Answer! an independent home builder’s annual profit, in thousands of dollars, can be modeled by the function p left parenthesis x right parenthesis equals 5.152 x cubed minus 143 x squared plus 1102 x minus 1673, where x is the number of houses built in a year. his company can build at most 13 houses in a year. find the y-intercept and explain what it means in this context. find the x-intercept(s) for the profit equation given in number 1 and explain what they mean in this context.

Solution-

The profit function given in the question,

Where,

x = the number of houses built in a year

We can calculate y-intercept by putting x=0, so

y-intercept is -1673, i.e when x=0 or the number of houses built is 0, their profit is -1673. Actually it is not the profit, but loss. So if they don't build any house, they will lose $1673

We can calculate x-intercept or zeros by putting y=0, so

Calculating the zeros by graphing calculator, they are as follows,

x-intercept shows that they need to built at least 15 (as number house can not be fraction) houses, in order to start profiting. Even though they start profiting after building 2 houses, but then the profit starts decreasing and reaches 0 again and so does happen after building 11th house. (It might happen due to the other costs and investments used for building the houses ). But after finally building 15th house they start profiting.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right