Answer:
10.4 miles
Step-by-step explanation:
Write an equation for the total cost paid as a function of the # of miles driven:
L(x) = $6.75 + ($3.20/mile)x
and set this equal to $40.03 to determine the # of miles Lupita rode:
L(x) = $6.75 + ($3.20/mile)x = $40.03
Isolate the x term by subtracting $6.75 from both sides:
($3.20/mile)x = $40.03 - $6.75 = $33.28
Finally, divide both sides by ($3.20/mile):
x = $33.28 / ($3.20/mile)
= 10.4 miles
Lupita rode 10.4 miles in the taxi.
Answer:
f(x) = 1.5x - 0.5x
Step-by-step explanation:
The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.
The triangular number general formula
x (x + 1) / 2
For example,
The sequence
1, 3, 6, 10
*
* * *
* * * * * *
* , * *, * * *, * * * *
_____________________________
The pentagonal numbers
The sequence:
1, 5, 12, 22, 35
As shown in the picture can be divided into three triangles
Triangle 2
x (x + 1) / 2
Triangle 1 and 3 (they are triangles one unit smaller than 2)
n (n + 1) / 2
n= x-1
Replacing n
(x-1) ((x-1) + 1) / 2
(x-1) (x) / 2
(x-1) x / 2
______________
Function represents the pattern
Triangle 2 + (Triangle 1 + Triangle 3)
Triangle 1 = Triangle 3
So then,
Triangle 2 + 2* Triangle 1
x (x +1) /2 + 2* (x -1) x/2
Rearranging
0.5 x (x +1) + x(x -1)
0.5x^2 + 0.5x + x^2 -x
(0.5 x^2 + x^2) + (0.5x -x )
1.5 x^2 - 0.5 x
______
Answer:
A
Step-by-step explanation:
Cost of the car in "n" years=25000*(1+0.05)^n
Cost of the car in 2 years=25000*(1+0.05)^2=25000*(1.05)^2=27562.5
Answer:
Total number of students= 7+ 9+4+5= 25
Tennis: total= 5:25= 1:5 (simplify by dividing both sides by 5
When an exponential function is given as
f(x)=ab^x, and
knowing that b^0=1, that means that
f(0)=ab^0=a value of function when x=0, or the initial value.
In the case of
f(x)=20.b^x, f(0)=20.b^0 = 20 (initial value)
If b=1.2, then the hourly growth rate is (1.2-1)=0.2=20%.
If b=1.85, then the hourly growth rate is (1.85-1)=0.85=85%.