Atree makes a shadow that is 14 ft long. rachel is 6 ft tall. when she is standing near the tree, her shadow is 3.5 ft long. which statement best explains why rachel can use a proportion to estimate the length of the tree? a) the triangles made by the tree and its shadow and rachel and her shadow are similar. b) the triangles made by the tree and its shadow and rachel and her shadow are adjacent. c) the triangles made by the tree and its shadow and rachel and her shadow are congruent. d) the triangles made by the tree and its shadow and rachel and her shadow are symmetric.

A) The triangles made by the tree and its shadow and Rachel and her shadow are similar.

Step-by-step explanation:

Since both the tree and the girl is standing vertical to the ground making right angle .

If we assume that the given measure took at same time, then the angle made by sun rays would be same for tree and Rachel. [Corresponding angles]

Thus triangles made by both of them are similar.

Since, the corresponding sides of similar triangles are proportional.

Therefore, the statement BEST explains the reason that Rachel can use a proportion to estimate the length of the tree :-

A) The triangles made by the tree and its shadow and Rachel and her shadow are similar.

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: