When 7 times a number is added to the square of the number, the sum is 3. what is the number?

Step-by-step explanation:

1. Set up the equation

  Let x = the number. Then

      7x = seven times the number and

       x² = the square of the number

x² + 7x = seven times the number added to the square of the number

x² + 7x = 3

Subtract 3 from each side

x² + 7x - 3 = 0

2. Solve the quadratic equation

Use the quadratic formula: a = 1; b = 7; c = -3.

The graph of your quadratic crosses the x-axis at (-7.405,0) and (0.405,0).

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5