<span>a2 – b2 = (a + b)(a – b) or (a – b)(a + b).
This is the 'Difference of Squares' formula we can use to factor the expression.
In order to use the </span><span>'Difference of Squares' formula to factor a binomial, the binomial must contain two perfect squares that are separated by a subtraction symbol.
</span><span>x^2 - 4 fits this, because x^2 and 4 are both perfect squares, and they are separated by a subtraction symbol.
All you do here to factor, is take the square root of each term.
√x^2 = x
√4 = 2
Now that we have our square roots, x and 2, we substitute these numbers into the form (a + b)(a - b).
</span>
<span>(a + b)(a - b)
(x + 2)(x - 2)
Our answer is final </span><span>(x + 2)(x - 2), which can also be written as (x - 2)(x + 2), it doesn't make a difference which order you put it in.
Anyway, Hope this helps!!
Let me know if you need help understanding anything and I'll try to explain as best I can.</span>
Answer:
x + y = 36.....Equation 1
x = 7 + 2y...... Equation 2
Step-by-step explanation:
Let the number of:
Orange goldfish = x
Black gold fish = y
Anna has a total of 36 goldfish in her aquarium, some are orange and some are black.
x + y = 36.....Equation 1
The number of orange goldfish is 7 more than twice the number of black goldfish.
x = 7 + 2y...... Equation 2
We can rewrite this as:
x - 2y = 7..... Equation 2
The system of equations below that can be used to describe the number of black and orange goldfish in Anna's aquarium is :
x + y = 36.....Equation 1
x = 7 + 2y...... Equation 2
Question 1
The given system of equations is:
Equate the two equations:
Rewrite in standard form:
When we put x=0, in y=3x +6, we get:
One solution is (0,6)
When we put x=-2, into y=3x+6, we get:
Another solution is (-2,0)
The solutions are; (0,6) and (-2,0)
Question 2:
The function is
Let us put x=-x,
This gives:
We can observe that:
This is the property of an even function.
Question 3:
The given function is
The average rate of change of f(x) from x=a to x=b is given as:
This is the slope of the secant line connecting the two points on f(x)
From x=2 to x=6, the average rate of change
The average rate of change is 11
To determine the value of X in the given equation substitute the value of y into the equation and solve for x.
1/5x - 2/3y = 30
1/5x - 2/3(15) = 30
1/5x -10 = 30
1/5x - 10 + 10 = 30 + 10
1/5x = 40
1 = 5x • 40
1 = 200x
X = 1/200.
