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Zina [86]
3 years ago
8

Write the equation for the line parallel to the given line 4x-3y=9 and through the point (3, -1). Then Write the answers in slop

e intercept and standard form
Mathematics
1 answer:
Katyanochek1 [597]3 years ago
7 0

k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2

We have:

4x-3y=9\ \ \ \ |-4x\\\\-3y=-4x+9\ \ \ \ |:(-3)\\\\y=\dfrac{4}{3}x-3\to m_1=\dfrac{4}{3}

y=m_2x+b\\\\m_2=m_1\to m_2=\dfrac{4}{3}

y=\dfrac{4}{3}x+b

The line passest through the point (3, -1). Substitute the coordinates of the point to the equation of a line:

-1=\dfrac{4}{3}\cdot3+b\\\\-1=4+b\ \ \ \ |-4\\\\b=-5

y=\dfrac{4}{3}x-5\ \ \ \ |\cdot3\\\\3y=4x-15\ \ \ \ |-4x\\\\-4x+3y=-15\ \ \ \ |\cdot(-1)\\\\4x-3y=15

Answer: \boxed{y=\dfrac{4}{3}x-5;\ 4x-3y=15}

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2 years ago
10x+8=3(x-2) 10x+8=3x-6
d1i1m1o1n [39]

Answer:

x = -2

Step-by-step explanation:

10x+8=3x-6

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subtract -6-8

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4 0
3 years ago
A soup kitchen makes 15 gallons of soup each day a quarter of the soup is served and the rest is saved for the next day , what i
Sophie [7]

Number of ounces left is 1120

Step-by-step explanation:

  • Step 1: Find number of ounces left after each day.

Given total soup prepared each day = 15 gallons

Amount served each day = 1/4 of 15 = 15/4 gallons

Amount left after each day = 15 - 15/4 = 60 - 15/4 = 35/4 gallons

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3 years ago
HELP ASAP PLSSSSSSSSSS
inysia [295]

Answer:

Neighborhood Q appears to have a bigger family size

Step-by-step explanation:

Mean = the sum of all data values divided by the total number of data values

Number of families in Neighborhood Q = 9

Mean family size of Neighborhood Q:

= (2 + 5 + 4 + 3 + 2 + 5 + 3 + 6 + 5) ÷ 9

= 35 ÷ 9

= 3.888888...

Number of families in Neighborhood S = 9

Mean family size of Neighborhood S:

= (2 + 3 + 2 + 3 + 7 + 2 + 3 + 3 + 2) ÷ 9

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= 3

The mean family size of Neighborhood Q is 3.88..  and the mean family size of Neighborhood S is 3.  Therefore, Neighborhood Q appears to have a bigger family size as it's average family size is bigger than that of Neighborhood S.

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2 years ago
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