Question

Plz help I have no idea how to answer it​

Answer 1

5. Answer: see explanation

Explanation:

If the roots are m and 3m, then x = m and x = 3m

⇒ x - m = 0 and x - 3m = 0

⇒ (x - m)(x - 3m) = 0

⇒ x² - 4mx + 3m² = 0

Since x² + px + q = 0 then p = -4m and q = 3m²

3p² = 3(-4m)² 16q = 16(3m²)

= 3(16m²) = 48m²

= 48m²

3p² = 48m² = 16q ⇒ 3p² = 16q

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6. Answer: 8 or 18

Explanation:

The Area of the entire rectangle (A = L × w) is 12 × 10 = 120

The Area of the shaded region is 72, so the Area of the non-shaded region is 120 - 72 = 48.

There are two non-shaded triangles.

• Bigger non-shaded Δ: L = 12-x, w = 10 ⇒
  `A = (10(12-x))/(2)`
• Smaller non-shaded Δ: L = x, w = x ⇒
  `A=(x(x))/(2)`

Combine the Areas of both triangles and set it equal to the Area of the non-shaded region:

`(x(x))/(2)+(10(12-x))/(2)=48\\\\\\(x^2)/(2)+(120-10x)/(2)=48\\\\\\(x^2-10x+120)/(2)=48\\\\\\x^2-10x+120=96\\\\x^2-10x+24=0\\\\(x-4)(x-6)=0\\\\x - 4 = 0\quad or\quad x-6=0\\x=4\qquad or\qquad x=6\\\\\text{Based on the image provided, it appears that the x-value will be the}\\\text{smallest of the two possible solutions (4), but both solutions are valid.}`

Area of ΔBEF:

`\text{when x = 4, A =}\ (4(4))/(2)=(16)/(2)=8\\\\\\\text{when x = 6, A =}\ (6(6))/(2)=(36)/(2)=18`