Can i please get some help im pretty desperate and will give brainiest to first answer with some steps, just try your best please

To calculate the vertex you can use the vertex form ( i searched about the vertex and found it) but i don't know how to use it so i used another method.

The vertex is where the function inverts (y values) so it is going to be or a maximum or a minimum of the function. To calculate the min/max you derivate the function and then equal it to zero.

1) y  = -3x^2 -12x -10

the derivative of y is y' = -6x -12 = -6(x+2)

y'=0 <=>  -6(x+2) = 0 <=> x+2=0 <=> x=-2

y(-2) = -3(-2)^2 -12*(-2) -10 = 2

So the vertex is the point (-2,2) .

Because the slope of the equation is negative that means that the vertex is going to be the maximum , so the maximum is (-2,2) .

To find another 4 points you just have to pick values of x and replace them in the equation y  = -3x^2 -12x -10  to find y.

2) y = -2x^2 -12x -16

Do the same thing we did in point 1

y'= -4x-12 = -4(x+3)

y'=0 <=>  -4(x+3) = 0 <=> x+3=0 <=> x=-3

y(-3) = -2(-3)^2 -12*(-3) -16 = 2

So the vertex is the point (-3,2) .

∠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.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2