Answer: Choice D
This basically says "the nth term is found by computing math, aka evaluating some function, based on the (n-1)th term".
As an example, we could have a function that simply squares the input
Let's say we started at 5. It squares to 25 which in turns squares to 625, and so on. Each new term is based on the old term. Namely, we squared the old n-1 term to get the new nth term.
From the definition of a function, a function associates every element of the domain to a unique element in the codomain.
In other words, if two elements are equal in the domain, then their images should also be equal.
Since, x represents the number of cars, we consider the universal set as N, the set of all natural numbers.
Let x, y ∈ N and x = y
Then, 0.75x = 0.75y
⇒ f(x) = f(y)
Therefore, images are equal, whenever elements are equal.
Hence, the function f(x) = 0.75x is a function. Also, note that the domain of the function is the set of all natural numbers and the range is the set of real numbers.
Answer:
paper clips = $1.85
index cards = $3.95
Step-by-step explanation:
Mark
12 paper clips = x
10 index cards = y
$61.70 total
Janice
15 paper clips = x
7 index cards = y
$55.40 total
12x + 10y = 61.70
15x + 7y = 55.40
*** you want to cancel out one of the letters
(12x + 10y = 61.70) * -7
(15x + 7y = 55.40) * 10
-84x -70y = -431.9
150x + 70y = 554.0
150x + 70y = 554.0
-84x -70y = -431.9
66x + 0 = 122.1
66x = 122.1
x = 122.1 ÷ 66
x = 1.85
plug it back in
15(1.85) + 7y = 55.40
27.75 + 7y = 55.40
7y = 55.40 - 27.75
7y = 27.65
y = 27.65 ÷ 7
y = 3.95
Answer:
160 miles
Step-by-step explanation:
Company A form $130 a day plus $0.30 per mile
Company A = 130 + 0.30x
Company B charges $50 a day plus $0.80 per mile
Company B = 50 + 0.80x
Where,
x = number of miles
Equate the cost of company A and company B
130 + 0.30x = 50 + 0.80x
Collect like terms
130 - 50 = 0.80x - 0.30x
80 = 0.50x
Divide both sides by 0.50x
x = 80 / 0.50
= 160
x = 160 miles
The number of miles in a day at which the rental costs for Company A and Company B are the same is 160 miles
Answer:
3x-22=80+x
3x-x=80+22
2x=102
x=51
Step-by-step explanation:
the exterior angle is (3x-22) and then is equal to sum of 80 and x
and then we get 51
