In the following function defined by an equation in the form y=ax^2+bx+c, identify the values of a, b, and c.

y= -x^2+5x

a) a=0, b=5, c=0
b) a= -1, b=5, c=0
c) a= 1, b=5, c=0
d) a=5, b= -1, c=0

B) a= -1, b=5, c=0

Step-by-step explanation:

This is a quadratic equation.

From the form given y=ax^2+bx+c, it can be deduced that a, b and c are the coefficient of x^2, x and the constant respectively.

As such, when y=ax^2+bx+c is compared with

y= -x^2+5x,

a = -1, b = 5 and c = 0

Hence option B) a= -1, b=5, c=0 is right.

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step-by-step explanation:

∠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.