The sum of a number and its square is 90. Find the number.

1 answer:

8 0

<h2><u>Answer: 9</u></h2><h2><u>Step-by-step explanation</u></h2><h2><u>Explanation:</u></h2><h2><u>Let n be the integer in question. Then we have</u></h2><h2><u>We now have a quadratic equation to solve. We could use the quadratic formula, however we know that </u></h2><h2><u>n</u></h2><h2><u> is an integer, so instead let's try to solve by factoring instead.</u></h2>

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The first step is to ignore the inequality symbol first and replace it with '=' sign. Then, find the x- and y-intercepts.

15x + 10y = 1,100

x-intercept:

15x + 0 = 1,100

x = 1,100/15 = 73.33

y-intercept:

0 + 10y = 1,100

y = 1,100/10 = 110

Now, plot points (73.33,0) and (0,110). Since the equality symbol is ≥, which has an equal sign to it, connect the points using a solid line.

Next, let's find a point on the graph. Suppose it is the origin at (0,0). Use this points to the equation.

15x + 10y ≥ 1,100

15(0) + 10(0) ? 1,100

0 ? 1,100

0 < 1,100

It makes the symbol ≥ false. Therefore, it means that the other region bounded by the line is the solution. So, you shade this area. The final graph is shown in the picture attached.