Answer:
an = 17n - 46
a50 = 804
Step-by-step explanation:
-29, -12, 5, 22, ...
Subtract each number from the next one.
-12 - (-29) = 17
5 - (-12) = 17
22 - 5 = 17
The common difference is 17. This is an arithmetic sequence which starts with -29, and in which each subsequent value is 17 more than the previous value.
a1 = -29
a2 = -29 + 17
a3 = -29 + 2(17)
a4 = -29 + 3(17)
Notice that for each term, you have -29 and something added to it. What you add to -29 is 17 multiplied by 1 less than the number of the term. For term 1, 1 less than 1 is 0. You add 0 * 17 to -29 and get -29. term 1 is -29. For term 2, 1 less than 2 is 1. You add 1 * 17 to -29 and get -12, etc.
For term n, 1 less than n is n - 1. Add (n - 1) * 17 to -29 to get term n.
an = -29 + 17(n - 1)
This formula can be simplified.
an = -29 + 17n - 17
an = -46 + 17n
an = 17n - 46
a50 = 17(50) - 46
a50 = 804
The delivery man can carry about 14 boxes of books
There are 1760 yards in a mile. 1760 x 3 = 5280
Hope this helped!
To get the solution, we are looking for, we need to point out what we know.
<span>1. We assume, that the number 42.5 is 100% - because it's the output value of the task. </span>
<span>2. We assume, that x is the value we are looking for. </span>
<span>3. If 42.5 is 100%, so we can write it down as 42.5=100%. </span>
<span>4. We know, that x is 76.8% of the output value, so we can write it down as x=76.8%. </span>
5. Now we have two simple equations:
1) 42.5=100%
2) x=76.8%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
42.5/x=100%/76.8%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 76.8% of 42.5
42.5/x=100/76.8
<span>(42.5/x)*x=(100/76.8)*x - </span>we multiply both sides of the equation by x
<span>42.5=1.30208333333*x - </span>we divide both sides of the equation by (1.30208333333) to get x
<span>42.5/1.30208333333=x </span>
<span>32.64=x </span>
x=32.64
<span>now we have: </span>
<span>76.8% of 42.5=32.64</span>
Given: In Δ ABC, ∠B =90° , ∠C = 30° , ∠A = 60° and Hypotenuse AC = 10 inches
It has been described in the attachment.
Now, we shall calculate side AB and BC by using Trigonometric Ratios.
Sin 30° = AB / AC
or, AB = 10 × Sin 30° = 10 × 0.5 = 5 inches
And, Cos 30° = CB / AC
or, CB = 10 × Cos 30° = 10 × 0.866 = 8.66 inches
Now, we shall calculate the perimeter of the given triangle
Perimeter of the triangle = AB + BC + CA
or, = (5.0 + 8.66 + 10.0 ) inches
or, = 23.66 inches ≈ 23.7 inches
Hence, the best estimate for the perimeter of the triangle ( round to the nearest tenth will be 23.7 inches.
