The <em>twelfth</em> element of the <em>geometric</em> sequence is equal to 4,096. (Correct choice: D)
<h3>How to find a determined element of a geometric sequence by exponential formulae</h3>
Sequences are series of elements generated according to at least one condition, usually equations. <em>geometric</em> sequences are generated according to a <em>exponential</em> formulas, whose form and characteristics are described below:
f(n) = a · bⁿ ⁻ ¹ (1)
Where:
- a - First element of geometric sequence
- b - Common ratio of the geometric sequence
- n - Element index within the geometric sequence
If we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:
f(12) = 4 · 2¹² ⁻ ¹
f(12) = 4 · 2¹¹
f(12) = 4 · 2,048
f(12) = 4,096
The <em>twelfth</em> element of the <em>geometric</em> sequence is equal to 4,096. (Correct choice: D)
To learn more on geometric sequences: brainly.com/question/4617980
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<h2>
Step-by-step explanation:</h2>
Given equations;
y₁ = 3x - 8 -------------------(i)
y₂ = 0.5x + 7 --------------------(ii)
To fill the table, substitute the values of x into equations (i) and (ii)
=> At x = 0
y₁ = 3(0) - 8 = -8
y₂ = 0.5(0) + 7 = 7
=> At x = 1
y₁ = 3(1) - 8 = -5
y₂ = 0.5(1) + 7 = 7.5
=> At x = 2
y₁ = 3(2) - 8 = -2
y₂ = 0.5(2) + 7 = 8
=> At x = 3
y₁ = 3(3) - 8 = 1
y₂ = 0.5(3) + 7 = 8.5
=> At x = 4
y₁ = 3(4) - 8 = 4
y₂ = 0.5(4) + 7 = 9
=> At x = 5
y₁ = 3(5) - 8 = 7
y₂ = 0.5(5) + 7 = 9.5
=> At x = 6
y₁ = 3(6) - 8 = 10
y₂ = 0.5(6) + 7 = 10
=> At x = 7
y₁ = 3(7) - 8 = 13
y₂ = 0.5(7) + 7 = 10.5
=> At x = 8
y₁ = 3(8) - 8 = 16
y₂ = 0.5(8) + 7 = 11
=> At x = 9
y₁ = 3(9) - 8 = 19
y₂ = 0.5(9) + 7 = 11.5
=> At x = 10
y₁ = 3(10) - 8 = 22
y₂ = 0.5(10) + 7 = 12
The complete table is attached to this response.
(ii) To find the solution of the system of equations using the table, we find the value of x for which y₁ and y₂ are the same.
As shown in the table, that value of <em>x = 6</em>. At this value of x, the values of y₁ and y₂ are both 10.
Answer:
112 tiles
Step-by-step explanation:
Area = 28ft sq
Tiles are 1/4 each sqft
We are working cube square inside cube ft square = 1 sq /4 (for multiplier).
= 4 x 28 = 112
112 x 0.25 = 28 to check.
112 x 0.25 x 4 = 112 is the multiplier to check again.
Answer:
The area of the shaded region is the difference between the areas of the rectangle and the square.
Step-by-step explanation:
Answer:
If you had 5 apples and Johnny gave you five more how much do you have? Lets count
10 OMG 5+5 is 10
