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icang [17]
3 years ago
13

The smiths counted 11 riders and 26 wheels passing by. There were no unicycles, only bicycles and tricycles with only one rider.

How many more bicycles than tricycles did they see?
Mathematics
1 answer:
zimovet [89]3 years ago
6 0
I only one person rode a tricycle - that would leave 23 wheels and you cannot make a complete number of bicycles
If 2 people rode tricycles that would leave 20 wheels which would seat 10 bicyclists.
But that totals up to 12 people

3 people riding tricyles leaves 15 wheels which will not complete a number of bicycles

4 people riding tricycles (4 x 3) leaves 14 wheels for 7 bicyclist and is the answer

4 trike riders (12 wheels) + 7 bike riders (14 wheels) = 11 people and 26 wheels

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A triangle with an area of 60 square inches has a height that is 16 less than 6 times its base.
PtichkaEL [24]

Step-by-step explanation:

the area of a triangle

baseline × height / 2

in our case

baseline × height / 2 = 60 in²

height = 6×baseline - 16

baseline × (6×baseline - 16) / 2 = 60

baseline × (3×baseline - 8) = 60

3×baseline² - 8×baseline = 60

baseline = x

3x² - 8x - 60 = 0

general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 3

b = -8

c = -60

x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =

= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =

= (8 ± 28)/6

x1 = (8 + 28)/6 = 36/6 = 6

x2 = (8 - 28)/6 = -20/6 = -10/3

x2 as a negative number is not a valid solution for a length in a geometric shape.

so, x = 6 in is our solution for the baseline.

height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in

base = 6 in

5 0
2 years ago
How many solutions does this system have?
densk [106]

Answer:

One solution since x=0

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