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1) gradient of line = Δ y ÷ Δ x
= (5 -2) ÷ (3 - (-6))
= ¹/₃
using the point-slope form (y-y₁) = m(x-x₁)
using (3,5)
(y - 5) = ¹/₃ (x -3)
y - 5 = ¹/₃x - 1
⇒ <span> y = ¹/₃ x + 4 [OPTION D]
</span>2) y = 2x + 5 .... (1)
<span> </span>y = ¹/₂ x + 6 .... (2)
by substituting y in (1) for y in (2)
2x + 5 = ¹/₂ x + 6
³/₂ x = 1
x = ²/₃
by substituting found x (2)
y = ¹/₂ (²/₃) + 6
y = ¹⁹/₃
∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]
3) Yes [OPTION A]
This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.
4) No [OPTION B]
Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.
The independent variable here is b, the number of mats; the dependent var. is p, the cost of b mats. Thus, p = f(b).
Here, 245 units^3 = pi*r^2*(5 units), or
245 units^3
r^2 = ------------------- = 15.61 units^2. Thus, the radius is sqrt(15.61 units^2), or
5(3.14) units 3.95 units. The DIAMETER is d = 2*r = 7.90 units.
Answer:
(x+12)^2=84
Step-by-step explanation:
x^2+24x+60=0
x^2+24x=-60
x^2+24x+(24/2)^2=-60+(24/2)^2
(x+24/2)^2=84
(x+12)^2=84 (ans)
Answer:
A
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
−y+4≥8
Step 2: Subtract 4 from both sides.
−y+4−4≥8−4
−y≥4
Step 3: Divide both sides by -1.
−y
−1
≥
4
−1
y≤−4
