Y = 3x - 7...the slope here is 3 while the y-intercept is -7
3x + 9y = 9
9y = -3x + 9
y = -1/3x + 1....the slope of this line is -1/3 and the y-intercept is 1
the slopes 3 and -1/3 are negative reciprocals of one another...therefor, these lines are perpendicular.
Response: ∠B = 42° ∠A = 23° ∠F = 115°
Detailed explanation:
∠B is congruent to ∠C alternate interior angles 42°
∠CDF is supplementary to ∠CDE,
thus m∠CDF = 23° and ∠FAB is congruent to ∠CDF therefore m∠FAB= 23°
also ∠A is congruent to ∠CDE corresponding angles 157° ∠FAB is supplementary to ∠A
which leads to 180 - 157 = 23 giving m∠FAB
The sum of angles in a triangle amounts to 180°, so m∠AFB = 180 -(23 +42)
This results in 180- 65 = 115 = m∠F
63. Step-by-step explanation: I'm fairly sure it's 63, but I might be mistaken; if so, I apologize.
Begin by determining the overhead costs. The selling price was $240. To calculate 20% of 240, multiply 240 by 0.20, yielding 48. Consequently, the overhead expenses total $48. To figure out the profit, subtract total expenses from the selling price. Mr. Lippman's selling price was $240, he paid $160 for the dryer, and incurred $48 in overhead expenses. Thus, 240 - 160 - 48 equals 32. Therefore, the profit is $32. To determine the profit rate, divide the profit by the total expenses. 32 / (240 + 160) results in 0.08. Hence, the profit rate is 8%.
