Answer:
1. y = -2x + 5
2. y = 3/5x + 5
3. y = -4/5x - 4
4. y = - 1
5. yes
6. yes
7. yes
8. no
Step-by-step explanation:
1. (4,-3) parallel to y= -2x
-3 = -2(4)+b
b=5
2. (-5,2) parallel to y = 3/5x
2= 3/5(-5)+b
b=5
3. (-5,0) -4/5x
0 = -4/5(-5)+b
b = -4
4. (-4,-1)
y= -1
5. yes
6. yes
7. yes
8. no
- Same slope = parallel ex. y = -5x +7, y = -5x +12
- opposite reciprocal = perpendicular ex. y = -5x +7, y = 1/5x + 12
- to find "b" with slope and point
(x,y) y = mx + b
plug in the y value and x value in the eqaution and m=slope, solve for b
Answer:
The radius of the circle P = 2√10 = 6.325
Step-by-step explanation:
∵ AB is a tangent to circle P at A
∴ (AB)² = BC × BE
∵ BC = 8 , AB = 12 , ED = 6
∵ BE = ED + DC + CB
∴ BE = 6 + CD + 8 = 14 + CD
∴ (12)² = 8 × (14 + DC) ⇒ (12)²/8 = 14 + CD ⇒ CD = (12)²/8 - 14
∴ CD = 4
Join PC and PE (radii)
In ΔBDC and ΔPDE ⇒ ∵ ∠PDC = Ф , ∴ ∠PDE = 180 - Ф
Use cos Rule:
∵ r² = (PD)² + (DC)² - 2(PD)(DC)cosФ
∴ r² = 16 + 16 - 32cosФ = 32 - 32cosФ ⇒ (1)
∵ r² = (PD)² + (DE)² - 2(PD)(DE)cos(180 - Ф) ⇒ cos(180 - Ф) = -cosФ
∴ r² = 16 + 36 + 48cosФ = 52 + 48cosФ ⇒ (2)
∵ (1) = (2)
∴ 32 - 32 cosФ = 52 + 48cosФ
∴ 32 - 52 = 48cosФ + 32cosФ
∴ -20 = 80cosФ
∴ cosФ = -20/80 = -1/4
∴ r² = 32 - 32(-1/4) = 32 + 8 = 40
∴ r = √40 = 2√10 = 6.325
Answer:
The equation of the relation ⇒ 
y = 18
Step-by-step explanation:
∵ y ∝ x/z
∴ y = kx/z
∵ y = 18 , x = 15 and z = 5
∴ 18 = 15k/5 ⇒ 18 = 3k
∴ k = 18/3 = 6
∴ y = 6x/z
∵ x = 21 and z = 7
∴ y = (6 × 21)/7 = 18
Answer:
30 divided by 0.40 = 75
The original price was $75
Step-by-step explanation:
Answer:
Step-by-step explanation:
8x + 12 = 3x + 5x + 12
8x + 12 = 8x + 12
Bringing like terms on one side
8x - 8x = 12 - 12
x = 0
