Answer:
Option A.
Step-by-step explanation:
y + 1 = -3x + 15
y = -3x + 14
A line perpendicular would have a slope of 1/3.
y = 1/3x + c
-6 = 1/3 * 4 + c
4/3 + c = -6
c = -18/3 - 4/3
c = -22/3
So, we have y = 1/3x - 22/3.
y + 6 = 1/3(x - 4)
y + 6 = 1/3x - 4/3
y = 1/3x - 4/3 - 18/3
y = 1/3x - 22/3
So, the correct answer is Option A.
Hope this helps!
Answer:
a) ∠2 and ∠4 are a linear pair
∠4 = 115°
b) ∠2 and ∠7 are alternate exterior angles
∠7 = 65°
c) ∠2 and ∠3 are vertical angles
∠3 = 65°
Step-by-step explanation:
Linear pair : a pair of adjacent angles formed when two lines intersect. The two angles of a linear pair are always supplementary (two angles whose measures add up to 180°)
Alternate exterior angles : when two parallel lines are cut by a transversal (a line that intersects two or more other, often parallel, lines), the resulting alternate exterior angles are <u>congruent</u>.
Vertical angles : a pair of opposite angles formed by intersecting lines. Vertical angles are always <u>congruent.</u>
a) ∠2 and ∠4 are a linear pair
⇒ ∠2 +∠4 = 180
⇒ 65 + ∠4 = 180
⇒ ∠4 = 180 - 65
⇒ ∠4 = 115°
b) ∠2 and ∠7 are alternate exterior angles
⇒ ∠2 ≅ ∠7
⇒ ∠7 = 65°
c) ∠2 and ∠3 are vertical angles
⇒ ∠2 ≅ ∠3
⇒ ∠3 = 65°
Answer:
x = 74
Step-by-step explanation:
4x - 2y ≤ 6 <em>subtract 4x from both sides</em>
-2y ≤ -4x + 6 <em>change the signs</em>
2y ≥ 4x - 6 <em>divide both sides by 2</em>
<h3>y ≥ 2x - 3</h3>
y = 2x - 3 - it's a linear function. We need only two points to plot the graph.
Choose any two values of x and calculate the values of y:
for x = 0 → y = 2(0) - 3 = 0 - 3 = -3 → (0, -3)
for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1)
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<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded to left
>, ≥ - shaded to right
