First, to the author of this piece of instruction. A system of equations would give multiple curves which intersect, as depicted here by a pair of crossing lines. But presumably here the solution space is intended to be the green area. That makes this a system of inequalities, not of equations. Fix it please, you're confusing the children.
We check each point to see if it's in the green space.
a) (2,2) CHECK
b) (0,4) nope
c) (6,1) CHECK
d) (1,6) nope
e) (-2,8) nope
Area of large triangle
= 1/2 bh
= 1/2 (5)(12)
= 1/2 (60)
= 30
area of un-shaded triangle
= 1/2bh
= 1/2(3)(4)
= 1/2 (12)
= 6
area of shaded = area of large triangle - area of un-shaded triangle
area of shaded = 30 - 6
area of shaded = 24
answer
24
The trick here is to recognize one or more factors common to each term. For example, 6x4 − 24x3 + 72x2 = x^2(6x^2 - 24x + 72), so x^2 is one common factor. Looking at (6x^2 - 24x + 72), you can easily see that 6 is a common factor, so now we have (6)(x^2)(x^2 - 4x + 12). These last 3 terms do not have a common factor, so the factoring process stops here:
(6)(x^2)(x^2 - 4x + 12)
Answer:
There are an infinite number of fractions in between numbers on a number line.
Step-by-step explanation:
The reason for this is because we have an infinite number of denominators to use. Therefore, we can not number the amount we use.
