Answer:
The equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18
Step-by-step explanation:
The coordinates of the point of intersection of the two lines = (5, 9)
The coordinates of a point on one of the two lines, line 1 = (-4, 4)
The slope of a line perpendicular to another line with slope, m = -1/m
Therefore, we have;
The slope, m₁, of the line 1 with the known point = (9 - 4)/(5 - (-4)) = 5/9
Therefore, the slope, m₂, of the line 2 perpendicular to the line that passes through the point (-4, 4) = -9/5
The equation of the line 2 is given as follows;
y - 9 = -9/5×(x - 5)
y - 9 = -9·x/5 + 9
y = -9·x/5 + 9 + 9
y = -9·x/5 + 18
Therefore, the equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18.
2 2/3 + 2/3 + 1/4 =
8/3 + 2/3 + 1/4 =
10/3 + 1/4 =
40/12 + 3/12 =
43/12 =
3 7/12 hrs <===
Answer:
Step-by-step explanation:
The slope-intercept form of an equation of a line:
m - slope
b - y-intercept
The formula of a slope:
From the graph we have two points (-5, -1) and (-2, -3).
<em>Look at the picture</em>.
Calculate the slope:
Put it to the equation in slope-intercept form:
We can't read the y-intercept from the graph. Therefore put the coordinates of the point (-5, -1) to the equation and calculate <em>b</em>:
<em>subtract 10/3 from both sides</em>
Finally:
We are tasked to solve the three angles given that we have the measurements of the sides such as
a = Zack to Rachel distance
b = Rachel to Maddie distance
c = Maddie to Zack distance
a =3
b =2.5
c =4
Solving the angles we need to use Law of Cosines:
cos A = 2.5² + 4² -3² /2*2.5*4
A = 48.59°
cos B=3² + 4² - 2.5² / 2*3*4
B = 38.625°
C=180 - 48.59° - 38.625°
C= 92.79°
The three angles are 48.59°,38.63° and 92.79°.
Answer: $55,489.20
Step-by-step explanation:
Given the following information :
Base salary = $10.20 per hour
Overtime pay = $10.20 * 1.5 = $15.3
Average sale per hour = $60
Tips = 20% of sale
Regular shift hour = 8hours
Work week:
3 10-hour shift = 24hrs regular (6 hrs overtime)
1 11 - hour shift = 8hrs regular (3 hrs overtime)
1 5 - hour shift = 5 hours
Total hours per week = 37hrs regular, 9hrs overtime
WEEKLY :
Income from tips = $60 * 46 * 0.2 = $552
Regular pay: 37 * 10.20 = $377.40
Overtime: 9 * $15.30 = $137.70
Total = $(137.70 + 377.40 + 552) = $1067.10
Number of weeks in a year = 52
Annual gross = $1067.10 * 52 = $55,489.20
