factor [tex]-\frac{1}{3}[/tex] out of [tex]4-\frac{2}{3}y[/tex]

[tex]4-\frac{2}{3}y=-\frac{1}{3}[/tex] ( BLANK + BLANK [tex]y[/tex])

Answer:

[tex]\bold{-\frac{1}{3}(-12 + 2y)}[/tex]

Step-by-step explanation:

The original expression is

[tex]4 - \frac{2}{3}y[/tex]

Let us write the factored result as
[tex]-\frac{1}{3} (a + by)[/tex]

where a and b are constants to be determined

[tex]-\frac{1}{3} (a + by) = -\frac{1}{3} (a) -\frac{1}{3} (by) = -\frac{a}{3} + -\frac{by} {3}[/tex]

Matching like terms to the original equation we get

[tex]-\frac{a}{3} = 4[/tex]  

Multiplying by -3 on both sides gives

a = -12

Matching the y terms we get
[tex]-\frac{by}{3} = -\frac{2}{3}y[/tex] ==> [tex]-\frac{b}{3} = - \frac{2}{3}[/tex]  ==> b = 2

So the factored expression is

[tex]\bold{-\frac{1}{3}(-12 + 2y)}[/tex]

We can verify this if we multiply the terms inside the parentheses by [tex]-\frac{1}{3}[/tex]

[tex]-\frac{1}{3}(-12) =4[/tex]

[tex]-\frac{1}{3} (2y) = -\frac{2}{3}y[/tex]

Choose the correct formula for combination.
A . n!/r!(n-r)!
B. n!/(n-r)!

I need help! (20 POINTS)

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Please answer quickly

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1. a value generated by a function when an input value is substituted into the function and evaluated
discrete data
2. a set of data in which the values are distinct and separate
output
3. the variable representing the second element of the ordered pairs in a function; the outputs
input
4. a relation in which for any given input value, there is only one output value
independent variable
5. a value that is substituted in for the variable in a function in order to generate an output value
function
6. a set of data in which values can take on any value within a given interval
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7. the number before a variable in an algebraic expression
continuous data
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I already got that answer which was 1.65 but the question I don’t understand is
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please answer asap thanks

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coins
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HELP ITS FOR MY EXTRA CREDIT!

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factor 1/7 out of 1/7x-2/7
1/7x-2/7=1/7(BLANK)