Ihave 4 question i need with but ut will only let me post 1 at a time so can yall me

A, (-∞,-1]

Step-by-step explanation:

we find a function's range by starting from the bottom to the top. a parabola that opens downward has a maximum point, meaning thats the maximum point the graph reaches.

if we start from the bottom, the graph goes down until negative infinity, so we would write -∞ as the first part of our range. an infinity symbol, no matter if its negative or positive, always starts with a parentheses, so we can eliminate options C and D.

the vertex of the parabola is (-2,-1) and to find the range, we use the y-coordinate to plot

since the parabola does not continue past -1, we would say that our range would be from -∞ to -1.

the interval is written as (-∞,-1], which is choice A

a bracket is used because the point (-2,-1) is located on the parabola and is therefore included in the solution.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.