Answer:
Step-by-step explanation:
We have the polynomial x^2 + 18x + 81 and are being asked to factor this into two binomials.
A rule that I follow is what two numbers multiplied make c (in this case 81) and when added make b (in this case is 18).
So what two numbers when :
A. Multiplied make 81
B. Added make 18
This would be 9.
Now that we have the answer, we can put it into binomials.
(x + 9)(x + 9)
Since these are the same, we can combine it and make it into one.
Answer:
Two sets are called disjoint if they have no elements in common. For example:
The sets S = { 2, 4, 6, 8 } and T = { 1, 3, 5, 7 } are disjoint.
Another way to define disjoint sets is to say that their intersection is the empty set,
Two sets A and B are disjoint if A ∩ B = 0.
In the example above,
S ∩ T = ∅ because no number lies in both sets.
Step-by-step explanation:
Now the width is w.
It's twice as long as wide, so now the length is 2w.
If the length is increased by 4 cm, the length will be 2w + 4.
The width is decreased by 3 cm, so the width will be w - 3.
The are of the new rectangle is 100 cm^2.
area = length * width
area = (2w + 4)(w - 3)
The area of the new rectangle is 100, so we get
(2w + 4)((w - 3) = 100
2w^2 - 6w + 4w - 12 = 100
2w^2 - 2w - 112 = 0
w^2 - w - 56 = 0
(w - 8)(w + 7) = 0
w - 8 = 0 or w + 7 = 0
w = 8 or w = -7
A width cannot be negative, so discard w = -7.
w = 8
The width is 8 cm.
The length is twice the width, so the length is 16 cm.
15x-10=20
+10 +10
15x=30
\15 /15
x=2
you add 10 to both -10 (they cancek eachother out) and 20 (equals 30)
Then you divide 30 by 15 (equals 2) and 15 by 15 (they cancel eachother out)
Then you get x=2
<u>Answer:</u>
<u>Step-by-step explanation:</u>
We can use the following rule of surds to solve the problem:
,
which means that when multiplying two numbers with the same bases, we can simply add their powers while keeping the base the same.
Applying this rule:
⇒ 
⇒ 
