9514 1404 393
Answer:
60, 57, 54, 51, ...
Step-by-step explanation:
The general term of an arithmetic sequence is ...
an = a1 +d(n -1)
We would like to find the first term (a1) and the common difference (d). We can use the two given terms to find these parameters.
a10 = 33 = a1 +d(10 -1)
a22 = -3 = a1 +d(22 -1)
Subtracting the first equation from the second, we get ...
(-3) -(33) = (a1 +21d) -(a1 +9d)
-36 = 12d
-3 = d
Using this value in the first equation, we can find a1.
33 = a1 +9(-3) = a1 -27
60 = a1 . . . . . . . . . . . . . . add 27 to both sides
So, our sequence has first term 60 and a common difference of -3.
The first 4 terms are ...
60, 57, 54, 51, ...
Answer:1.1 ft^2
Step-by-step explanation:
Φ=55°
Radius=r=4
π=3.14
Area of segment=area of sector - area of triangle
Area of sector=Φ/360 x π x r x r
area of sector=55/360 x 3.14 x 4 x 4
Area of sector=(55x3.14x4x4) ➗ 360
Area of sector=2763.2 ➗ 360
Area of sector=7.7 ft^2
Area of triangle=0.5 x r x r x sinΦ
Area of triangle=0.5 x 4 x 4 x sin55
Area of triangle=0.5 x 4 x 4 x 0.8192
Area of triangle=6.6 ft^2
Area of segment=area of sector - area of triangle
Area of segment=7.7-6.6
Area of segment=1.1 ft^2
Answer:
7x -2y = 6
Step-by-step explanation:
The perpendicular bisector has a slope that is the opposite of the reciprocal of the slope of the segment between the two points. It must go through the midpoint of the segment.
The latter can be found by averaging the coordinates of the end points:
((-5, 6) +(9, 2))/2 = ((-5+9)/2, (6+2)/2) = (2, 4)
The difference in endpoint coordinates is ...
(Δx, Δy) = (9-(-5), 2-6) = (14, -4)
For our purpose, we're only interested in the ratio of these values, so we can divide both by the common factor of 2:
(Δx, Δy) = (7, -2)
A line perpendicular to this segment through the point (h, k) can be written as ...
Δx·x +Δy·y = Δx·h +Δy·k
7x -2y = 7(2) -2(4)
7x -2y = 6 . . . . . . . standard form equation for the perpendicular bisector
Answer:
Step-by-step explanation:
The y-intercept is 2 and the line of symmetry is the y-axis.
