1. Given that 4x²- 16x + 15 = a(x-p)²+ q for all values of x. (a) Find the values of the constants a, p and q.

a = 4, p = 2, q = - 1

Step-by-step explanation:

Expand the right side of the identity, then compare the coefficients of like terms with those on the left side.

a(x - p)² + q ← expand (x - p)² using FOIL

= a(x² - 2px + p²) + q  ← distribute parenthesis

= ax² - 2apx + ap² + q

Compare coefficients of x² term

a = 4

Compare coefficients of x- term

- 2ap = - 16, that is

- 2(4)p = - 16

- 8p = - 16 ( divide both sides by - 8 )

p = 2

Compare constant terms

ap² + q = 15 , that is

4(2)² + q = 15

16 + q = 15 ( subtract 16 from both sides )

q = - 1

Thus a = 4, p = 2, q = - 1

there are no figures how am i supposed to answer this question

step-by-step explanation:

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'.