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My name is Ann [436]
3 years ago
10

Which equation is parallel to the line LaTeX: y=\frac{1}{2}x+3y = 1 2 x + 3and passes through the point (10, -5)?

Mathematics
1 answer:
sukhopar [10]3 years ago
8 0

Answer:

Equation\ of\ line:\ y=\frac{1}{2}x-10

Step-by-step explanation:

Let\ the\ required\ equation\ is\ y=mx+c\\\\where\ m\ is\ the\ slope\ of\ the\ equation\ and\ c\ is\ y-intercept\\\\It\ is\ parallel\ to\ the\ equation\ y=\frac{1}{2}x+3\\\\Hence\ slope\ of\ these\ two\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{2}x+3\ is\ \frac{1}{2}\\\\Hence\ slope\ of\ y=mx+c\ is\ \frac{1}{2}\Rightarrow m=\frac{1}{2}\\\\Equation:y=\frac{1}{2}x+c\\\\Line\ passes\ through\ (10,-5).\ Hence\ this\ point\ satisfies\ the\ equation\ of\ line.\\\\-5=\frac{1}{2}\times 10+c

-5=-5+c\\\\c=-10

Equation\ of\ line:\ y=\frac{1}{2}x-10

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AleksAgata [21]
L = lenght
W = width

L * W = 60 \\
2L + 2W=32\\\\
L = \frac{32-2W}{2}\\
\frac{32-2W}{2}*W = 60\\
(16-W)*W = 60\\
-W^{2} + 16W -60 = 0\\\\

d = 16^{2} - 4*1*60 =  256 - 240 = 16 \\\\
W1 = \frac{-16+\sqrt{16}}{-2} =  \frac{-12}{-2} = 6\\
W2 = \frac{-16-\sqrt{16}}{-2} =  \frac{-20}{-2} = 10\\

L1 = 10\\
L2 = 6\\


so

{L,W} = {6,10} or {10,6}

but L > W  so

L = 10
W = 6
7 0
4 years ago
A total of 31,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is
kupik [55]

Answer:

Bonds: $42,000

Certificates of deposit: $41,000

Step-by-step explanation:

Total invested = Amount in bonds + Amount in CDs

 

Amount in bonds = Amount in CDs + 1000

 

Let the amount in bonds = B and the amount in CDs = C

 

 

1. 83,000 = B + C

 

2. B = C+1000

 

Since the above expression (#2) defines B, you can substitute it for the B in the first equation (#1).

 

83,000 = C + 1000 + C

 

Now, you can solve for C.

 

83,000 = 2C + 1000

82,000 = 2C

41,000 = C

 

You know that the amount invested in bonds is $1000 greater than the amount invested in CDs, so add $1000 to C and you find B, $42,000.

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Step-by-step explanation:

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