The game has 12 three-minute rounds. If the players stop after two minutes of the twelfth round, how many minutes did they play?

Answer:

y = -3x + 9 is your answer.

Step-by-step explanation:

So your y-intercept is the slope. Here is the equation we are going to use:

y - y_1 = m(x - x_1)

y_1 = 0

x_1 = 3

m = -3.

y - 0 = -3(x - 3)

y - 0 = -3x + 9

y = -3x + 9 is your answer.

Final answer:

The standard form of the line is y = x - 3.

Explanation:

To find the standard form of a line, we need two pieces of information: the slope of the line and a point on the line. Given that the line has a y-intercept of -3, we know that the y-coordinate is equal to -3 when the x-coordinate is 0. So, we have the point (0, -3). We also know that the line passes through the point (3, 0). Using these two points, we can calculate the slope of the line:

Slope (m) = (change in y) / (change in x) = (0 - (-3)) / (3 - 0) = 3/3 = 1.

Now that we have the slope and a point on the line, we can use the point-slope form of a line to write the equation:

y - y1 = m(x - x1), where (x1, y1) are the coordinates of a given point and m is the slope of the line.

Substituting the values of (x1, y1) = (3, 0) and m = 1 into the equation, we get:

y - 0 = 1(x - 3)

y = x - 3

Therefore, the standard form of the line that contains a y-intercept of -3 and passes through the point (3,0) is y = x - 3.

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The equivalent value of the fraction is A = 64

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p = 16

Let the denominator of the fraction be q

where q = 1/4

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 16 / ( 1/4 )

A = 16 x 4

On further simplification , we get

A = 64

Therefore , the value of A = 64

Hence , the expression is A = 64

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Answer:

{-1, 3}

Step-by-step explanation:

Please use " ^ " to denote exponentiation:   f(x) = x^2 - 2x - 3.

To find the zeros of this quadratic, set it equal to zero first:

f(x) = x^2 - 2x - 3 = 0.

Now factor this result:  (x - 3)(x + 1) = 0.

The zeros are {-1, 3}