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:
You set it up like this.
It says "the difference", so you put a minus sign: -
It says that the minuend, or the part being taken away from is a quantity equal to the product of 4 and "some number" (we'll use x), so now you have: (4 * x) -
Next, it says the subtrahend, or part being removed, is the square of "the number", meaning we use the "some number", x, from before, so now you have: (4 * x) - x^2
Answer:
A = P (1 + i)^n A is the final amount
P is the initial amount
i = interest / period
n = number of periods
A = 315 * (1 + .015)^1.5 = 322.11
To solve for the distance the car is required to stop after the driver
steps on the break is by jus substituting the given value to the equation
given. Since the car is traveling at 50 miles per hour
24d = (50)^2
D = 2500/24
<span>D =104 ft</span>
The height of the object at the time of launch is 100 meters.
To find this, we simply have to put 0 in for x, as this is when there has been no time (at launch)
h(x)=-5(x-4)^2+180
h(0)=-5(0-4)^2+180
h(0)=-5(-4)^2+180
h(0)=-5(16)+180
h(0)=-80+180
h(0) = 100
