David looks into two brick companies to construct the brick border for his garden. Evergreen landscapers charges an installation fee of $250 plus $0.20 per brick. Garden Works charges an installation fee of $400 plus $0.05 per brick. For what amount of bricks do the two companies charge the same amount?

For 1,000 bricks, the amount charged will be the same

Step-by-step explanation:

Let the number of bricks for which they charge the same amount be $x

Thus;

The total cost from the first company will

be;

250 + 0.2(x) = 250 + 0.2x

The second will charge;

400 + 0.05(x) = 400 + 0.05x

Since the amount charged will be equal at x bricks, we need to equate both;

400 + 0.05x = 250 + 0.2x

400-250 = 0.2x-0.05x

150 = 0.15x

x = 150/0.15

x = 1,000

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

the area of a triangle is determined by the formula: base x height * 1/2

you'll need to assign a base to the triangle. based on the vertices given, the simplest base would be the line segment from (-2,1) to (2,1). the distance between any two numbers is found by just subtracting them. here, you should subtract the x values to find the distance of this side.

2 - (-2) = 4.

so the distance (aka the length of the base) is 4. the height of the triangle is the distance between the base and the highest point on the triangle which is (3,4). we should subtract the y values this time to find the height/distance.

4 - 1 = 3

so the height is 3.

base = 4

height = 3

hope this if needed hmu