Answer: The answer is 8.
Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;
Y^2 - 40.
Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,
Y^2 - 40 = 3Y
If we move all expressions to one side of the equation, what we would have is,
Y^2 - 3Y -40 = 0
(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
We now have a quadratic equation
Y^2 -3Y - 40 = 0
By factorizing we now have
(Y -8) (Y + 5) = 0
Therefore Y - 8 = 0 or
Y + 5 = 0
Hence, Y = 8 or Y = -5
Since we are asked to calculate the positive solution, Y = 8
Option c is your answer 3xy + 7x4
Answer:
y = 3x - 2
Step-by-step explanation:
Use the point-slope equation since we are given a point that the line passes through and its slope:
y - y1 = m(x - x1)
(-2, -8), m = 3
Substitute these values into the equation.
- y - (-8) = 3(x - (-2))
- y + 8 = 3(x + 2)
- y + 8 = 3x + 6
- y = 3x - 2
The equation of the line that passes through the point (-2, -8) and has a slope of 3 is y = 3x - 2.
9514 1404 393
Answer:
- 3n+6 (n = smallest)
- 3n (n = middle)
Step-by-step explanation:
The usual method for doing this is to let n represent the smallest one. Then the three integers are ...
n, n+2, and n+4
and their sum is ...
(n) +(n+2) +(n+4) = 3n+6 . . . . sum of 3 consecutive odd integers (n = smallest)
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Personally, for consecutive number problems, I prefer to let the variable represent the average value. If n is the average value of 3 consecutive odd integers, is is the middle integer. Of course, the sum will be 3 times the average:
(n-2) +(n) +(n+2) = 3n . . . . sum of 3 consecutive odd integers (n = middle one)
