50 Points + 50 points +

1. Find the measurements of DE

2. Find the lengths of BC EC

3. Find the 1) width, 2) height only workings.

Do not need perimeter or area for question 3. So just need exact workings

for 1, 2 and 3 width and height parts. if answering questions.

see below

Step-by-step explanation:

Angle ACE = DCE since they are vertical angles

Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles

Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles

When all three angles are equal, the triangles are similar.

We can use ratios to find DE

DE         CE  

=

AB           AC

DE         8

=

12           10

Using cross products

10 DE = 8*12

10 DE = 96

Divide by 10

DE = 9.6

2nd problem

Angle ADE is congruent to ABC  because corresponding angles are conguent  when parallel lines cut by a transversal

Angle AED is congruent to ACB  because corresponding angles are conguent  when parallel lines cut by a transversal

Angle A equals angle A  by the reflexive property

When all three angles are equal, the triangles are similar.

We can use ratios to find BC

AD         DE 

=

AB           BC

8            5 

=

8+6           BC

Using cross products

8 BC = 5 (14)

8 BC =70

Divide each side by 8

BC =8.75

We can use ratios to find EC

AD         AE 

=

AB           AC

8            4.2 

=

8+6           4.2+EC

Using cross products

8 (4.2+EC) = 4.2*14

33.6 +8EC = 58.8

Subtracting 33.6

8EC =25.2

Dividing by 8

EC =3.15

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

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step-by-step explanation:

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