Which function has a domain of x greater-than-or-equal-to 5and a range of y less-than-or-equal-to 3? y = StartRoot x minus 5 EndRoot + 3
y = StartRoot x + 5 EndRoot minus 3
y = negative StartRoot x minus 5 EndRoot + 3
y = negative StartRoot x + 5 EndRoot minus 3

The function that has a domain of 'x' greater-than-or-equal-to 5 and a range of 'y' less-than-or-equal-to 3 is;

.

Step-by-step explanation:

The domain of a function are the possible 'x' values of the function

The range of a function are the possible 'y' values of the function

The given possible functions are;

1)

The range of values for the above function are;

Domain; x ≥ 5

Range; y ≥ 3

2)

The range of values for the above function are;

Domain; x ≥ -5

Range; y ≥ -3

3)

The range of values for the above function are;

Domain; x ≥ 5

Range; y ≤ 3

4)

The range of values for the above function are;

Domain; x ≥ -5

Range; y ≤ -3

Therefore, the required function is the third function, .

∠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.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it