Answer:
1
Step-by-step explanation:
you are just multiplying by the reciprocal here which would make this equal to 1
It is a binomial. Two terms: 3x, 1
A) We are told that at 2 hours, the velocity is 18 km/h and at 4 hours, the velocity is 4 km/h. Since we are relating two variables - let's give them names.
Let x = time and y = velocity. Since the velocity depends on the time (that is, the time influences velocity), this is a linear function. Any linear function can be written in slope intercept form as y = mx + b. The problem wants the situation in standard from of Ax + By = C, which can be found from slope intercept form.
So now we can make our line. Consider the ordered pairs of (2,18) and (4, 4) with them in (x, y) form. Finding the slope, m, between these points is as such:
m = y₂-y₁ / x₂-x₁
m = 4 - 18 / 4 - 2
m = -14 / 2 = -7.
Our slope is -7.
We take m = -7, x = 4, and y = 4 (it goes 4 km/h in 4 hrs) and use those three things to find the y-intercept.
y = mx + b
4 = -7 * 4 + b
4 = -28 + b
32 = b
So our equation of the line is y = -7x + 32. To put the equation into standard form, we need to place all the variables on one side of the equals sign, all the numbers on the other.
y = -7x + 32
7x + y = 32
In standard form, the equation for this situation is 7x + y = 32
***
To find out the velocity at 8 hours, we evaluate our function at x = 8. Either equation (standard form or slope intercept) works; we use standard form.
7x + y = 32
7*8 + y = 32
56 + y = 32
y = -24
At a time of eight hours, the bicycle is moving at -24 km/h.
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1) Write this as a ratio...
77.5 miles / 3.1 gallons = x miles / 8.2 gallons
Solve for x... multiply by 8.2 gallons on both sides (that cancels it on the right) side of the equation.
8.2 gallons * 77.5 miles / 3.1 gallons = x
635.5/ 3.1 = x
211.83 miles = x
Justin travels 211.83 miles on 8.2 gallons of gas
2) If we let boys = b, then girls has to be b + 15 (since there are 15 more girls than boys). Now together there are 85 members of the band so... boys + girls = 85 and since girls is b + 15, then...
b + b+15 = 85
Now solve for b. First combine like terms...
2b + 15 = 85
Now subtract 15 from each side (cancels the 15 on the left)
2b + 15 - 15 = 85 - 15
2b = 70
Now divide each side by 2 (cancels 2 on the left)
2b / 2 = 70 / 2
b = 35
So there are 35 boys in the band.
Just FYI, that also means there are 35+15 = 50 girls. Just so happens that 50 + 35 = 85 so our work checks!
