Answer:
Morning's average rate = 50 mph, and Afternoon's average rate = 25 mph.
Step-by-step explanation:
Suppose he drove 150 miles for X hours, then his average rate in the morning was (150/X) mph.
Given that he spent 5 hours in driving.
And he drove 50 miles for (5-X) hours, then his average rate in the afternoon was 50/(5-X) mph.
Given that his average rate in the morning was twice his average rate in the afternoon.
(150/x) = 2 * 50/(5-x)
150/x = 100/(5-x)
Cross multiplying terms, we get:-
150*(5-x) = 100*x
750 - 150x = 100x
750 = 100x + 150x
750 = 250x
x = 750/250 = 3.
It means he spent 3 hours in the morning and 2 hours in the afternoon.
So morning's average rate = 150/3 = 50 mph.
and afternoon's average rate = 50/(5-3) = 25 mph.
Using quadratic formula
x = [-18 +-sq root (324 -4 *3*15)] / 2*3
x = [-18 +-sq root (144)]/6
x1 = (-18 + 12) / 6 = -1
x2 = (-18 -12) / 6 = -30/6 = -5
Answer:
New cars sold = 20,
Used cars sold = 25
Cars serviced = 290
Step-by-step explanation:
In a month they sold fifteen less used cars than twice the number of new cars.
Lets say 'x' number of new cars were sold, then:
The number of used car sold is:
![2\times x-15=2x-15](https://tex.z-dn.net/?f=2%5Ctimes%20x-15%3D2x-15)
In the same month they serviced fifty more than twelve times the number of new cars sold. So the number of cars serviced is:
![12\times x+50=12x+50](https://tex.z-dn.net/?f=12%5Ctimes%20x%2B50%3D12x%2B50)
Altogether they sold or serviced 335 cars, so the sum of all the cars sold and serviced should be 335:
![x+(2x-15)+(12x+15)=335](https://tex.z-dn.net/?f=x%2B%282x-15%29%2B%2812x%2B15%29%3D335)
Solving for 'x' we get:
![x+2x+12x-15+50=335](https://tex.z-dn.net/?f=x%2B2x%2B12x-15%2B50%3D335)
![15x+35=335](https://tex.z-dn.net/?f=15x%2B35%3D335)
![15x=335-35=300](https://tex.z-dn.net/?f=15x%3D335-35%3D300)
![x=\frac{300}{15}=20](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B300%7D%7B15%7D%3D20)
Therefore, the number of new cars sold in that month is 20.
Number of used car sold ![=2x-15=2\times 20-15=40-15=25](https://tex.z-dn.net/?f=%3D2x-15%3D2%5Ctimes%2020-15%3D40-15%3D25)
Number of cars serviced ![=12\times x+50=12\times20+50=240+50=290](https://tex.z-dn.net/?f=%3D12%5Ctimes%20x%2B50%3D12%5Ctimes20%2B50%3D240%2B50%3D290)
We can also cross check by summing them up:
![290+25+20=335](https://tex.z-dn.net/?f=290%2B25%2B20%3D335)
Answer:
True
Step-by-step explanation:
same numbers on both sides = equivalent expression
Answer:
![\frac{8h}{\sqrt{2}} + 16h](https://tex.z-dn.net/?f=%5Cfrac%7B8h%7D%7B%5Csqrt%7B2%7D%7D%20%2B%2016h)
Step-by-step explanation:
First we need to compute the side length as a function of h
So x be the side length of the right isosceles triangle, in Pythagorean formula we have
![x^2 + x^2 = h^2](https://tex.z-dn.net/?f=x%5E2%20%2B%20x%5E2%20%3D%20h%5E2)
![2x^2 = h^2](https://tex.z-dn.net/?f=2x%5E2%20%3D%20h%5E2)
![x = \frac{h}{\sqrt{2}}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7Bh%7D%7B%5Csqrt%7B2%7D%7D)
The cost for the legs is
![C_l = 4*2x = \frac{8h}{\sqrt{2}}](https://tex.z-dn.net/?f=C_l%20%3D%204%2A2x%20%3D%20%5Cfrac%7B8h%7D%7B%5Csqrt%7B2%7D%7D)
The cost for the hypotenuse is
![C_h = 16h](https://tex.z-dn.net/?f=C_h%20%3D%2016h)
So the total cost in term of h is
![C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h](https://tex.z-dn.net/?f=C%20%3D%20C_l%20%2B%20C_h%20%3D%20%5Cfrac%7B8h%7D%7B%5Csqrt%7B2%7D%7D%20%2B%2016h)