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:
260%
Step-by-step explanation:
For the coffee;
cost price (
) = $5/kg
selling price (
) = $18/kg
Percentage profit (%P) = 
%
Substitute the right values into the above;
%P = 
%
%P = 
%
%P = 260%
Therefore, the percentage profit compared to the original cost of the coffee is 260%
Answer:
b is the odd one out
Step-by-step explanation:
30/70= .428
12/30= .4
9/21= .428
6/14= .428
all are equal except 12/30
hope this helped!
Answer:
It is called a linear system. :)
Answer:
this is the anwser
Step-by-step explanation:
4 12 13 triangle
Obtuse scalene triangle.
Sides: a = 4 b = 12 c = 13
Area: T = 23.894
Perimeter: p = 29
Semiperimeter: s = 14.5
Angle ∠ A = α = 17.839° = 17°50'19″ = 0.311 rad
Angle ∠ B = β = 66.782° = 66°46'55″ = 1.166 rad
Angle ∠ C = γ = 95.379° = 95°22'46″ = 1.665 rad
Height: ha = 11.947
Height: hb = 3.982
Height: hc = 3.676
Median: ma = 12.349
Median: mb = 7.517
Median: mc = 6.144
Inradius: r = 1.648
Circumradius: R = 6.529
Vertex coordinates: A[13; 0] B[0; 0] C[1.577; 3.676]
Centroid: CG[4.859; 1.225]
Coordinates of the circumscribed circle: U[6.5; -0.612]
Coordinates of the inscribed circle: I[2.5; 1.648]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 162.161° = 162°9'41″ = 0.311 rad
∠ B' = β' = 113.218° = 113°13'5″ = 1.166 rad
