One polynomial identity that crops up often in various areas is the difference of squares identity:
A2-b2=(a-b) (a+b)
We meet this in the context of rationalising denominators.
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Rewrite the second equation in same form as the first So we have
c + 4d = 8
c - 4d = -6 Now add:-
2c + 0 = 2
2c = 2
c = 1
Now substitute c = 1 in the first equation:-
1 + 4d = 8
4d = 7
d = 7/4 = 1 3/4
Answer c = 1 and d = 1 3/4 Answer
Answer:
(-1.703, 2.396)
(1.37, 6.493)
Step-by-step explanation:
We can easily solve this question by using a plotting tool or any graphing calculator,
The solution to the system of equation is given by the intersection points between the graphs of
y1 = −x^2 + x + 7
y2 = x^2 + 3x + 7
Please, see attached picture below.
The solutions are:
(-1.703, 2.396)
(1.37, 6.493)
Answer:
11.33 * 16.33 meters to the nearest hundredth.
Step-by-step explanation:
Let the width of the pool be x meters, then the length is x+5 meters.
The length of whole area = x + 5 + 2(3) = x + 11 meters and the width is
x + 2(3) = x + 6 meters.
So we have the equation (x + 6)(x + 11) = 387.
x^2 + 17x + 66 = 387
x^2 + 17x - 321 = 0
x = [-17 +/- sqrt (17^2 - 4*1*-321)] / 2
x = 11.33 meters
So the width is 11.3 m and the length is 16.33 meters.
