If x^2 + kx + 6 = (x+n)(x + 3) for all values of x, where k and n are constants, what is the value of k?
A) 5
B) 3
C) 2
D) 1

A) 5

Step-by-step explanation:

We are given that:

Where k and n are constants.

And we want to find the value of k.

We can expand the right-hand side:

Hence:

The coefficients of each term must be equivalent. In other words:

Solve for n:

Now, we can solve for k:

Our answer is A.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

i believe that the answer is

b. y-1=-2(x-4)

hope this !