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monitta
1 year ago
11

What is the equation of the line that passes through the point (5, 1) and has a slope of 1/5 ?

Mathematics
1 answer:
OverLord2011 [107]1 year ago
5 0

Answer: y=\frac{1}{5}x

Step-by-step explanation:

y-1=\frac{1}{5}(x-5)\\\\y-1=\frac{1}{5}x-1\\\\y=\frac{1}{5}x

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Option D:

\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7

Solution:

Given expression is \left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right).

<u>To find the product of the expression:</u>

\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)

Multiply each term of the first term with each term of the 2nd term.

           =y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)

Using the exponent rule: a^m \cdot a^n = a^{m+n}

           =\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)

           =8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7

Arrange the terms with same power.

           =8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7

           =8 y^{4}+25 y^{3}+60 y^{2}+10y+7

Hence option D is the correct answer.

\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7

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