5. Answer: see explanation
<u>Step-by-step explanation:</u>
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
<u>Step-by-step explanation:</u>
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 ⇒

- Smaller non-shaded Δ: L = x, w = x ⇒

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

Area of ΔBEF:

Answer:
360 = 2(2w+76)
Step-by-step explanation:
.25 because .5 is the same as .50 and 25 divided by 2 is 25 and its .25 as a final
Answer:
The slope of a line parallel to the given line is m = -3/2.
Step-by-step explanation:
Here, the given equation is 
The given equation is of the form y = mx + C : where m is the slope and C is y-intercept.
Here, comparing m = (-3/2) and C = 0
So, slope of the given equation is m = -(3/2)
Also, two equations are said to be parallel if they have equal slopes.
⇒Slope of the line parallel to the given equation: m = (-3/2)
Hence, the slope of a line parallel to the given line is m = -3/2.