|4x-9|=5x
subtract 4 to both sides
and that will give you
|-9|=x then the 9 turns positive because of the brackets
9=X
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
The quadratic function given by:
is in vertex form. The graph of 
is a parabola whose axis is the vertical line 
and whose vertex is the point 
. So:
To translate the graph of a function to the right, left, upward or downward we have:
By knowing this things, we can solve our problem as follows:
FIRST.
- Translating <em>11 units to the left:</em>
- Then translating<em> 5 units down:</em>
Since the new function is fatter, the factor we need to multiply the term 
<em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.
<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>
SECOND.
- Translating <em>8 units to the right:</em>
- Then translating<em> 1 unit down:</em>
As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.
<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>
The total area is 1289.41 units².
The total perimeter is 281.32 units.
<h3>What is the total area and perimeter?</h3>
The first step is to determine the side lengths of the other squares:
- Length of the second square = 2/3 x 27 = 18
- Length of the third square = 2/3 x18 = 12
- Length of the fourth square = 2/3 x 12 = 8
- Length of the fifth square = 2/3 x 8 = 5.33
Area of a square = length²
Perimeter of a square = 4 x length
- Area of the first square = 27² = 729
- Area of the second square = 18² = 324
- Area of the first square = 12² = 144
- Area of the first square = 8² = 64
- Area of the first square = 5.33² = 28.41
Total area = sum of the areas of the 5 squares = 1289.41 units²
- Perimeter of the first square = 4 x 27 = 108 units
- Perimeter of the second square = 4 x 18 = 72
- Perimeter of the third square = 4 x 12 = 48
- Perimeter of the fourth square = 4 x 8 = 32
- Perimeter of the fifth square = 4 x 5.33 = 21.32
Total perimeter = 281.32 units
To learn how a square, please check: brainly.com/question/9030544
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Answer:
Step-by-step explanation:
To calculate the result of that mutiplication you have to firs evaluate the first term of the second function multipying the whole first function, woudl be like this:
Now that you have this, you multiply the second term from the second function to obtain:
Now you just have to add both results:
+ 
And the result of the sum would be:
