Answer:
f(n) = - 0.5n + 6
Step-by-step explanation:
Because Vince cuts down his television watching at a steady pace, his situation models a linear function. As such, we can use slope-intercept form to write and predict his hours watching tv in n weeks.
Slope-intercept form is y=mx+b. In this case, we are choosing to use f(n) instead of y to show the number of hours he is watching tv. We are also choosing to use n weeks instead of x. So we have the form f(n)=mn+b.
We know that Vince starts out at watching 6 hours a week. This is our initial value known as the y-intercept and represented by b. As each week passes, he will decrease from the previous week by 30 minutes or -0.5 hours since 30 out of 60 minutes is 0.5. And since he is decreasing it should be a negative rate of -0.5 and is represented by m.
We substitute b=6 and m=0.5 into our form to get f(n)=-0.5n+6. Let's test week 1. After 1 week he should be down from 6 hours to 5.5 hours or 5 hours and 30 minutes. Let's substitute n=1.
f(n)=-0.5(1)+6=-0.5+6=5.5
We can substitute for any n week and find the amount.
Answer:
Step-by-step explanation:
We can write the following system of equations:
, where 
is the number of dimes she has and 
is the number of nickels she has.
Multiply the second equation by 
and add both equations to solve for :
.
Plug 
into any equation to solve for :
Answer:
40.374 ft
Step-by-step explanation:
We assume that the height of the goal on the football field is <em>h </em>(ft)
As it can be seen, the height of the goal is equal to the total of the man's height and the length of AB.
=> h = 5.5 + AB
The triangle ABC in the figure is the right angled triangle with Angle B = 90 degree and BC = 10 ft
In a right triangle, we have the equation as following:
+) tan of an acute angle = length of opposite side/ length of the adjacent side
We have: Angle C = 74 is an acute angle, its opposite side is AB, adjacent side is BC
=> tan Angle C = AB/ BC
=> tan 74° = AB/ 10
=> AB = 10. tan 74° = 34.874 ft
=> h = 5.5 + AB =5.5 + 34.874 = 40.374 ft
The density is 0.1019g/cm3
