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4 years ago

5. & 7. simplify 9. & 11. factor completely

Mathematics

1 answer:

snow_tiger [21]4 years ago

5 0

5)

= - i - 2 - 3i
= - 4i - 2
= - 2 (2i + 1)

7)

= - 4 [(2 -2i - i (8 - 4i)]
= - 4 (2 - 2i - 8i + 4i^2)
= - 4 (4i^2 - 10i + 2)
= (- 4) (2) (2i^2 - 5i + 1)
= - 8 (2i^2 - 5i + 1)

9)

= p^2 - 4p - 4p + 16
= p (p - 4) - 4 (p - 4)
= (p - 4) (p - 4)
= (p - 4) ^2

11)

= p^2 - 8p - 8p + 64
= b (b - 8) - 8 (b - 8)
= (b - 8) (b - 8)
= (b - 8)^2

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Based on the types of compounding and the interest rates, the following are true:

Part A - The group will have $750
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When using simple interest, the amount the group will have is:

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2 years ago

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3 years ago

At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 600 vines are p

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The number of additional vines to plant in order to maximize production is 200

The total number of vines to maximize production is 800

Step-by-step explanation:

Notice that the expression for the number of pounds of grapes per acre is in fact a quadratic expression in the variable "n":

$A(n)=(600+n)(10-0.01n)\\A(n)= 6000-6n+10n-0.01n^2\\A(n) = 6000+4n-0.01n^2$

which is clearly associated with a parabola with arms pointing down (negative coefficient in the variable "n" squared). So by finding the vertex of the parabola, we can give the answer to what "n" (number of additional vines to plant).

Recall that the vertex of a parabola of the general shape: $y=ax^2+bx+c$ has an x-component defined by:

$x_{vertex}=\frac{-b}{2a}$

then in our case, the "n" value for that vertex is: $n_{vertex}= \frac{-4}{2(-0.01)} =200$

Then the additional number of vines to maximize grape production is 200

So the total should be: 600 + 200 =800

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