Let's call the width . Since the length is three more than the width, it is
.
The area (which we know to be 70) is given by the multiplication of width and length:
To solve this equation, you can use the usual quadratic formula: given an equation , the two solutions are
which in your case becomes
So, two solutions are
Since we can't accept a negative length, we only accept the second solution.
So, the dimensions are 7 and 10
Answer:
Step-by-step explanation:
We can use the second expression to substitute for y in the first expression. Then we have ...
... 1/2x +11 = -7x^2 -9x +6
Subtracting the right side, we get
... 7x^2 +(9 1/2)x +5 = 0
Eliminating fractions by multiplying by 2, this is ...
... 14x^2 +19x +10 = 0
The discriminant of this equation will tell the number and kind of roots. For a=14, b=19, c=10, the discriminant is ...
... b^ -4ac = 19^2 -4·14·10 = 361 - 560 = -199
Since this value is negative, we know the two roots to the quadratic will be complex. There are no real solutions.
_____
The graph shows the two curves do not intersect, hence there are no values of x that will make the y-values match.
