Triangle e d f has sides that are of varying lengths. side e d has a length of 4 and side e f has a length of 9.
which statements about the diagram are true? select three options.

d e + e f greater-than d f
triangle d e f is an isosceles triangle.
5 less-than d f less-than 13
d e + d f less-than e f
triangle d e f is a scalene triangle.

D E + E F greater-than D F

5 less-than D F less-than 13

Triangle D E F is a scalene triangle

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

we have the triangle EDF

where

Applying the triangle inequality theorem

1)

2)

so

The length of DF is the interval -----> (5,13)

The triangle DEF is a scalene triangle (the three length sides are different)

therefore

The statements that are true are

D E + E F greater-than D F

5 less-than D F less-than 13

Triangle D E F is a scalene triangle

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.

idk

step-by-step explanation: