Answer: Maximum 6 miles
Step-by-step explanation: In total you have $20.
Base fare of taxi is $5.
Per mile cost is $2.50.
Your total cost is where x is the number of miles. Since you're on a budget of maximum $20, the cost should be less than or equal to $20. We can write:
To find how many miles we can write, let's solve the inequality:
.
This means 6 is the maximum number of miles you can ride with $20.
Answer:
Step-by-step explanation:
1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)
Two numbers that work are -6 and +1
-6 x +1 = -6
-6 + -1 = -5
2. Split the middle term into the two numbers that you found.
3x^2 -6x +x -2 = 0
I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.
3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'
3x (x-2) +1 (x-2) = 0
4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.
(3x + 1) (x-2) = 0
5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.
3x + 1 = 0 x-2 = 0
3x = -1 x = 2
x = -1/3
6. The solutions to this equation are x = 2 and x = -1/3
Answer:
b
Step-by-step explanation:
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is 35º. Find the height of the tree to the nearest foot.
