Answer:
the 21st day
Step-by-step explanation:
21 is 3 and 7's least common multiple
(x-8) ^ 2 = 121
(x-8) = + / - root (121)
x = 8 +/- root (121)
The solutions are:
x1 = 8 + root (121)
x2 = 8 - root (121)
2a ^ 2 = 8a-6
2a ^ 2-8a + 6 = 0
a ^ 2-4a + 3 = 0
(a-1) (a-3) = 0
The solutions are:
a1 = 1
a2 = 3
x ^ 2 + 12x + 36 = 4
x ^ 2 + 12x + 36-4 = 0
x ^ 2 + 12x + 32 = 0
(x + 4) (x + 8) = 0
The solutions are:
x1 = -8
x2 = -4
x ^ 2-x + 30 = 0
x = (- b +/- root (b ^ 2 - 4 * a * c)) / 2 * a
x = (- (- 1) +/- root ((- 1) ^ 2 - 4 * (1) * (30))) / 2 * (1)
x = (1 +/- root (1 - 120))) / 2
x = (1 +/- root (-119))) / 2
x = (1 +/- root (119) * i)) / 2
The solutions are:
x1 = (1 + root (119) * i)) / 2
x2 = (1 - root (119) * i)) / 2
Answer:
[Vertex form]
Step-by-step explanation:
Given function:

We need to find the vertex form which is.,

where
represents the co-ordinates of vertex.
We apply completing square method to do so.
We have

First of all we make sure that the leading co-efficient is =1.
In order to make the leading co-efficient is =1, we multiply each term with -3.


Isolating
and
terms on one side.
Subtracting both sides by 15.


In order to make the right side a perfect square trinomial, we will take half of the co-efficient of
term, square it and add it both sides side.
square of half of the co-efficient of
term = 
Adding 36 to both sides.


Since
is a perfect square of
, so, we can write as:

Subtracting 21 to both sides:


Dividing both sides by -3.

[Vertex form]
Answer:
4
hours
Step-by-step explanation:
he was gone for 5
hours, he spent
an hour driving.
5
-
= 4
hours at work.
1/2 = 0.5
12 & 1/2 = 12 + 1/2 = 12 + 0.5 = 12.5
4 & 1/2 = 4 + 1/2 = 4 + 0.5 = 4.5
Refer to the diagram below. Note how I divided the figure into two rectangles.
The larger red rectangle is 12.5 feet by 10 feet. It has area 12.5*10 = 125 square feet.
The smaller blue rectangle has dimensions 4.5 feet by 5 feet (the 5 is from 15-10 = 5), so it has area 4.5*5 = 22.5 square feet
Now add up those individual areas to get the total area
125+22.5 = 147.5
Then convert that to a mixed number
147.5 = 147 + 0.5 = 147 + 1/2 = 147 & 1/2
<h3>The correct area is 147 & 1/2 feet</h3>