Assume independence because there are probably a lot of widgets. 1/100 x 1/100 = 1/10,000
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.
Step-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question
The length is 3x + 7
The width is 2x + 2
The perimeter is
<h3>2( 3x + 7) + 2( 2x + 2)</h3>
Simplify
6x + 7 + 4x + 4
Group like terms
6x + 4x + 7 + 4
We have the final answer as
<h3>10x + 11</h3>
Hope this helps you
