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Ad libitum [116K]
3 years ago
15

Into a bucket, 3.705 liters of water flowed in 7.8 minutes. Enter the number of liters that flowed into the bucket each minute a

s a decimal.
Mathematics
1 answer:
alina1380 [7]3 years ago
5 0
Just divide the numbers of liter by the number of mins to get the units liter/min.
3.705/7.8

0.475L/min
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Answer:

(A)\ a=-6;b=4\\\\ (B)\ a=6;b=-4

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+c

Where "m" is the slope and "c" is the y-intercept.

By definition:

1. If the lines of the System of equations are parallel (whrn they have the same slope), the system has No solutions.

2. If the they are the same exact line, the System of equations has Infinite solutions.

(A) Let's solve for "y" from the first equation:

3x-2y=-1\\\\-2y=-3x-1\\\\y=\frac{3}{2}x+\frac{1}{2}

You can notice that:

m=\frac{3}{2}\\\\c=\frac{1}{2}

In order make that the System has No solutions, the slopes must be the same, but the y-intercept must not. Then, the values of "a" and "b" can be:

a=-6\\\\b=4

Substituting those values into the second equation and solving for "y", you get:

-6x+4y=-2\\\\4y=6x-2\\\\y=\frac{6}{4}x-{2}{4}\\\\y=\frac{3}{2}x-\frac{1}{2}

You can idenfity that:

m=\frac{3}{2}\\\\c=-\frac{1}{2}

Therefore, they are parallel.

(B) In order make that the System has Infinite solutions, the slopes and the y-intercepts of both equations must be the same. Then, the values of "a" and "b" can be:

a=6\\\\b=-4

If you substitute those values into the second equation and then you solve for "y", you get:

6x+(-4y)=-2\\\\-4y=-6x-2\\\\y=\frac{-6}{-4}x-\frac{2}{-4}\\\\y=\frac{3}{2}x+\frac{1}{2}

You can identify that:

m=\frac{3}{2}\\\\b=\frac{1}{2}

Therefore, they are the same line.

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3 years ago
Enter the values for the highlighted variables that show how to subtract the rational expressions correctly:
sladkih [1.3K]

The highlighted variables a = 6 , b = 2, c=6 , d =2 , e=6 , f =6 , g =1

<h3>What is an Expression ?</h3>

An expression is a mathematical statement which consists of variables , constants and mathematical operators.

\rm \dfrac{2}{x^2-36}-\dfrac{1}{x^2+36}\\= \dfrac{2}{(x+6)(x-6)}-\dfrac{1}{x(x+a)}\\=\dfrac{bx}{x(x+6)(x-6)}-\dfrac{x-c}{x(x+6)(x-6)}\\\\=\dfrac{dx-x+e}{x(x+6)(x-6)}\\\\= \dfrac{x+f}{x(x+6)(x-6)}\\\\=\dfrac{g}{x(x-6)}

In the given expression

a = 6 , b = 2, c=6 , d =2 , e=6 , f =6 , g =1

To know more about Expression

brainly.com/question/14083225

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Answer:

12

Step-by-step explanation:

f(-7) = 5-(-7)=5+7=12

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Answer:

y=-x

Step-by-step explanation:

The y-intercept is 0 and the slope is -1 so -x.

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