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alina1380 [7]
3 years ago
13

Indicate the equation of the given line in standard form.

Mathematics
1 answer:
Lorico [155]3 years ago
7 0
We have that
<span>triangle ABC
where
A(-5, 5), B(1, 1), and C(3, 4) are the vertices

using a graph tool
see the attached figure

the hypotenuse is the segment AC

find the equation of the line AC
</span>A(-5, 5) C(3, 4) 
<span>
step 1
find the slope m
m=(y2-y1)/(x2-x1)-----> m=</span>(4-5)/(3+5)-----> m=-1/8

step 2
with C(3,4) and m=-1/8
find the equation of a line
y-y1=m*(x-x1)-----> y-4=(-1/8)*(x-3)----> y=(-1/8)*x+(3/8)+4
y=(-1/8)*x+(3/8)+4----> multiply by 8----> 8y=-x+3+32
8y=-x+35
the standard form is Ax+By=C
so
x+8y=35
A=1
B=8
C=35

the answer is
x+8y=35


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Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p
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Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

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Step-by-step explanation:

From the question, we are given that the profit function is;

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For the maximum value of the profit function,

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Since, p(x) = -x³ + 4x² + x

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x = -0.12 or 2.79

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(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

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p(x) = 12.2088 (in thousand dollars) ≈ $12,209

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