Answer:
-13a^2 + 170ab - 13b^2.
Step-by-step explanation:
1. 36(a+b)^2 - 49(a-b)^2
This is the difference of 2 squares: a^2 - b^2 = (a + b)(a - b).
36(a+b)^2 - 49(a-b)^2
= (6(a + b) + 7(a - b))( 6(a + b) - 7(a - b))
= (6a + 7a + 6b - 7b)( 6a - 7a + 6b + 7b)
= (13a - b)(-a + 13b)
If you require the expansion of this it is:
-13a^2 + 170ab - 13b^2.
Answer:
x = -4 , y = 3
Step-by-step explanation:
5x - 7y = -41 ... (i)
-3x - 5y = -3 ... (ii)
Multiplying (i) by -3 and (ii) by 5 ;
-15x + 21y = 123 ... (i)
-15x - 25y = -15 ... (ii)
Subtracting (i) by (ii) ;
0 + 46y = 138
46y = 138
y = 138 ÷ 46 = 3
Returning to equation (ii) ;
-3x - 5(3) = -3
-3x = -3 + 15
-3x = 12
x = -4
Note that the 2nd equation can be re-written as y=8x-10.
According to the second equation, y=x^2+12x+30.
Equate these two equations to eliminate y:
8x-10 = x^2+12x+30
Group all terms together on the right side. To do this, add -8x+10 to both sides. Then 0 = x^2 +4x +40. You must now solve this quadratic equation for x, if possible. I found that this equation has NO REAL SOLUTIONS, so we must conclude that the given system of equations has NO REAL SOLUTIONS.
If you have a graphing calculator, please graph 8x-10 and x^2+12x+30 on the same screen. You will see two separate graphs that do NOT intersect. This is another way in which to see / conclude that there is NO REAL SOLUTION to this system of equations.
Answer:
The correct option is (A).
Step-by-step explanation:
The function representing the growth of number, in billions, of the DNA sequences in a database x years since 2010 is:
The general growth function can be represented as:
Here,
<em>y</em> = final value
<em>a</em> = initial value
<em>r</em> = growth rate
<em>t</em> = time
Com-paring the two functions we get:
This implies that the annual increase rate in number, in billions, of the DNA sequences is 32%.
Thus, the correct option is (A).
