Answer:
Hence, the conjecture for the sum of first 20 positive integer is:
20×21=420
Step-by-step explanation:
The table is given as:
2 = 2 =1.2
2+4 = 6 = 2.3
2+4+6 = 12 = 3.4
2+4+6+8 = 20 = 4.5
2+4+6+8+10 = 30 = 5.6
Hence, we see the pattern as:
2+4+6+....+2n= n(n+1)
which is the sum of first n even positive integers.
Hence, we are asked to find the sum of first 20 positive even numbers that is we are asked to find the sum when n=20.
i.e. the sum of:
2+4+6+8+..........+40=20(20+1)
2+4+6+8+........+40=20×21=420.
Hence, the conjecture for the sum of first 20 positive integer is:
20×21=420
Answer:
8 cubes are painted on 3 sides
24 cubes are painted on 2 sides
22 cubes are painted on 1 sides
6 cubes are painted on 0 side
E = 3 * 8/60 + 2 * 24/60 + 1 * 22/60 + 0 * 6/60 = 47/30 = 1.567
How can you verify Euler’s formula for this net of a cube?
Step-by-step explanation:
for this the Pythagoras equation must be true :
c² = a² + b²
c is the Hypotenuse the dude opposite of the right angle in a right-angled triangle.
as such it had to be the longest side.
so, c = 26
and we get
26² = 24² + 25²
676 = 576 + 625 = 1201
wrong, 1201 is not equal to 676, so, 24, 25, 26 are NOT a pythagorean triplet.
theinitialstatementisfalse.
B. 112
C. 64
D. 96
The area of the given trapezoid is 56 sq.units.
A quadrilateral with at least one pair of parallel sides is called a trapezoid.
Given that, the two bases of a trapezoid are 3 and 11 and the altitude is 8
Area of a trapezoid = (sum of the two bases) / 2 × height
= (3+11) / 2 × 8
= 14 / 2 × 8
= 7 × 8
= 56
Hence, the area of the given trapezoid is 56 sq.units.
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a+b/2×h
3+11/2×8
14/2×8
7×8= 56 which is :A