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9514 1404 393

  factors: (x +5) and (2x -1)

  zeros: -5 and 1/2

Step-by-step explanation:

The factorization can be aided by considering the factors of ac=2·(-5) that have a sum of b=9.

  -10 = -1×10 = -2×5

The sums of these factors are ...

  -1+10 = 9 (the pair we want), and -2+5 = 3

This means we can rewrite the function as ...

  g(x) = 2x² +10x -x -5

and factor by grouping.

  g(x) = (2x² +10x) -(x +5)

  g(x) = 2x(x +5) -1(x +5) = (2x -1)(x +5)

The factors of g(x) are (x +5) and (2x -1).

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The zeros of the function are the values of x that make these factors be zero.

  x+5 = 0   ⇒   x = -5

  2x -1 = 0   ⇒   2x = 1   ⇒   x = 1/2

The image of circle A is missing, so i have attached it;

x = 17

Step-by-step explanation:

In Δs EAB and EAD

We are told that;

∠BAE ≅ ∠DAE

AB = AD = AE

Now,

The Two triangles have two corresponding equal sides and the angles between them are equal, thus, we can say that the two triangles are congruent by SAS (Side Angle Side) postulate of congruence

By using the result of congruence, we can say that;

EB ≅ ED

We are given that;

EB = 3x - 24 and ED = x + 10

Thus,

3x - 24 = x + 10

∴ 3 x - 24 = x + 10

Add 24 to both sides to give;

3x = x + 34

Subtract x from both sides to give;

2x = 34

Divide both sides by 2 to give;

x = 17