Douglas bought a $20 game card at a game center. The go-karts cost $3.50 each
time you race. He wants to have at least
$7.75 left on his card to play arcade games.
Write and solve an inequality to determine
how many times Douglas can race the
go-karts. Then interpret the solution.

Douglas should race 3 or fewer times to make sure he has at least $7.75 left on his card.

Given to us

Douglas bought a $20 game card at a game center.

The go-karts cost $3.50 each time you race.

Douglas wants to have at least $7.75 left on his card to play arcade games.

Assumption

Let's assume that Douglas races x number of times on go-kart.

As we know the total balance on the card is $20. And the cost of go-karts is $3.50 each time we race. Also, we need to save $7.75 on the card, therefore, Inequality can be written as,

$20 - ($3.5)x ≤ $7.75

$20 - ($3.5)x ≤ $7.75

Hence, Douglas should race 3 or fewer times to make sure he has at least $7.75 left on his card.

Learn more about Inequality:

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Douglas can race the go-karts at least 3 times.

Step-by-step explanation:

Given that:

Worth of game card = $20

Cost of go-kart = $3.50 each time

Amount Douglas wants to left = $7.75

Let,

x be the times Douglas can ride go-kart.

20 - 3.50x ≤ 7.75

-3.50x ≤ 7.75 - 20

-3.50x ≤ -12.25

3.50x ≤ 12.25

Dividing both sides by 3.50

Hence,

Douglas can race the go-karts at least 3 times.

step-by-step explanation:

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2