The height of a triangle is 5cm more than half the base of the triangle. The area of the triangle is 6cm^2. Find the base and height of the triangle

Base = 2 cm and height = 6 cm.

Step-by-step explanation:

Area = 1/2 * base + height

Let b be the base and h = height of the given triangle, then

6 = b/2 * h

6 = b/2(b/2 + 5)

b^2/4 + 5b/2 - 6 = 0

b^2 + 10b - 24 = 0

(b + 12)(b - 2) = 0

b = 2  (we neglect the negative b = -12)

So h = b/2 + 5 = 2/2 + 5 = 6.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

go and ask your mom to you