 answer:

STALIN [3.7K]3 years ago

5 0

Answer:

A x² +2x +4
D x² +10x +26

Step-by-step explanation:

One way to determine if the equation has any real solutions is to look at its discriminant. For the equation ax²+bx+c = 0, the discriminant is ...

d = b² -4ac

When the discriminant is negative, both solutions to the quadratic are complex. There are no real solutions in that case.

We can find the discriminant values to be ...

A: d = 2² -4(1)(4) = -12 . . . . no real zeros

B: d = 0² -4(3)(-5) = 60 . . . two real zeros

C: d = 8² -4(-2)(0) = 64 . . . two real zeros

D: d = 10² -4(1)(26) = -4 . . .no real zeros

Expressions A and D have no real zeros.

_____

Comment on the question

You are given an expression, not an equation. There is no equal sign. Hence, we cannot talk about solutions. We can only talk about zeros, values of x that make the expression have a value of zero.

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Answer:

From the graph attached, we know that $\angle 1 \cong \angle 5$ by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like $\angle 1$ and $\angle 5$ .

We also know that, by definition of linear pair postulate, $\angle 3$ and $\angle 1$ are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.

They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that $\angle 3$ and $\angle 1$ together are 180°, because they are on a straight angle. That is, $m \angle 3 + m \angle 1 = 180\°$

If we substitute $\angle 5$ for $\angle 1$ , we have $m \angle 3 + m \angle 5 = 180\°$ , which means that $\angle 3$ and $\angle 5$ are also supplementary by definition.