Answer:
56
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₆ = 17 and a₁₃ = 38, then
a₁ + 5d = 17 → (1)
a₁ + 12d = 38 → (2)
Subtract (1) from (2) term by term to eliminate a₁
7d = 21 ( divide both sides by 7 )
d = 3
Substitute d = 3 into (1) and evaluate for a₁
a₁ + 5(3) = 17
a₁ + 15 = 17 ( subtract 15 from both sides )
a₁ = 2
Thus
= 2 + (18 × 3) = 2 + 54 = 56
To evaluate, we need to follow the order of operations. Below are the steps taken in order:
16 * 3 + [(17 - 3) / 2] - 43
16 * 3 + [14 / 2] - 43
16 * 3 + 7 - 43
48 + 7 - 43
55 - 43
12
Therefore the answer is 12.
Answer:
The ratio that compares the diameter of the first circle to the diameter of the second circle is
Step-by-step explanation:
Circumference of a circle:
The circumference of a circle of diameter d is given by:
In which d is the diameter.
One circle has a circumference half as large as that of a second circle.
We have that:
So
Simplifying by
The ratio that compares the diameter of the first circle to the diameter of the second circle is
4x - 2y ≤ 6 <em>subtract 4x from both sides</em>
-2y ≤ -4x + 6 <em>change the signs</em>
2y ≥ 4x - 6 <em>divide both sides by 2</em>
<h3>y ≥ 2x - 3</h3>
y = 2x - 3 - it's a linear function. We need only two points to plot the graph.
Choose any two values of x and calculate the values of y:
for x = 0 → y = 2(0) - 3 = 0 - 3 = -3 → (0, -3)
for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1)
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<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded to left
>, ≥ - shaded to right