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svet-max [94.6K]
3 years ago
6

Mr. Parker's farm borders a river. He buys 1,000 ft of fencing

Mathematics
1 answer:
Gelneren [198K]3 years ago
8 0
When one side of a quadrilateral is not to be fenced (ex. a river, as in this case), the optimal fencing to maximize the area is always to use half the fencing for the length, and one-fourth for each of the two widths

A) For 1000 ft of fencing which is to be used to cover 1 length and 2 widths:
L = 1000/2 = 500, and W = 1000/4 = 250. The optimal dimensions will be 250 x 500 ft.

B) This will result in an area of 250*500 = 125,000 sq. ft.
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Identify the vertex and the y-intercept of the graph of each function. Show your work
olga2289 [7]
<u>vertex</u>
y = 3(x - 2)² - 4
y = 3((x - 2)(x - 2)) - 4
y = 3(x² - 2x - 2x + 4) - 4
y = 3(x² - 4x + 4) - 4
y = 3(x²) - 3(4x) + 3(4) - 4
y = 3x² - 12x + 12 - 4
y = 3x² - 12x + 8
3x² - 12x + 8 = 0
x = <u>-(-12) +/- √((-12)² - 4(3)(8))</u>
                       2(3)
x = <u>12 +/- √(144 - 96)</u>
                   6
x = <u>12 +/- √(48)
</u>              <u> </u> 6<u>
</u>x =<u> 12 +/- 6.93</u>
 <u />             6
x = 2 +/- 1.155
x = 2 + 1.155      x = 2 - 1.155
x = 3.155            x = 0.845
y = 3x² - 12x + 8
y = 3(3.155)² - 12(3.155) + 8
y = 3(1.334025) - 3.786 + 8
y = 4.002075 - 3.786 + 8
y = 0.216075 + 8
y = 8.216075
(x, y) = (3.155, 8.216075)
or
y = 3x² - 12x + 8
y = 3(0.845)² - 12(0.845) + 8
y = 3(0.714025) - 10.14 + 8
y = 2.142075 - 10.14 + 8
y = -7.857925 + 8
y = 0.142675
(x, y) = (0.845, 0.142675)
<u>y-intercept</u>
y = 3x² - 12x + 8
y = 3(0)² - 12(0) + 8
y = 3(0) - 0 + 8
y = 0 - 0 + 8
y = 0 + 8
0 = -y + 8
y = 8
(x, y) = (0, 8)
-------------------------------------------------------------------------------------------
<u>vertex</u>
y = 4(x - 5)² = 1
y = 4(x - 5)² - 1
y = 4((x - 5)(x - 5)) - 1
y = 4(x² - 5x - 5x + 25) - 1
y = 4(x² - 10x + 25) - 1
y = 4(x²) - 4(10x) + 4(25) - 1
y = 4x² - 40x + 100 - 1
y = 4x² - 40x + 99
4x² - 40x + 99 = 0
x = <u>-(-40) +/- √((-40)² - 4(4)(99))</u>
                         2(4)
x = <u>40 +/- √(1600 - 1584)</u>
                     8
x = <u>40 +/- √(16)</u>
              8
x = <u>40 +/- 4</u>
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x = 5 +/- 1/2
x = 5 + 1/2      x = 5 - 1/2
x = 5 1/2         x = 4 1/2
y = 4x² - 40x + 99
y = 4(5 1/2)² - 40(5 1/2) + 99
y = 4(30 1/4) - 220 + 99
y = 121 - 220 + 99
y = -99 + 99
y = 0
(x, y) = (5 1/2, 0)
or
y = 4x² - 40x + 99
y = 4(4 1/2)² - 40(4 1/2) + 99
y = 4(20 1/4) - 180 + 99
y = 81 - 180 + 99
y = -99 + 99
y = 0
(x, y) = (4 1/2, 0)
<u>y-intercept</u>
y = 4x² - 40x + 99
y = 4(0)² - 40(0) + 99
y = 4(0) - 0 + 99
y = 0 - 0 + 99
y = 0 + 99
y = 99
(x, y) = (0, 99)
--------------------------------------------------------------------------------------------
<u>vertex</u>
y = (x - 1)² = 2
y = (x - 1)² - 2
y = ((x - 1)(x - 1)) - 2
y = (x² - x - x + 1) - 2
y = x² - 2x + 1 - 2
y = x² - 2x - 1
x² - 2x - 1 = 0
x = <u>-(-2) +/- √((-2)² - 4(1)(-1))</u>
                     2(1)
x = <u>2 +/- √(4 + 4)</u>
                2
x = <u>2 +/- √(8)</u>
             2
x = <u>2 +/- 2.83</u>
             2
x = 1 +/- 1.415
x = 1 + 1.415    x = 1 - 1.415
x = 2.415          x = 0.415
y = x² - 2x - 1
y = (2.145)² - 2(2.145) - 1
y = 4.60125 - 4.029 - 1
y = 0.57225 - 1
y = 0.42775
(x, y) = (2.415, 0.42775)
or
y = x² - 2x - 1
y = (0.415)² - 2(0.415) - 1
y = 0.172225 - 0.83 - 1
y = -0.657775 - 1
y = -1.657775
(x, y) = (0.415, -1.657775)
<u>y-intercept</u>
y = x² - 2x - 1
y = (0)² - 2(0) - 1
y = 0 - 0 - 1
y = 0 - 1
y = -1
(x, y) = (0, -1)
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3 years ago
Write a unit rate for the situation. $1.98 for 6 bananas
USPshnik [31]
A unit rate is when you find a rate when one variable (or value) is equal to one.

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1.98/6= 0.33

It is 33 cents for one banana. That is the unit rate. 

I hope this helps!
~kaikers
4 0
3 years ago
7 (5х + 2) = 3х + 14<br> Need help solving
FinnZ [79.3K]
Answer: 0

35X +14=3X +14
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Answer:

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tester [92]
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