Answer:
the 73rd term of the arithmetic sequence is -964.
Step-by-step explanation:
The common difference in this arithmetic sequence is 13. This is obtained by subtracting 28 from 41. The first term is a(1) = -28.
The arithmetic sequence formula is a(n) = a(1) + d(n - 1), where d is the common difference and -28 the first term.
Then, in this case, a(n) = -28 - 13(n - 1), and
a(73) = -28 - 13(73 - 1) = -964
Answer:
A. Dashed line, shaded above.
Step-by-step explanation:
If the sign is < or > it's dashed line. If it's or equal to it's always solid.
If the sign is > it's shaded above, if it's < it's shaded below.
^Virtuoso helper^
Answer:
1. A = 2x; P = 4x+2. A = 4; P = 10.
2. A = y² +2; P = 4y +2. A = 27; P = 22.
Step-by-step explanation:
1. The area is the sum of the marked areas of each of the tiles:
A = x + x
A = 2x
__
The perimeter is the sum of the outside edge dimensions of the tiles. Working clockwise from the upper left corner, the sum of exposed edge lengths is ...
P = 1 + (x-1) + x + 1 + (x+1) + x
P = 4x +2
__
When x=2, these values become ...
A = 2·2 = 4 . . . . square units
P = 4·2+2 = 10 . . . . units
_____
2. Again, the area is the sum of the marked areas:
A = y² + 1 + 1
A = y² +2
__
The edge dimension of the square y² tile is presumed to be y, so the perimeter (starting from upper left) is ...
P = y +(y-2) +1 +2 +(y+1) +y
P = 4y +2
__
When y=5, these values become ...
A = 5² +2 = 27 . . . . square units
P = 4·5 +2 = 22 . . . . units
It is helpful to plot the points, then mentally test the answers for plausibility. Translation of E 1 unit to the right puts it at (2, 1), then rotation counterclockwise 90° about the origin puts it at (-1, 2), the location of E'.
The appropriate choice seems to be
A translation 1 unit to the right followed by a 90-degree counterclockwise rotation about the origin_____
Translation 1 unit right: (x, y) ⇒ (x+1, y)
Rotation 90° CCW: (x, y) ⇒ (-y, x)
Both transformations in that order: (x, y) ⇒ (-y, x+1)
Answer: 10 including 645,000
Step-by-step explanation:
644,995
644,996
664,997
664,998
664,999
665,000
665,001
665,002
665,003
665,004
