The break-even point is when revenue, R(h) is the same as cost, C(h). R(h)=C(h) 220h-160 = 20h²-400 Gather all the variables on one side by subtracting 220h: 220h-160-220h = 20h²-400-220h -160=20h²-220h-400 (we can move these around so long as we take their respective signs with them) We want our quadratic equation to equal 0 to solve it, so add 160 to both sides: -160+160=20h²-220h-400+160 0=20h²-220h-240 All 3 terms of this quadratic are divisible by 20, we can factor 20 out: 0 = 20(h² - 11h - 12) The quadratic that is left is easily factorable. We want factors of -12 that sum to -11; that would give us -12*1, because -12+1 = -11. Thus we have 0 = 20(h - 12)(h + 1) Using the zero product property, we know that one of the factors must be 0 in order for the product to be 0. 20 ≠ 0, so it must be either h-12 or h+1: h-12 = 0 Add 12 to both sides: h - 12 + 12 = 0 + 12 h = 12
h+1 = 0 Subtract 1 from both sides: h + 1 - 1 = 0 - 1 h = -1
Since a negative number of hours is not realistic, the answer must be h = 12 hours.
there are 100 cm in every meter which means that dividing will convert ot to meters. you can make the conversion quick and easy by simply moving the decimal point in your measurement 2places or place values to left