let "a number" = x
(x) + (x + 1) + (x + 2) = 72
Simplify. Combine like terms
3x + 3 = 72
Isolate the x. Note the equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS.
3x + 3 (-3) = 72 (-3)
3x = 72 - 3
3x = 69
3x/3 = 69/3
x = 69/3
x = 23
23 is the smallest number
hope this helps
Answer:
No solution
Step-by-step explanation:
-x + y = 8..............(1)
1/2x - 1/2y = 3......(2)
Multiply (2) by 2
x - y = 6 ............(3)
Adding (1) and (3)
-x + x + y - y = 8 + 3
x and y are both eliminated so no solution
Answer:
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Answers:
- Part A) There is one pair of parallel sides
- Part B) (-3, -5/2) and (-1/2, 5/2)
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Explanation:
Part A
By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.
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Part B
The midsegment has both endpoints as the midpoints of the non-parallel sides.
The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.
x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3
y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2
The midpoint of segment PS is (-3, -5/2)
Repeat those steps to find the midpoint of QR
x coord = (x1+x2)/2 = (-2+1)/2 = -1/2
y coord = (x1+x2)/2 = (3+2)/2 = 5/2
The midpoint of QR is (-1/2, 5/2)
Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.
Answer:
512 in³
Step-by-step explanation:
The height perpendicular to the base is the leg of a right triangle with hypotenuse 10 in and other leg 8 in. Using the Pythagorean theorem, we can find it as ...
h² +8² = 10²
h² = 100 -64 . . . . . subtract 8²
h = 6 . . . . . . . . . . . . take the square root of 36
Then the volume is found using ...
V = (1/3)Bh = (1/3)(16 in)²(6 in) = 512 in³
The volume is 512 cubic inches.
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The 8-inch dimension used above comes from half the distance between the center of one side of the base to the center of the opposite side. (16 in)/2 = 8 in.
