Hello
<span>an equation for the line in point-slope form and general form is :
y = ax+b a : </span>slope ; the <span>Passing through (x' ; y')
</span>y' = ax'+b
y-y' =a(x-x') and : x' =2 y' = - 1
calculate a :
let : y = ax+b .....(D)
....<span>3y-x=7</span>....(D') or y = (1/3)x+7/3
.(D) perpendicular to(D') : slope (D) × slope (D') = -1
slope (D') = 1/3
slop(D)×(1/3) = -1
slope (D) = -3
equation for the line : y-y' =a(x-x')
y+1 =(-3) (x-2)
Answer:
2.2 hr
Step-by-step explanation:
Let t = time
95t = distance of westbound train
105t = distance of eastbound train
95t + 105t = 440
200t = 440
t = 2.2 hr.
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.
Based on the graph,
f(x) = 1/2x+3
g(x) = -x+4
so, h(x) = -1/2 x +7
Since h'(x) is the derivative or slope of h(x) and h is a line,
h'(x) = -1/2, Answer C.
