Formula of Area of triangle.... A=1/2bh where A is area, b is the base, and h is height.
h= 3b-1
Area=12
At this point you want to plug in what you know into the equation.
12=1/2b(3b-1)
Then you can solve for b. First multiply each side by 2 to cancel the fraction.
24=b(3b-1)
Then distribute the b term.
24=3b^2 - b
Then set the equation equal to zero.
0=3b^2-b-24
Then either factor or use the quadratic equation to solve for b.
0=(3b-8)(b-3)
which means that b=3 and b=8/3
You then plug both answers back into the original equation (12=1/2b(3b-1))and see if there are any extraneous solutions. When you do, you can see that 8/3 as an answer does not equal 12. Therefore, the correct answer and the base of the triangle is equal to 3.
This statement is true.
A pyramidal number tells the number of balls that could be stacked evenly with square bases. If were are looking for the nth pyramidal number, that is a pyramid with a square base that is n by n.
1. Let <em>y</em> represent the amount of money earned, and <em>x</em> the number of cars they wash. Then
<em>y</em> = 5<em>x</em>
Why? Each car wash costs $5. So no car washes means no earnings; 1 car wash earns $5; 2 washes earn $10; 3 washes earn $15, and so on, so that <em>x</em> car washes generate $5<em>x</em>.
2. No matter how many cars they end up washing, they will have spent $75 to set up the operation, so you subtract 75 from the equation is part (1).
3. Taking into account the setup cost of $75, the profit they make is given by
<em>y</em> = 5<em>x</em> - 75
4. When <em>x</em> = 0, meaning no cars get washed, the profit is -$75, meaning the team loses $75.
5. Set the profit function equal to 0 and solve for <em>x</em> :
5<em>x</em> - 75 = 0
5<em>x</em> = 75
<em>x</em> = 75/5
<em>x</em> = 15
So the team has to wash at least 15 cars to break even.
Using the Pythagorean theorem the length of x is 15.6 cm rounded to the nearest tenth.