1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175
2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.
3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.
4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
Answer:
<h3>No, it is not a right triangle</h3>
Step-by-step explanation:
In order to know whether the triangle is a right angle, we need to show that the square of the longest side is equal to the sum of the square of the other two sides
Longest side = 17in
other two sides = 8in and 9in
Check:
17² = 289
Sum of the square of other two sides
= 8² +9²
= 64 + 81
= 145
Since 17² ≠ 8² +9², hence the triangle that Landon created is not a right triangle
Answer:
they will need 18 tokens each because 2 + 3 + 4 x 2 = 9
Step-by-step explanation:
The answer is 21.
First you Add both AB and BC which is 10x +14. Then you put 64 into the equation. 10x+14=64. Subtract 14 from 64 which is 50. So 10x=50. Then divide 10 from 50. which would be x=5. So if you plug it in. It would be 21.
The answer is 22/5
You multiply 5 and 4, which you get twenty, then you add 2 and you get 22. Divide that by 5, and you get 22/5.
To double check, divide 22 by five and you should get 4.4, or 4 2/5 as a fraction
