Answer:
rule: f(n) = n³
missing numbers: 125, 216, 343, 512, 729
Step-by-step explanation:
Your familiarity with the cubes of small integers helps you recognize each of these numbers is a cube. Their sequence is the sequence of cubes of increasing natural numbers.
1 = 1·1·1 = 1³
8 = 2·2·2 = 2³
27 = 3·3·3 = 3³
64 = 4·4·4 = 4³
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The rule is ...
f(n) = n³
The cubes of 5 through 9 will complete the set of numbers ...
1, 8, 27, 64, 125, 216, 343, 512, 729
The measurements are:
b₁ = 8.4 inches; b₂ = 14 inches; leg₁ = 2.8 inches; leg₂ = 2.8 inches
Let x = length of base and leg
The formula for perimeter of isosceles trapezoid is P = b₁ + b₂ + 2(leg)
Where: b = base
P = b₁ + b₂ + 2(leg)
28 = 3x + 5x + 2(x)
28 = 8x + 2x
28/10 = 10x/10
2.8 = x
Now, substitute the values:
P = b₁ + b₂ + 2(leg)
28 = 3(2.8) + 5(2.8) + 2(2.8)
28 = 8.4 + 14 + 5.6
28 = 28
Hence the measurements are:
b₁ = 8.4 inches; b₂ = 14 inches; leg₁ = 2.8 inches; leg₂ = 2.8 inches
9514 1404 393
Answer:
₹14000
Step-by-step explanation:
Let c represent the cost price, and m represent the marked price.
c × (1 +40%) = m
m × (1 -15%) - c = ₹1900
Using the first expression for m, the second equation becomes ...
1.40c×0.85 -c = ₹1900
0.19c = ₹1900
c = ₹1900/0.19 = ₹10000
Then the marked price was ...
m = 1.40c = 1.40×₹10000 = ₹14000
The marked price was ₹14000.
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The selling price was ₹11900.
Any number that can be writen as a fraction example: 0.75, -15, 0, 9
