The value of k is 2 if the polynomial x³ - 3x² - 10x + 24 is divided by the expression (x - 2).
<h3>What is synthetic division?</h3>
In the case of dividing by a linear factor, the synthetic division is a shorthand, or quicker, a technique of polynomial division.
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We have a polynomial:
x³ - 3x² - 10x + 24
Which is divided by (x - 2)
We can divide using the synthetic division:
The first row: 1 -3 -10 24
The entry outside the row: 2
The missing value which is 2
k = 2
Thus, the value of k is 2 if the polynomial x³ - 3x² - 10x + 24 is divided by the expression (x - 2).
Learn more about the synthetic division here:
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Answer:
0.555555556
Step-by-step explanation:
A) 5000 m²
b) A(x) = x(200 -2x)
c) 0 < x < 100
Step-by-step explanation:
b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground:
A(x) = x(200 -2x)
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a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m²
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c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.
Answer:
A. 40x + 10y + 10z = $160
B. 8 Roses, 2 lilies and 2 irises
C.
1. 20x + 5y + 5z = $80
2. 4x + y + z = $16
3. 8x + 2y + 2z = $32
Step-by-step explanation:
Cost for each flower = $160/5 = $32
So we have $32 for each bouquet consisting of 12 flowers each.
Roses = x = $2.50 each
lilies = y = $4 each
irises = z = $2 each
8x + 2y + 2z = $32
8($2.50) + 2($4) + 2($2) = $32
$20 + $8 + $4 = $32
$32 = $32
a. Maximum budget is $160
40x + 10y + 10z = $160
40($2.50) + 10($4) + 10($2) = $160
$100 + $40 + $20 = $160
$160 = $160
b. From above
8x + 2y + 2z = $32
8 Roses, 2 lilies and 2 irises
c. No. There are other solutions If total cost is not limited
1. 20x + 5y + 5z
20($2.50) + 5($4) + 5($2)
$50 + $20 + $10
= $80
2. 4x + y + z
4($2.50) + $4 + $2
$10 + $4 + $2
= $16
3. 8x + 2y + 2z
8($2.50) + 2($4) + 2($2)
$20 + $8 + $4
= $32
